
    Ug                       d Z ddlZddlZddlZddlZddlmZ ddlZddlZddl	Z	ddl
mZmZmZmZmZmZmZmZmZmZmZ ddlZddlmZ ddlZddlmZmZ ddlmZ ddlm Z  dd	l!m"Z" dd
l#m$Z$m%Z%m&Z&m'Z' ddl(m)Z) ddl*m+Z+ ddl,Zddl-m.Z.m/Z/m0Z0 ddl1m2Z2m3Z3 ddl4m5Z5m6Z6 ddl7m8Z8m9Z9 ddl:m;Z;m<Z<m=Z= ddl>m?Z? ej@        jA        dk    ZBej	        dk    o e	jC                    dk    ZDddgZEddZFd ZGd ZH G d d          ZIddZJd ZKejL        M                    dg d           d!             ZN G d" d#          ZO G d$ d%          ZP G d& d'          ZQ G d( d)          ZR G d* d+          ZS G d, d-          ZT G d. d/          ZU G d0 d1          ZV G d2 d3          ZW G d4 d5          ZX G d6 d7          ZY G d8 d9          ZZ G d: d;          Z[ G d< d=          Z\ G d> d?          Z] G d@ dA          Z^ G dB dC          Z_ G dD dE          Z` G dF dG          Za G dH dI          Zb G dJ dK          Zc G dL dM          Zd G dN dO          Ze G dP dQ          Zf G dR dS          Zg G dT dU          Zh G dV dW          Zi G dX dY          Zj G dZ d[          Zk G d\ d]          Zl G d^ d_          Zm G d` da          Zn G db dc          Zo G dd de          Zp G df dg          Zq G dh di          Zr G dj dk          Zs G dl dm          Zt G dn do          Zu G dp dq          Zv G dr ds          Zw G dt du          Zx G dv dw          Zy G dx dy          Zz G dz d{          Z{ G d| d}          Z| G d~ d          Z} G d d          Z~ G d d          Z G d d          Z G d d          Zdd ej        ddej        z  z            z  dd ej        ddej        z  z            z  dd ej        ddej        z  z            z  dd ej        ddej        z  z            z  dd ej        ddej        z  z            z  g	fd ej        ddej        z  z            dd ej        ddej        z  z            z  dd ej        ddej        z  z            z  dz  dd ej        ddej        z  z            z  dz  dd ej        ddej        z  z            z  dz  g	fdd ej        dej        z            z  ddd ej        dej        z            z  z  ddd ej        dej        z            z  z  ddd ej        dej        z            z  z  ddd ej        dej        z            z  z  ddd ej        dej        z            z  z  ddd ej        dej        z            z  z  dgfgZ G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d dæ          ZdĄ Z G dń dƦ          Z G dǄ dȦ          Z G dɄ dʦ          Z G d˄ d̦          Z G d̈́ dΦ          Z G dτ dЦ          Z G dф dҦ          Zdӄ Z G dԄ dզ          Z G dք dצ          Z G d؄ d٦          Z G dڄ dۦ          Z G d܄ dݦ          Z G dބ dߦ          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          Zd Zd Zd  ZejL                            eBd          d             Zd Zd Zd Zd Zd Zd	 Zd
 Zd Zd Zd ZejL        M                    dg d          d             Zd Zd Zd Zd ZÐd ZĐd ZejL        M                    dg d          d             ZƐd Zǐd ZȐd Zɐd Zʐd Zːd ZejL        M                    d d! ej        d"d#g          fd$ ej        d%d&g          fd' ej        d(d)g          fd* ej        d+d,g          fg          d-             Z͐d. Zΐd/ Zϐd0 ZАd1 ZejL        M                    d2g d3          d4             ZejL        M                    d5g d6          d7             ZejL        M                    d8g d9          d:             ZԐd; ZejL        M                    d2g d<          d=             Z֐d> Z G d? d@e)j                  Z G dA dBe)j                  Z G dC dDe)j                  Z G dE dFe)j                  Z G dG dH          Z G dI dJ          ZejL                            eBdK          dL             ZߐdM ZdN ZdO ZdP ZdQ ZdR ZdS ZdT ZdU ZdV ZdW ZdX ZejL        M                    d2g dY          dZ             ZejL        M                    d[d\d]g          d^             ZejL        M                    d_ddg d`fdadbg d`fdcddg defg          df             Zdg Zdh ZejL                            ej        dik    dj          dk             Z G dl dm          Zdn Z G do dp          Z G dq dr          Z G ds dt          Z G du dv          Zdw ZejL        M                    dxe6e3z             dy             Zdz Zd{ ZejL        M                    d5d|d}g          d~             ZejL        M                    d8g d          d             Zd Zd Z d Z G d d          Z G d d          Z G d d          Z G d d          Z G d d          ZejL        M                    dg d          d             ZdS (  z!
Test functions for stats module
    N)Path)assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_assert_warnsassert_array_lesssuppress_warningsassert_array_max_ulpIS_PYPY)raises)	typecodesarray)rec_append_fields)special)check_random_state)IntegrationWarningquad	trapezoidcumulative_trapezoid)
argsreduce)xlogy	polygammaentr)distcontinvdistcont   )distdiscreteinvdistdiscrete)FitDataError
_argus_phi)rootfmindifferential_evolution)productdarwinx86_64tukeylambdapearson3c                 V    ||  d| }t          t          | |          |           d S )Nz does not have attribute msg)r	   hasattr)abr.   s      c/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattrr3   4   s;    
{00Q00GAqMMs######    c                  D    t          t          j        j        d           d S )Nf_gen)r3   scipystatsdistributions r4   r2   test_api_regressionr;   :   s    EK-w77777r4   c                      t          t          j        j        j                  } d t
          D             }d t          D             }g d}||z   |z   }t          t          d |                    }| |k    sJ d S )Nc                     g | ]
}|d          S r   r:   .0dists     r2   
<listcomp>z0test_distributions_submodule.<locals>.<listcomp>A   s    ///d$q'///r4   c                     g | ]
}|d          S r>   r:   r?   s     r2   rB   z0test_distributions_submodule.<locals>.<listcomp>B   s    111DQ111r4   )rv_discreterv_continuousrv_histogramentropytrapzc                 H    t          |                               d           S )N<)str
startswithss    r2   <lambda>z.test_distributions_submodule.<locals>.<lambda>I   s    A(9(9#(>(>$> r4   )setr7   r8   r9   __all__r   r    filter)actual
continuousdiscreteotherexpecteds        r2   test_distributions_submodulerX   ?   s    *233F//h///J11L111H! ! !EH$u,H 6>>IIJJHXr4   c            	       v   e Zd Zej                            dg d          ej                            dddej        ddg          d                         Zd	 Z	d
 Z
ej                            dg d          d             Zej                            dg d          d             Zd Zej                            dg d          d             Zd Zej        j        ej                            dddg          ej                            dg d          ej                            dddg          ej                            dddg          d                                                             Zej        j        d             Zej                            d d!dg          d"             Zd# Zd$ Zd% Zd&S )'TestVonMisesk)皙?r   e   xr   r   
   d   c                     d }d } ||dd|            ||dd|            ||dd|            ||dd|            ||dd|            ||dd|           d S )Nc                     t          j        | ||          }t          |                    |          |                    |dt          j        z  |z  z                       d S )Nlocscale   )r8   vonmisesr   pdfnppir[   LrN   r^   vms        r2   check_vonmises_pdf_periodiczHTestVonMises.test_vonmises_periodic.<locals>.check_vonmises_pdf_periodicR   sS    q222Bq		266!q25y1}2E+F+FGGGGGr4   c                     t          j        | ||          }t          |                    |          dz  |                    |dt          j        z  |z  z            dz             d S )Nrc   r   rf   )r8   rg   r   cdfri   rj   rk   s        r2   check_vonmises_cdf_periodiczHTestVonMises.test_vonmises_periodic.<locals>.check_vonmises_cdf_periodicV   sl    q222Bq		A "qAIM': ; ;a ?A A A A Ar4   r   r   r_   r:   )selfr[   r^   rn   rq   s        r2   test_vonmises_periodicz#TestVonMises.test_vonmises_periodicO   s    	H 	H 	H	A 	A 	A
 	$#Aq!Q///##Aq!Q///##Aq"a000##Aq!Q///##Aq!Q///##Aq"a00000r4   c                     t          t          j        j        t          j                    t          t          j        j        t          j                   d S N)r   r8   vonmises_liner0   ri   rj   r1   rr   s    r2   test_vonmises_line_supportz'TestVonMises.test_vonmises_line_supportc   s:    U(*RUF333U(*BE22222r4   c                 t    t          j        d          }t          |                    d          d           d S )N   r         ?)r8   rg   r   rp   )rr   rm   s     r2   test_vonmises_numericalz$TestVonMises.test_vonmises_numericalg   s1    ^C  BFF1IIs+++++r4   zx, kappa, expected_pdf))r\   {Gz?g|65?)r\         9@g?U?)r\   rz   g"?)       @r}   gDfI?)r   r~   g1<)r   rz           c                 j    t           j                            ||          }t          ||d           d S NV瞯<rtol)r8   rg   rh   r   )rr   r^   kappaexpected_pdfrh   s        r2   test_vonmises_pdfzTestVonMises.test_vonmises_pdfu   s6     n  E**\666666r4   zkappa, expected_entropy))r   gA	?)   g,eޞ?)r`   gBb9d22)  g
G )  gc                 h    t           j                            |          }t          ||d           d S NvIh%<=r   )r8   rg   rG   r   )rr   r   expected_entropyrG   s       r2   test_vonmises_entropyz"TestVonMises.test_vonmises_entropy   s5     .((//!1>>>>>>r4   c                 h   d}t           j                            |          }t           j                            |          }t           j                            |          }t          j        ddd                              |          }t          j        ddt           j        z  d                              |          }t          j        dddt           j        z  t          |          z  dz                                 |          }t          ||d           t          ||d           d S )	Ni@}r   r   rc   random_staterf   r   atol)	ri   randomdefault_rngr8   rg   rvsrj   absr   )rr   seedrng1rng2rng3rvs1rvs2rvs3s           r2   test_vonmises_rvs_gh4598z%TestVonMises.test_vonmises_rvs_gh4598   s   y$$T**y$$T**y$$T**~aQa00044$4GG~aQruWA666:::MM~aQ%&ruWSYY%6q%8; ; ;;>3D3;Q;Q 	d////d//////r4   zx, kappa, expected_logpdf))r\   r}   gEJ?)r\   r~   goι?)r\   rz   g0,)r   r}   gdty)r   r~   gʹw[A)r   rz   gc                 j    t           j                            ||          }t          ||d           d S r   )r8   rg   logpdfr   )rr   r^   r   expected_logpdfr   s        r2   test_vonmises_logpdfz!TestVonMises.test_vonmises_logpdf   s6     &&q%00e<<<<<<r4   c                 :   t           j                            d          }|                    d          dz  \  }}}t          j        ||                              d           }t          |d           t          j        |j        t           j	                  sJ ||dt           j
        z  z   f} t          j        ||          j        d g|R  }t          |d           t          j        |j        t           j	                  sJ ||dt           j
        z  z   f} t          j        ||          j        d	 g|R d
di}t          t          j        |          |dt           j
        z  z             t          j        |j        t           j                  sJ dS )a   
        Test that the vonmises expectation values are
        computed correctly.  This test checks that the
        numeric integration estimates the correct normalization
        (1) and mean angle (loc).  These expectations are
        independent of the chosen 2pi interval.
           kD +xNn    r_   rd   r   c                     dS Nr   r:   r^   s    r2   rO   z3TestVonMises.test_vonmises_expect.<locals>.<lambda>       A r4   r   rf   c                     dS r   r:   r   s    r2   rO   z3TestVonMises.test_vonmises_expect.<locals>.<lambda>   r   r4   c                 0    t          j        d| z            S )Ny              ?)ri   expr   s    r2   rO   z3TestVonMises.test_vonmises_expect.<locals>.<lambda>   s    BF2a4LL r4   complex_funcN)ri   r   r   r8   rg   expectr   
issubdtypedtypefloatingrj   anglecomplexfloating)rr   rngrd   r   lbresboundss          r2   test_vonmises_expectz!TestVonMises.test_vonmises_expect   s    i##$788A+UBnE22299++FFQ}SY44444R!be)^#9enE2229++OOOOQ}SY44444R!be)^#9enE2229:P:P S;AS S SPQS Ssag777}SY(:;;;;;;;r4   rvs_locrf   	rvs_shape)r   r`       חAfix_locTF	fix_shapec                 .   |r|rt          j        d           t          j                            d          }t
          j                            |d||          }ddi}|r||d<   |r||d<   t          t
          j        |t
          j        j	        fi | d S )	NzNothing to fit.r   r   )sizerd   r   fscaler   flocf0)
pytestskipri   r   r   r8   rg   r   _assert_less_or_close_loglikennlf)rr   r   r   r   r   r   datakwdss           r2   test_fit_MLE_comp_optimizerz(TestVonMises.test_fit_MLE_comp_optimizer   s      	+ 	+K)***i##$788~!!)$G/2 " 4 4 !} 	#"DL 	#"DJ%end&+n&9	C 	C=A	C 	C 	C 	C 	Cr4   c                 @   g d}t          j        |          }dt           j        z  }t          j                            ||          \  }}}|t          j        t                    j        k    sJ t          t          j        |t          j        j
        d|           d S )N)g!*Kg4,%OԿgZ۵?g
ge_@g-8gPghn?g<t?g.6@gjb?g0]o@g݅ZgSsgx7W?g%H?g65Jg:m2?g@g;,gM^lsF      ࿩r   r   )r   r   )ri   asarrayrj   r8   rg   fitfinfofloattinyr   r   )rr   r   rd   	kappa_fitloc_fit	scale_fits         r2   test_vonmises_fit_bad_flocz'TestVonMises.test_vonmises_fit_bad_floc   s    M M M z$RUl(-(:(:4c(:(J(J%	7IBHUOO00000%end&+n&9!#	O 	O 	O 	O 	O 	Or4   signc                    t           j                            d          }t          j        |dz  t           j        z  d                              d|          }|dt           j        z  z   }t          j                            |          \  }}}t          j                            |          \  }}	}
t          ||	           t          ||           |dk    sJ t           j         |cxk     rt           j        k     sn J d S )	Nr   r{   r_   r   順 r      r   )	ri   r   r   r8   rg   rj   r   r   r   )rr   r   r   r   shifted_datar   r   r   kappa_fit_shiftedloc_fit_shifted_s              r2    test_vonmises_fit_unwrapped_dataz-TestVonMises.test_vonmises_fit_unwrapped_data   s    i##$788~$s(25.;;;??MP @ R Rag~(-(:(:4(@(@%	7I050B0B<0P0P-?A111	#4555A~~~~v''''"%''''''''r4   c                    t          j        d          }t          |                    d          ddt          j        z  z  d           t          |                    t          j        dz            dd           t          |                    t          j         dz            dd           t          |                    d          t          j        dz  d           t          |	                                dd	           t          |
                                dd	           t	          j        t	          j        |                    d
d                    t          j        k              sJ d S )Nr   r   rf   r   r         ??皙?r   r_     r   r   )r8   rg   r   rh   ri   rj   rp   sfppfmeanr   allr   r   )rr   rA   s     r2   test_vonmises_kappa_0_gh18166z*TestVonMises.test_vonmises_kappa_0_gh18166   s&   ~a  Q!be)_5AAAAq))4e<<<<q))4e<<<<ruSyu====		QU3333qu5555vbfTXX2DXAABBbeKLLLLLLLr4   c                 v    t           j                            dg          \  }}}|dk    r|dk    r|dk    sJ d S )Nr   g 7yACr   )r8   rg   r   )rr   r   rd   re   s       r2   test_vonmises_fit_equal_dataz)TestVonMises.test_vonmises_fit_equal_data  sA    !N..s33sE}}eqjjjjjjr4   c                     t           j        j                            ddgd           t           j        j                            t          j        dz  dz  gd           d S )Nr   gl=c>r   rf   gd?)r7   r8   rg   r   ri   rj   rw   s    r2   test_vonmises_fit_boundsz%TestVonMises.test_vonmises_fit_bounds
  sZ     	  !WA 666 	  "%'9"5!6Q ?????r4   N)__name__
__module____qualname__r   markparametrizeri   rj   rs   rx   r|   r   r   r   r   r   xslowr   slowr   r   r   r   r   r:   r4   r2   rZ   rZ   N   s       [S---00[S1aC"8991 1 :9 101$3 3 3, , , [5/ / /0 07 70 07 [6; ; ;< <? ?< <?0 0 0  [8B B BC C= =C C=< < <4 [[YA//[[---88[Yu66[[4-88C C 98 76 98 0/ 
C$ [
O 
O 
O [Vb!W--
( 
( .-
(	M 	M 	M9 9 9
@ @ @ @ @r4   rZ   Fc                    || j         } | j        |fi |} t          t          |           |           j        |fi |}|st	          j        ||k              sJ  |||          } |||          }||k    st	          j        ||d          sJ d|v r|d         |d         k    sJ d|v r|d         |d         k    sJ dS dS )a^  
    This utility function checks that the negative log-likelihood function
    (or `func`) of the result computed using dist.fit() is less than or equal
    to the result computed using the generic fit method.  Because of
    normal numerical imprecision, the "equality" check is made using
    `np.allclose` with a relative tolerance of 1e-15.
    Nr   r   r   r   r   )r   r   supertyperi   anyallclose)	rA   r   funcmaybe_identicalr   mle_analyticalnumerical_optll_mle_analyticalll_numerical_opts	            r2   r   r     s!    |yTXd++d++N/E$t**d++/====M
  7vn566666^T22tM400!111K)+;%HHH 211
 ~~b!T&\11114b!T(^3333 33r4   c           
         ddg}| j         r6t          | j                             d                    }|g dd |         z  }t          t	          |t          j        t          |                                        }g d}t          j        t          d          5   | j
        |fi | d d d            n# 1 swxY w Y   t          j        t          d          5  | 
                    t
          j        g           d d d            n# 1 swxY w Y   t          j        t          d          5  | 
                    t
          j        g           d d d            n# 1 swxY w Y   t          j        t          d	          5  | 
                    |d
           d d d            n# 1 swxY w Y   t          j        t          d          5   | j
        |gdgt          |          dz
  z  R   d d d            d S # 1 swxY w Y   d S )Nr   r   ,)r   f1f2r   rf   r   3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:rf   )extra_keywordzToo many positional arguments.r   )shapeslensplitdictzipri   aranger   r   RuntimeErrorr   
ValueErrornaninf	TypeError)rA   paramnshapes	all_fixedr   s        r2   assert_fit_warningsr  :  sL   XE{ .dk'',,--###HWH--S	#e** 5 56677I99D	|&
' 
' 
' $ $ 	#####$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 
zB
D 
D 
D  "&               
zB
D 
D 
D  "&               
y(D	E	E	E ( (Q'''( ( ( ( ( ( ( ( ( ( ( ( ( ( (	y(H	I	I	I . .-SZZ!^,----. . . . . . . . . . . . . . . . . .sZ   B88B<?B<!DDD1!EE"%E"F((F,/F,#G>>HHrA   )alpha	betaprimefatiguelifeinvgammainvgauss
invweibull	johnsonsblevylevy_llognormgibratpowerlognormrayleighwaldc                    t          t                    }||          }t          t          |           } t	           | j        | j        g|R  d           t           | j        | j        g|R  t          j
                    t	           | j        | j        g|R  d           t           | j        | j        g|R  t          j
                    dS )zgh-6235r   N)r  r   getattrr8   r   rh   r0   r   r   ri   r  r1   )rA   dctargss      r2   test_supportr0  Q  s     x..Ct9D5$D/$///333TV+d+++bfW555/$///333TV+d+++bfW55555r4   c                   &    e Zd Zd Zd Zd Zd ZdS )TestRandIntc                 D    t           j                            d           d S Nr   ri   r   r   rw   s    r2   setup_methodzTestRandInt.setup_methodd      
	tr4   c                 v   t           j                            ddd          }t          t	          j        |dk               t	          j        |dk              z             t          t          |          dk               t           j                            ddd          }t          t	          j        |          dk               t          |j        j	        t          d         v            t           j                            dd          }t          |dk    |dk     z             t          t          |t          j                  t          t          |                    	           t          j        dd                              d
          }t          |j        j	        t          d         v            d S )Nr      r`   r   rf   2   
AllInteger   .   r-   r   )r8   randintr   r	   ri   r   r  shaper   charr   
isinstance
ScalarTypereprr   rr   valsvals      r2   test_rvszTestRandInt.test_rvsg  sW   }  BS 11tby!!BF419$5$55666D		S !!!}  BW 55')***
9\#::;;;mB''sRx()))
3..DcOODDDDmB##''**	)L"99:::::r4   c                     t           j        dd         }t          j        |dk    |dk     z  dd          }t          j                            |dd          }t          ||           d S )Nr   $   r   r9  {Gz?)ri   r_wherer8   r@  pmfr   )rr   r[   outrG  s       r2   test_pdfzTestRandInt.test_pdft  s`    E!B$KhQ1r6*J::}  Ar**!$,,,,,r4   c                    t          j        ddd          }t          j        |          }t          j        |dk    |dk    gd|dz
  dz   d	z  gd          }t          j                            |dd          }t          ||d
           d S )Nr   rK  r`   r9  r         ?      @r   r~      decimal)ri   linspacefloorselectr8   r@  rp   r   )rr   r^   r[   rP  rG  s        r2   test_cdfzTestRandInt.test_cdfz  s    K2s##HQKKib!q&)C!C%'F1C+DaHH}  Ar**!$R888888r4   N)r   r   r   r6  rI  rQ  r[  r:   r4   r2   r2  r2  c  sP          ; ; ;- - -9 9 9 9 9r4   r2  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )	TestBinomc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestBinom.setup_method  r7  r4   c                    t           j                            ddd          }t          t	          j        |dk              t	          j        |dk              z             t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            dd          }t          t          |t                               t          j        dd                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S Nr_   r   r;  r:  r   r=  r   )r8   binomr   r	   ri   r   rA  r   rB  r   rC  intndarrayrF  s      r2   rI  zTestBinom.test_rvs  s	   {r4g66tqy!!BF42:$6$66777')***
9\#::;;;koob$''
3$$%%%k"d##''**
3
++,,,	)L"99:::::r4   c                     t           j                            ddd          }t           j                            ddd          }t          |ddd           t          |ddd           d S )Nr`   r   r   rS  r   r   r   r8   ra  rO  r   )rr   vals1vals2s      r2   test_pmfzTestBinom.test_pmf  sd    S!,,3**sQ7777sQ777777r4   c                    t          j        dd          }t          j        g d          }t	          t          ||                     }|                                }t          ||           t          j        dd          }|                                }t          |d           t          j        dd          }|                                }t          |d           d S )Nrf   r{   )      ?r{   rk  r   rS  )	r8   ra  ri   r   sumr   rG   r   r   )rr   r1   
expected_p
expected_hhs        r2   test_entropyzTestBinom.test_entropy  s    K3X///00
%
J77888
IIKK:&&&K3IIKKQK3IIKKQr4   c                 j   t          j                    5  t          j        dt                     t	          t          j        dd                                          d           t	          t          j        dd                                          d           d d d            d S # 1 swxY w Y   d S )Nerrorrf   r   np)	warningscatch_warningssimplefilterRuntimeWarningr   r8   ra  r   stdrw   s    r2   test_warns_p0zTestBinom.test_warns_p0  s    $&& 	9 	9!'>:::qA...3355q999qA...2244a888	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9s   BB((B,/B,c                 Z    d}t           j                            d|d          |k    sJ d S )Nr   333333?rS  )qrt  ru  )r8   ra  r   rr   rt  s     r2   test_ppf_p1zTestBinom.test_ppf_p1  s2    {S11Q666666r4   c                     d}d}t          j        d          }t          j                            |||          }t          j                            |||z            }t          ||d           d S )NglyCgq]\	T3<r   rs  缉ؗҜ<r   )ri   r  r8   ra  rO  poissonr   )rr   rt  ru  r^   r   refs         r2   test_pmf_poissonzTestBinom.test_pmf_poisson  sh    "IaLLkooa1o**m1q5))Su------r4   c                     d}d}d}t           j                            |||          }t           j                            |||          }t	          ||d           d S )NgJ-DgO
;r   r  r   )r8   ra  rO  rp   r   )rr   rt  ru  rr   r  s         r2   test_pmf_cdfzTestBinom.test_pmf_cdf  sZ    kooaA&&kooaA&&Su------r4   c                 l    t           j                            ddd          }t          |dd           d S )Nr   r   +?r   r  r   rf  )rr   r   s     r2   test_pmf_gh15101zTestBinom.test_pmf_gh15101  s4    kooau--QU++++++r4   N)r   r   r   r6  rI  ri  rp  r{  r  r  r  r  r:   r4   r2   r]  r]    s          	; 	; 	;8 8 8   9 9 97 7 7
. . .. . ., , , , ,r4   r]  c                       e Zd Zd ZdS )TestArcsinec                     t           j                            ddg          }t          |t          j        t          j        g           d S Nr   r   )r8   arcsinerh   r   ri   r  rr   ru  s     r2   test_endpointszTestArcsine.test_endpoints  s<     Mq!f%%Q()))))r4   N)r   r   r   r  r:   r4   r2   r  r    s#        * * * * *r4   r  c                        e Zd Zd Zd Zd ZdS )TestBernoullic                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestBernoulli.setup_method  r7  r4   c                    t           j                            dd          }t          t	          j        |dk              t	          j        |dk              z             t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nr   r;  r:  r   r   r=  r   )r8   	bernoullir   r	   ri   r   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestBernoulli.test_rvs  s   ""4g"66tqy!!BF419$5$55666')***
9\#::;;;o!!$''
3$$%%%od##''**
3
++,,,	)L"99:::::r4   c                    t          j        d          }dt          j        d          z  dt          j        d          z  z
  }|                                }t          ||           t          j        d          }|                                }t          |d           t          j        d          }|                                }t          |d           d S )Nrk        пr   r   rS  )r8   r  ri   logrG   r   r   )rr   r1   rn  ro  s       r2   rp  zTestBernoulli.test_entropy  s    OD!!26$<<'$rvd||*;;
IIKK:&&&OC  IIKKQOC  IIKKQr4   N)r   r   r   r6  rI  rp  r:   r4   r2   r  r    sA          	; 	; 	;    r4   r  c                       e Zd Zd ZdS )TestBradfordc                     d}t          j        dd          }t          j                            ||          }t          j                            ||          }t          ||           d S )Nr\   )ri   logspacer8   bradfordrp   r   r   )rr   cr^   r~  xxs        r2   test_cdf_ppfzTestBradford.test_cdf_ppf  s\    KR  Nq!$$^1%%2r4   N)r   r   r   r  r:   r4   r2   r  r    s#            r4   r  c                       e Zd ZdZdZd Zd Zej        	                    ddefdg          d             Z
ej        	                    dg d	          d
             ZdS )TestChignT9;g2 >h?@c                 t    t           j                            dd          }t          || j        d           d S )Nr_   r   r   r   )r8   chir   r   CHI_SF_10_4rr   rN   s     r2   test_sfzTestChi.test_sf  s5    ILLQ4+%888888r4   c                 t    t           j                            | j        d          }t	          |dd           d S )Nr   r_   r   r   )r8   r  isfr  r   rr   r^   s     r2   test_isfzTestChi.test_isf  s5    IMM$*A..2E******r4   df, ref     @@)g  ļBgcAc                 d    t          t          j                            |          |d           d S N-q=r   )r   r8   r  r   rr   dfr  s      r2   	test_meanzTestChi.test_mean  s-    
 		r**Ce<<<<<<r4   ))-C6?gQ(݂)r   ńjɮ9?)r  gWr4'?)    _Bgr$h(?)}Ô%ITgs$h(?c                 r    t          t          j        |                                          |d           d S r   )r   r8   r  rG   r  s      r2   rp  zTestChi.test_entropy&  s3     		"--//5AAAAAAr4   N)r   r   r   r  CHI_MEAN_1000r  r  r   r   r   r  rp  r:   r4   r2   r  r    s         'K $M9 9 9+ + + [Y"M279 = =	 = [Y; ; ;< <B B< <B B Br4   r  c                   &    e Zd Zd Zd Zd Zd ZdS )
TestNBinomc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestNBinom.setup_method1  r7  r4   c                    t           j                            ddd          }t          t	          j        |dk                         t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            dd          }t          t          |t                               t          j        dd                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S r`  )r8   nbinomr   r	   ri   r   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestNBinom.test_rvs4  s    |Dw77tqy!!"""')***
9\#::;;;lr4((
3$$%%%l2t$$((++
3
++,,,	)L"99:::::r4   c           	      2   t          t          j        t          j                            ddd                    t          j                            ddd                     t          j        j                            ddd          }t          |d           d S )Ni  i  gp=
ף?r   r   )	r   ri   r   r8   r  logpmfrO  r7   r   )rr   rH  s     r2   ri  zTestNBinom.test_pmf?  s    u|223TBBCC((c488	: 	: 	: k ''1a00S!r4   c                     t           j                            g ddd          }t          j        t           j                            g ddd                    }t          ||           d S )N)r   r   r   r   333333@?rs  )r8   r  logcdfri   r  rp   r   rr   rG  r  s      r2   test_logcdf_gh16159zTestNBinom.test_logcdf_gh16159G  sb    |""<<<3$"??fU\%%lllcT%BBCCc"""""r4   N)r   r   r   r6  rI  ri  r  r:   r4   r2   r  r  0  sP          	; 	; 	;  # # # # #r4   r  c                       e Zd Zd Zej        j        d             Zej        j        d             Zej        j        d             Z	ej        j        d             Z
d Zd Zd Zd	 Zd
S )TestGenInvGaussc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestGenInvGauss.setup_methodO  r7  r4   c                     t          j        dd          }t          j        |                    dd          |j                  \  }}t          |dk    d           d S )Nffffff@      ?  r   r   皙?Tr8   geninvgausskstestr   rp   r   rr   gigr   ru  s       r2   test_rvs_with_mode_shiftz(TestGenInvGauss.test_rvs_with_mode_shiftR  W     S))|CGGDGAA37KK1QXt$$$$$r4   c                     t          j        dd          }t          j        |                    dd          |j                  \  }}t          |dk    d           d S )Nr   r   r  r   r   r  Tr  r  s       r2   test_rvs_without_mode_shiftz+TestGenInvGauss.test_rvs_without_mode_shiftY  sW     T**|CGGDGAA37KK1QXt$$$$$r4   c                     t          j        dd          }t          j        |                    dd          |j                  \  }}t          |dk    d           d S )Nr\   皙?r  r   r   r  Tr  r  s       r2   test_rvs_new_methodz#TestGenInvGauss.test_rvs_new_method`  r  r4   c                     d }t           |dd          d           t           |dd          d           t           |dd          d           d S )Nc                     t          j        | |          }|                    dd          }t          j        ||j                  d         dk    S )Nr  r   r   r   r  )r8   r  r   r  rp   )ru  r1   r  r   s       r2   my_ks_checkz4TestGenInvGauss.test_rvs_p_zero.<locals>.my_ks_checki  sG    #Aq))C''t$'77C<SW--a0477r4   r   r  Tr   r  )r   )rr   r  s     r2   test_rvs_p_zerozTestGenInvGauss.test_rvs_p_zerog  sm    	8 	8 	8
 	[[C(($///[[C(($///[[C(($/////r4   c                     t          t          j        dd                              dd          dt          j        dd                              dd          z             d S )N      rf   r_   r   r   r   r  )r   r8   r  r   rw   s    r2   test_rvs_negative_pz#TestGenInvGauss.test_rvs_negative_pr  sn    !$**..BT.JJE%c1--11r1MMM	O 	O 	O 	O 	Or4   c                 H   t           j                            dddd          }t          t          j        |ddg          d         dk    d	           d
t          j        ddd          }}t           j                            |dd|z  |          }t          |t          j	        |                              |                     t           j        
                    |dd|z  |          }t          |t          j	        |          
                    |                     d S )Nr  r   r   r   )r   ru  r1   r   r"  r/  333333?Tr`   r}   r_   )ru  r1   re   )r8   r  r   r   r  ri   rX  rh   r   r"  rp   )rr   igmur^   pdf_igcdf_igs         r2   test_invgausszTestGenInvGauss.test_invgaussx  s   """MMU\"js;;;A>EtLLLR[q"--A"&&qDAF"&EEr 2 2 6 6q 9 9:::"&&qDAF"&EEr 2 2 6 6q 9 9:::::r4   c                     t          j        g d          }t          j        ddd          }t          |t          j                            |dd                     d S )N)
g;g8y8?g\}Z?ghܲ<?g&Khdd?g7!L?g	Cf?g_诱?g>0|?gRq?r}   r   r_   r{   r   )ri   r   rX  r   r8   r  rh   )rr   vals_Rr^   s      r2   
test_pdf_RzTestGenInvGauss.test_pdf_R  sd      , , , - - Ka$$ 1 5 5aa @ @AAAAAr4   c                     t          t          j                            ddd          d           t          t          j                            ddd          d           d S )Nr   r{   g    >Ar<  rf   )r   r8   r  rh   rw   s    r2   test_pdf_zerozTestGenInvGauss.test_pdf_zero  sT    U&**1c377;;; 	U&**3A66:::::r4   N)r   r   r   r6  r   r   r   r  r  r  r  r  r  r  r  r:   r4   r2   r  r  N  s           [% % % [% % % [% % % [0 0 0O O O	; 	; 	;	B 	B 	B; ; ; ; ;r4   r  c                       e Zd Zd Zd Zd Zej                            dg d          d             Z	ej                            dg d          d             Z
d	 Zd
 Zd Zd Zd Zd ZdS )TestGenHyperbolicc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestGenHyperbolic.setup_method  r7  r4   c                     t          j        g d          }d\  }}}d\  }}|||z  ||z  f}t          j        |||d}t          j        ddd          }	t          |                    |	          |dd	           d S )
N)
gF^T=g{X'=gNunƢsy>g7!t?gɫzI?g̸?g?gq6.?gmPZz?g:PgN?rf   rf   r   r{   r  rc   r_   r   r   r   r   )ri   r   r8   genhyperbolicrX  r   rh   
rr   r  lmbdar  betar  deltar/  ghr^   s
             r2   
test_pdf_rzTestGenHyperbolic.test_pdf_r  s           %ud	EuU{DJ/ $Be<<<KR$$q		6>>>>>>r4   c                     t          j        g d          }d\  }}}d\  }}|||z  ||z  f}t          j        |||d}t          j        ddd          }	t          |                    |	          |dd	           d S )
N)
g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?r  r  rc   r  r_   r   ư>r  )ri   r   r8   r  rX  r   rp   r  s
             r2   
test_cdf_rzTestGenHyperbolic.test_cdf_r  s           %ud	EuU{DJ/ $Be<<<KR$$q		6======r4   zx, p, a, b, loc, scale, ref)
)rf   r   r  r{   r  g8ɹvF(;)r  r_   r  rk  r   r   g[Ϡ?)r  r_   r  g      ?r   r   g ✝`D;)r        ?r  ):?r   r   gdL;)r   r  r  r  r   r   gzK^7?)r         r  r  r   r   gj?)r   r  r     r   r   ga=vG:)   r  r   r	  r   r   g?)(   r  r   r	  r   r   g1bV?)<   r  r   r	  r   r   g?c                 t    t           j                            ||||||          }t          ||d           d S Nrc   dy=r   )r8   r  rp   r   )	rr   r^   ru  r0   r1   rd   re   r  rp   s	            r2   test_cdf_mpmathz!TestGenHyperbolic.test_cdf_mpmath  sB     !%%aAqc%GGSu------r4   ))r   r  rU  r   r   r   gC!,?)r   r         @      @r   r   g,Ћf?)r  r   r  r  r   r   rS  )   rf   r   r  r{   r  gm"چ>),  r_   r  rk  r   r   g:;)r  r  r   r	  r   r   gw=)K   r  r   r	  r   r   g3Z0&K<c                 t    t           j                            ||||||          }t          ||d           d S r  )r8   r  r   r   )	rr   r^   ru  r0   r1   rd   re   r  r   s	            r2   test_sf_mpmathz TestGenHyperbolic.test_sf_mpmath  sB      ##Aq!QCu#EECe,,,,,,r4   c                     g d}d\  }}}d\  ||z  |z  ffdt          dd          D             }t          ||dd	           d S )
N)g@쐧@g@쐧 @g܊B@gvGăi@r  r  c                 Z    g | ]'}t          j        d                     |          (S )rc   )r8   r  moment)r@   ir/  r  r  s     r2   rB   z4TestGenHyperbolic.test_moments_r.<locals>.<listcomp>  sI        2U;;;BB1EE  r4   r   r   r   r   r  )ranger   )	rr   r  r  r  r  vals_usr/  r  r  s	         @@@r2   test_moments_rz TestGenHyperbolic.test_moments_r  s    5 5 5 %ud	EuU{DJ/     1a[[  
 	ae<<<<<<r4   c                     d\  }}}d\  }}|||z  ||z  f}t          j        |||d}t          j        |                    dd          |j                  \  }}	t          |	dk    d           d S )	Nr  r  rc   r  r   r   r  T)r8   r  r  r   rp   r   )
rr   r  r  r  r  r  r/  r   r   ru  s
             r2   rI  zTestGenHyperbolic.test_rvs  s     %ud	EuU{DJ/ $Be<<<|BFF4F@@"&II1QXt$$$$$r4   c                 2   t          j        ddd          }t          j        |d          t          j        t           j                  j        z  d}}dt          j        |          }}| dz  ||f}t          j        |||d}t          j        |	                    d          |	                    d          d	          d d t           j
        f         }t          |                    |          t          j                            ||          dd
           d S )Nr   r9  r_   rf   r   rc   r}   Gz?r<  r  r  )ri   rX  float_powerr   float32epssqrtr8   r  r   newaxisr   rh   t)	rr   r  r  r  r  r  r/  r   r^   s	            r2   
test_pdf_tzTestGenHyperbolic.test_pdf_t  s    [B## nR++BHRZ,@,@,DDatrwr{{EAud# $Be<<<KtbffTllB772:FFF1IIuw{{1b))	 	 	 	 	 	r4   c                    dt          j        t           j                  j        d}}}d\  }}|||f}t	          j        |||d}t          j        |                    d          |                    d          d          d d t           j        f         }t          |
                    |          t          j        
                    |          dd	           d S )
Nr   r   )r   r   rc   r}   r!  r<  r  r  )ri   r   r#  r$  r8   r  rX  r   r&  r   rh   cauchy)	rr   r  r  r  r  r  r/  r   r^   s	            r2   test_pdf_cauchyz!TestGenHyperbolic.test_pdf_cauchy#  s    
 "28BJ#7#7#;Qdu	Eud# $Be<<<KtbffTllB772:FFF1IIu|''**	 	 	 	 	 	r4   c                    t          j        ddd          }t          j        t           j                  j        }d\  }}}|||z  ||z  f}t          j        |||d}t          j        ddd          d d t           j        f         }t          |	                    |          t
          j
        	                    ||d          d	d
           d S )Nr  r_   )r   r   r   rc   r  r
  r<  r   r   dy=r  )ri   rX  r   r#  r$  r8   r  r&  r   rh   laplace)	rr   rd   r  r  r  r  r/  r   r^   s	            r2   test_pdf_laplacez"TestGenHyperbolic.test_pdf_laplace4  s    k#r2&& $$($uduU{DJ/  $Cu===KR$$QQQ
]3FF1IIu}((1(==	 	 	 	 	 	r4   c           
      p   t          j        ddd          t          j        ddd          t          j        dt          d                    z  t          j        ddd          t          j        ddd          f\  }}}}d	}|||z  ||z  f}t	          j        |||d
}t          j        |                    d          |                    d          d          d d t           j        f         }t          |	                    |          t          j
        	                    |||||          dd           d S )Nr   r
  r_   r      r   r`   r   rc   r}   r!  r<  )r0   r1   rd   re   r   r  )ri   rX  r"  r  r8   r  r   r&  r   rh   norminvgauss)	rr   r  r  r  r  r  r/  r   r^   s	            r2   test_pdf_norminvgaussz'TestGenHyperbolic.test_pdf_norminvgaussI  s/    Ar2&&Ar2&&r~b%))'D'DDAq"%%D#r**	"tUB uu}dUl3 $Be<<<KtbffTllB772:FFF1IIu)--Ud% . 9 9	 	 	 	 	 	r4   N)r   r   r   r6  r  r  r   r   r   r  r  r  rI  r(  r+  r/  r4  r:   r4   r2   r  r    s"         ? ? ?,> > >4 [%		< 		< 		< . . . [%	@ 	@ 	@	 	- -	 	-= = =.% % %  $  "  *    r4   r  c                       e Zd Zej                            dddg          d             Zej                            dddg          d             Zd	S )
TestHypSecantzx, reference)r9  gA0=)r<  g!b;c                 h    t           j                            |          }t          ||d           d S N+<r   )r8   	hypsecantr   r   )rr   r^   	referencer   s       r2   r  zTestHypSecant.test_sfe  s4     _""IE222222r4   zp, reference)r  g9bT*@)r  gTW-;@c                 h    t           j                            |          }t          ||d           d S r8  )r8   r:  r  r   )rr   ru  r;  r^   s       r2   r  zTestHypSecant.test_isfo  s4     O""95111111r4   Nr   r   r   r   r   r   r  r  r:   r4   r2   r6  r6  `  s        
 [^9:<= =3 3= =3 [^89;< <2 2< <2 2 2r4   r6  c                       e Zd Zd Zd Zd Zej                            dg d          d             Z	d Z
d Zd	 Zd
 ZdS )TestNormInvGaussc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestNormInvGauss.setup_methodx  r7  r4   c                     t          j        g d          }t          j        g d          }t          j                            |dd          }t          ||d           d S )N)gp~٧>g @X>g}e?g{)߳?gwH?ir      r>  r   r{   r0   r1   &.>r   )ri   r   r8   r3  rp   r   )rr   r_cdfx_testvals_cdfs       r2   
test_cdf_RzTestNormInvGauss.test_cdf_R{  sr      < < < = =,,,--%))&A)==%d333333r4   c                     t          j        g d          }t          j        g d          }t          j                            |dd          }t          ||d           d S )N)gp϶>g\H55$?geСt&?go NiH?g]u>rB  r   r{   rE  rF  r   )ri   r   r8   r3  rh   r   )rr   r_pdfrH  vals_pdfs       r2   r  zTestNormInvGauss.test_pdf_R  sp     < < < = =,,,--%))&A)==%d333333r4   zx, a, b, sf, rtol))r   r   r   !7?r   )r  r   r   ?=r  )r   r   r  gy5`?r  )r_   r   r  gMLC9rF  c                     t           j                            |||          }t          |||           t           j                            |||          }t          |||           d S Nr   r8   r3  r   r   r  )rr   r^   r0   r1   r   r   rN   r  s           r2   test_sf_isf_mpmathz#TestNormInvGauss.test_sf_isf_mpmath  sh     !!!Q**2D))))""2q!,,14((((((r4   c                     ddg}ddg}d}ddg}t           j                            |||          }t          ||dd	           t           j                            |||          }t          ||d
           d S )Nr   r  r   r   rN  rO  r   r  re  r  r   rR  )rr   r^   r0   r1   r   rN   r  s          r2   test_sf_isf_mpmath_vectorizedz.TestNormInvGauss.test_sf_isf_mpmath_vectorized  s    HF "89!!!Q**2E6666""2q!,,14((((((r4   c                     t          j        dd          }t          j        ddd          }|                    |          }|                    |          }t          ||           d S )Nr   r   r
  rf   )r8   r3  ri   r  r   r  r   )rr   dstr^   r   r  s        r2   test_gh8718zTestNormInvGauss.test_gh8718  s[     A&&IaQVVAYYggbkkQr4   c                 .   d\  }}t          j        |dz  |dz  z
            }||z  |dz  |dz  z  d|z  |t          j        |          z  z  ddd|dz  z  |dz  z  z   z  |z  f}t          |t          j                            ||d                     d S )	Nr   r{   rf   r         @r   r   mvskmoments)ri   r%  r   r8   r3  )rr   r0   r1   gammav_statss        r2   
test_statszTestNormInvGauss.test_stats  s    11q!t$$u9adUAXosQw!bgenn:L/M!a!Q$hAo-.68We066q!V6LLMMMMMr4   c                     d\  }}t          j        g d          }t          j                            |||          }t          |t          j                            |||                     d S )NrZ  MbP?r{   r  )ri   r   r8   r3  r   r   rp   )rr   r0   r1   rH  rG  s        r2   test_ppfzTestNormInvGauss.test_ppf  sf    1---..!%%fa33 2 6 6tQ B BCCCCCr4   N)r   r   r   r6  rJ  r  r   r   r   rS  rU  rX  ra  re  r:   r4   r2   r?  r?  w  s          
4 
4 
44 4 4 [0J J JK K
) )K K
)	) 	) 	)     N N ND D D D Dr4   r?  c                   J    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 ZdS )TestGeomc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestGeom.setup_method  r7  r4   c                    t           j                            dd          }t          t	          j        |dk                         t          t	          j        |          dk               t          |j        j        t          d         v            t           j                            d          }t          t          |t                               t          j        d                              d          }t          t          |t          j                             t          |j        j        t          d         v            d S )Nr   r;  r:  r   r=  r   )r8   geomr   r	   ri   r   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestGeom.test_rvs  s    z~~d~11tqy!!"""')***
9\#::;;;jnnT""
3$$%%%j""1%%
3
++,,,	)L"99:::::r4   c                 P   t           j                            d          }t          j                            t          j        d          d|          }|j        t           j        k    sJ t          j	        |t          j
        t           j                  j        k              sJ d S )Nl   A: ir   r   )ri   r   r   r8   rj  r   r   r   int64r   iinfoint32max)rr   r   r   s      r2   test_rvs_9313zTestGeom.test_rvs_9313  s     i##O44jnnRVC[[qsnCCyBH$$$$vcBHRX..223333333r4   c                 n    t           j                            g dd          }t          |g d           d S )Nr
  r{   )r{   rk  r  )r8   rj  rO  r   rr   rG  s     r2   ri  zTestGeom.test_pmf  s8    z~~iii--!$(:(:(:;;;;;r4   c                 8   t          j        t          j                            g dd                    }t          j                            g dd          }t          ||dd           t          j                            dd          }t          |d           d S )Nr
  r{   r   r   re  r   r   )ri   r  r8   rj  rO  r  r   r   )rr   rg  rh  rH  s       r2   test_logpmfzTestGeom.test_logpmf  s    uz~~iii5566
!!)))S11u5q9999 j1%%S#r4   c                     t           j                            g dd          }t           j                            g dd          }t	          g d          }t          ||           t          |d|z
             d S )Nr
  r{   r{   r         ?r   )r8   rj  rp   r   r   r   rr   rG  vals_sfrW   s       r2   test_cdf_sfzTestGeom.test_cdf_sf  sr    z~~iii--*--			3//+++,,!$111!'1X:66666r4   c                 :   t           j                            g dd          }t           j                            g dd          }t	          g d          }t          |t          j        |                     t          |t          j        |                      d S )Nr
  r{   rv  )	r8   rj  r  logsfr   r   ri   r  log1prx  s       r2   test_logcdf_logsfzTestGeom.test_logcdf_logsf  s    z  C00*""999c22+++,,!$x(8(8999!'28XI+>+>?????r4   c                     t           j                            g dd          }t          g d          }t	          ||           d S )Nrv  r{   )rS  r   r[  )r8   rj  r   r   r   rr   rG  rW   s      r2   re  zTestGeom.test_ppf  sE    z~~000#66))!$11111r4   c                 f    t          t          j                            dd          dd           d S )N#B;rS  +=r   )r   r8   rj  r   rw   s    r2   test_ppf_underflowzTestGeom.test_ppf_underflow  s-    
ue44cFFFFFFr4   c                 v    t          j        d                                          }t          |dd           d S )Ng<,Ԛ?g۩@r   r   )r8   rj  rG   r   )rr   ro  s     r2   test_entropy_gh18226zTestGeom.test_entropy_gh18226  s;     Jv&&((,5999999r4   N)r   r   r   r6  rI  rp  ri  rt  rz  r~  re  r  r  r:   r4   r2   rg  rg    s          	; 	; 	;4 4 4< < <  7 7 7@ @ @2 2 2
G G G: : : : :r4   rg  c                        e Zd Zd Zd Zd ZdS )
TestPlanckc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestPlanck.setup_method  r7  r4   c                     t           j                            g dd          }t          g d          }t	          ||           d S )Nr
  rT  )g|dy?g8'\>ggrU!>)r8   planckr   r   r   r  s      r2   r  zTestPlanck.test_sf  sQ    |yyy"-- 2 2 2 3 3 	"$11111r4   c                     t           j                            g dd          }t          g d          }t	          ||           d S )N)r       @@     p@r  )g    P.g    h>g    TF)r8   r  r|  r   r   r  s      r2   
test_logsfzTestPlanck.test_logsf  sJ    |!!"7"7"7??:::;;!$11111r4   N)r   r   r   r6  r  r  r:   r4   r2   r  r    sA          2 2 22 2 2 2 2r4   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestGennormc                     g d}t           j                            |d          }t           j                            |          }t	          ||           d S Nr
  r   )r8   gennormrh   r.  r   rr   pointspdf1pdf2s       r2   test_laplacezTestGennorm.test_laplace  sM    }  ++}  ((D$'''''r4   c                     g d}t           j                            |d          }t           j                            |d          }t	          ||           d S Nr
  rf   g;f?re   )r8   r  rh   normr   r  s       r2   	test_normzTestGennorm.test_norm  sO    }  ++z~~fF~33D$'''''r4   c                    t           j                            d           t          j        d          }|                    d          }t          j        ||j                  j        dk    sJ t          j        d          }|                    d          }t          j	                            d          }t          j
        ||          j        dk    sJ t          j        d          }|                    d          }t          j                            dd	          }t          j
        ||          j        dk    sJ d S )
Nr   r{   r   r:  r\   r   rf   g;f?re   r   )ri   r   r   r8   r  r   r  rp   pvaluer.  ks_2sampr  )rr   rA   r   rvs_laplacervs_norms        r2   rI  zTestGennorm.test_rvs!  s   
	q}S!!hhDh!!|C**1C7777}QhhDh!!m''T'22~c;//6<<<<}QhhDh!!:>>t><<~c8,,3c999999r4   c                    t           j                            d           t          j        ddgddgg          }|                    g d          }t          j        |d d ddf         t          j        d          j                  d         d	k    sJ t          j        |d d ddf         t          j        d          j                  d         d	k    sJ t          j        |d d ddf         t          j        d          j                  d         d	k    sJ t          j        |d d ddf         t          j        d          j                  d         d	k    sJ d S )
Nr   r{   rS  r   rT  )r   rf   rf   r:  r   r\   )ri   r   r   r8   r  r   r  rp   )rr   rA   r   s      r2   test_rvs_broadcastingz!TestGennorm.test_rvs_broadcasting2  sC   
	q}sBi"b233hhLLLh))|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJJJr4   N)r   r   r   r  r  rI  r  r:   r4   r2   r  r    sU        ( ( (( ( (: : :"K K K K Kr4   r  c                   Z    e Zd Zej                            dddg          d             ZdS )
TestGibratx, sfx)r  gD.?)  gJ]b<c                     t          t          j                            |          |d           t          t          j                            |          |d           d S N+=r   )r   r8   r(  r   r  rr   r^   sfxs      r2   test_sf_isfzTestGibrat.test_sf_isfJ  sR     	**Ce<<<<((--qu======r4   N)r   r   r   r   r   r   r  r:   r4   r2   r  r  <  sV         [X(A(E(G H H> >H H> > >r4   r  c                       e Zd Zd Zej                            dg d          d             Zej                            dg d          d             ZdS )	TestGompertzc                     t           j                            t           j                            dd          d          }t	          |d           d S N0.++r   )r8   gompertzr   rp   r   r  s     r2   test_gompertz_accuracyz#TestGompertz.test_gompertz_accuracyS  sA    Nu~11&!<<a@@6"""""r4   z	x, c, sfx))r   r  g|t?)r   r  g(fMr;)r  r   g[?)g      @r   gg[<c                     t          t          j                            ||          |d           t          t          j                            ||          |d           d S Nr  r   )r   r8   r  r   r  )rr   r^   r  r  s       r2   r  zTestGompertz.test_sf_isfd  sX    
 	))!Q//5AAAA**322AEBBBBBBr4   c, ref))r  geUT8?)r   gtqq?)r   gs{)r  gN*6c                 d    t          t          j                            |          |d           d S r  )r   r8   r  rG   rr   r  r  s      r2   rp  zTestGompertz.test_entropys  s/    
 	..q113UCCCCCCr4   N)	r   r   r   r  r   r   r   r  rp  r:   r4   r2   r  r  Q  s        # # #" [[ +M +M +M N NC C	N NC [X (E (E (E F FD D	F FD D Dr4   r  c                   Z    e Zd Zej                            dddg          d             ZdS )TestFoldNorm	x, c, ref)r  :0yE>g:0N<?)r  r  g:?c                 f    t          t          j                            ||          |d           d S r   )r   r8   foldnormrp   rr   r^   r  r  s       r2   r[  zTestFoldNorm.test_cdf  s1     	**1a00#EBBBBBBr4   N)r   r   r   r   r   r   r[  r:   r4   r2   r  r  {  s[         [[+N+M+O P PC CP PC C Cr4   r  c                      e Zd Zej                            dddg          d             Zej                            dg d          d             Zej                            dd	d
g          ej                            dg d          ej                            dddg          ej                            dddg          d                                                 Zd Z	dS )TestHalfNormr  )r   |N?)r_   Oul2;c                     t          t          j                            |          |d           t          t          j                            |          |d           d S r  )r   r8   halfnormr   r  r  s      r2   r  zTestHalfNorm.test_sf_isf  sT     	))!,,c>>>>**3//??????r4   x, ref))Ww'&l7g;G<^͛7)C]r2<gE~o-<)rD  g?c                 d    t          t          j                            |          |d           d S r   )r   r8   r  rp   rr   r^   r  s      r2   r[  zTestHalfNorm.test_cdf  s/     	**1--s??????r4   r   h㈵>r  	rvs_scaler}   r`   r   r   TF	fix_scalec                    t           j                            d          }t          j                            ||d|          }|r[|rYd}t          j        t          |          5  t          j	        
                    |||           d d d            n# 1 swxY w Y   d S i }|r||d<   |r||d<   t          t          j        |fi |d	d
i d S Nr   r   rd   re   r   r   r  r  r   r   r   r   r  T)ri   r   r   r8   r  r   r   r   r  halflogisticr   r   	rr   r   r  r   r  r   r   	error_msgr   s	            r2   r   z(TestHalfNorm.test_fit_MLE_comp_optimizer  s^    i##$788~!!gYT/2 " 4 4  	y 	%I|9=== M M"&&t')&LLLM M M M M M M M M M M M M M MF 	#"DL 	'&DN 	&end 	< 	<d 	< 	<6:	< 	< 	< 	< 	< 	<   $#BBBc                     t          j        t                    5  t          j                            g dd           d d d            d S # 1 swxY w Y   d S Nr
  rf   r   )r   r   r"   r8   r  r   rw   s    r2   test_fit_errorzTestHalfNorm.test_fit_error  s    ]<(( 	2 	2Nyyyq111	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2   $AAAN)
r   r   r   r   r   r   r  r[  r   r  r:   r4   r2   r  r    sK        [X(?(C(E F F@ @F F@ [X (A (A (A B B@ @B B@ [Yt55[[*:*:*:;;[Yu66[[4-88< < 98 76 <; 65<22 2 2 2 2r4   r  c                   2   e Zd Zej                            dddg          ej                            dddg          ej                            ddd	g          ej                            d
dd	g          d                                                 Zd ZdS )TestHalfCauchyr   r  r  r  r}   r   r   TFr  c                    t           j                            d          }t          j                            ||d|          }|r[|rYd}t          j        t          |          5  t          j	        
                    |||           d d d            n# 1 swxY w Y   d S i }|r||d<   |r||d<   t          t          j	        |fi | d S )	Nr   r   r  r  r  r  r   r   )ri   r   r   r8   r  r   r   r   r  
halfcauchyr   r   r  s	            r2   r   z*TestHalfCauchy.test_fit_MLE_comp_optimizer  s=    i##$788~!!gYT/2 " 4 4  	y 	%I|9=== K K $$T	$JJJK K K K K K K K K K K K K K KF 	#"DL 	'&DN%e&6EEEEEEEr  c                     t          j        t                    5  t          j                            g dd           d d d            d S # 1 swxY w Y   d S r  )r   r   r"   r8   r  r   rw   s    r2   r  zTestHalfCauchy.test_fit_error  s    ]<(( 	4 	4   333	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4r  N)r   r   r   r   r   r   r   r  r:   r4   r2   r  r    s        [Yt55[[4+66[Yu66[[4-88F F 98 76 76 65F,4 4 4 4 4r4   r  c                      e Zd Zej                            dddg          d             Zej                            dg d          d             Zej                            dd	d
g          ej                            dg d          ej                            dddg          ej                            dddg          d                                                 Zd Z	dS )TestHalfLogisticr  )r`   ]6)   L-c                 d    t          t          j                            |          |d           d S r   )r   r8   r  r   r  s      r2   r  zTestHalfLogistic.test_sf  s0     	*--a00#EBBBBBBr4   q, ref))r  r`   )r  r  )gv?g   .!>)g?g      <c                 d    t          t          j                            |          |d           d S r   )r   r8   r  r  rr   r~  r  s      r2   r  zTestHalfLogistic.test_isf  s0    
 	*..q113UCCCCCCr4   r   r  r  r  r  r   TFr  c                    t           j                            d          }t          j                            ||d|          }i }|r[|rYd}t          j        t          |          5  t          j        	                    |||           d d d            n# 1 swxY w Y   d S |r||d<   |r||d<   t          t          j        |fi |d	d
i d S r  )ri   r   r   r8   r  r   r   r   r  r   r   )	rr   r   r  r   r  r   r   r   r  s	            r2   r   z,TestHalfLogistic.test_fit_MLE_comp_optimizer	  s`    i##$788!%%'36 & 8 8  	y 	%I|9=== M M"&&t')&LLLM M M M M M M M M M M M M M MF 	#"DL 	'&DN 	&e&8$ 	< 	<$ 	< 	<6:	< 	< 	< 	< 	< 	<s   &#BBBc                     d}t          t          |          5  t          j                            g dd           d d d            d S # 1 swxY w Y   d S )Nz; Maximum likelihood estimation with 'halflogistic' requiresr  )r   rf   r   r   r   )assert_raisesr"   r8   r  r   rr   r.   s     r2   test_fit_bad_flocz"TestHalfLogistic.test_fit_bad_floc&  s    L<s333 	6 	6""9991"555	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6s   $A

AAN)
r   r   r   r   r   r   r  r  r   r  r:   r4   r2   r  r    sK        [X(D(D(F G GC CG GC [X (K (K (K L LD D	L LD [Yt55[[*:*:*:;;[Yu66[[4-88< < 98 76 <; 65<26 6 6 6 6r4   r  c                        e Zd Zd Zd Zd ZdS )TestHalfgennormc                     g d}t           j                            |d          }t           j                            |          }t	          ||           d S r  )r8   halfgennormrh   exponr   r  s       r2   
test_exponzTestHalfgennorm.test_expon-  sL     $$VQ//{v&&D$'''''r4   c                     g d}t           j                            |d          }t           j                            |d          }t	          ||           d S r  )r8   r  rh   r  r   r  s       r2   test_halfnormzTestHalfgennorm.test_halfnorm4  sS     $$VQ//~!!&!77D$'''''r4   c                     g d}t           j                            |d          }t           j                            |d          }t	          |d|z             d S )Nr
  g
(?rf   )r8   r  rh   r  r   r  s       r2   test_gennormzTestHalfgennorm.test_gennorm;  sT     $$VW55}  11D!D&)))))r4   N)r   r   r   r  r  r  r:   r4   r2   r  r  ,  sA        ( ( (( ( (* * * * *r4   r  c                        e Zd Zd Zd Zd ZdS )TestLaplaceasymmetricc                     t          j        g d          }t          j                            |d          }t          j                            |          }t          ||           d S r  )ri   r   r8   laplace_asymmetricrh   r.  r   r  s       r2   r  z"TestLaplaceasymmetric.test_laplaceD  sX    )))$$'++FA66}  ((d#####r4   c                     t          j        g d          }d}d|z  }t          j                            ||          }t          j                            ||dz  z  |          }t          ||           d S )Nr
  rf   r   )ri   r   r8   r  rh   r   )rr   r  r   kapinvr  r  s         r2   test_asymmetric_laplace_pdfz1TestLaplaceasymmetric.test_asymmetric_laplace_pdfK  sr    )))$$5'++FE::'++FE1H,=vFFd#####r4   c           
         t          j        t          j        d           t          j        d          g          }d}t          j                            ||          }t          j                            ||          }t          j                            ||          }t          j        ddg          }t          j        ddg          }t          j        dd	g          }t          j                            ||          }	|}
t          j        	                    ||          }|}t          t          j        ||||	|f          t          j        ||||
|f                     d S )
N   r_   rf   r\   gMbp?r  gV-?r   gMb`?)ri   r   r  r8   r  rh   rp   r   r   r  r   concatenate)rr   r  r   r  cdf1sf1r  cdf2sf2ppf1ppf2isf1isf2s                r2   !test_asymmetric_laplace_log_10_16z7TestLaplaceasymmetric.test_asymmetric_laplace_log_10_16T  s9   BF2JJ;r

344'++FE::'++FE::&))&%88xu&&xi())hU|$$'++D%88'++C77dCt'DEEdCt'DEE	G 	G 	G 	G 	Gr4   N)r   r   r   r  r  r  r:   r4   r2   r  r  C  sF        $ $ $$ $ $G G G G Gr4   r  c                      e Zd Zd Zej                            dg d          d             Zej                            dg d          d             Zd Z	d Z
d	 Zd
 Zd Zd Zd Zg dg dg dg ddej        ddddgej         dddddgg dg dg dg	Z ej        e          Zej                            de          d             Zd Zd Zd  Zd! Zd" Zd# Zd$S )%TestTruncnormc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestTruncnorm.setup_methodg  r7  r4   	a, b, ref))r   r`   r  )333333?ffffff?gܲl)r  g>g+c                 f    t          t          j                            ||          |d           d S N绽|=r   r   r8   	truncnormrG   rr   r0   r1   r  s       r2   rp  zTestTruncnorm.test_entropyj  s1    $ 	//155sGGGGGGr4   ))r-  r  ghiɮ9?)r  r  r  )g0.+r  r  )}Ô%Ir  Z_2?c                 f    t          t          j                            ||          |d           d S r  r  r  s       r2   test_extreme_entropyz"TestTruncnorm.test_extreme_entropy~  s1      	//155sGGGGGGr4   c           	          t           j                            g ddddgdz  d          }t          j        t          j        dd	dd
dt          j        g          }t          ||           d S )Nr   r   r  r{   H.?r   rf         rS  r      rf   rc   r   fO?l@r   )r8   r  r   ri   r   r  r   r  s      r2   test_ppf_ticket1131z!TestTruncnorm.test_ppf_ticket1131  n    ""#E#E#EsB()s1uA # 7 78RVQ
Az1bfMNN!$11111r4   c           	          t           j                            g ddddgdz  d          }t          j        t          j        dd	dd
dt          j        g          }t          ||           d S )Nr   r"  rS  r   r#  rf   rc   r   r%  r$  r   )r8   r  r  ri   r   r  r   r  s      r2   test_isf_ticket1131z!TestTruncnorm.test_isf_ticket1131  r'  r4   c                    d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d S )N)ir  r   r   r_   r:  )r_      r8   r  r   r	   minro  rr   lowhighr^   s       r2   test_gh_2477_small_valuesz'TestTruncnorm.test_gh_2477_small_values  s    	TOT1ab99aeegg........$....///	TOT1ab99aeegg........$..../////r4   c                    d\  }}t           j                            ||ddd          }t          ||                                cxk    o|                                cxk    o|k    nc           t          |||g          f d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d S )	N)r`   r]   r   r   r_   r:  )r     )'  i'  )i)r8   r  r   r	   r-  ro  rK   r.  s       r2   test_gh_2477_large_valuesz'TestTruncnorm.test_gh_2477_large_values  s   	TOT1ab99quuww1111!%%''1111T111122CdA4G4GGG 	TOT1ab99aeegg........$..../// 	TOT1ab99aeegg........$....///"	TOT1ab99aeegg........$..../////r4   c                    ddgddgfD ]\  }}t          j        t           j         ||t           j        g          }||z   dz  }t          j                            |||          }t          j                            |||          }t          j                            |||          }t          j        g d          }t          j        g d          }	t          j        g d          }
|d	k     rt          j        g d
          }
t          ||           t          ||	           t          ||
           t          t          j	        |
d         |
d         z            |dz              t          j        g d          }t          j        
                    |||          }t          j        |t          j        |          dz  |g          }t          ||           |d	k     r_t          t          j                            |||          d           t          t          j                            |||          d           n^t          t          j                            |||          d           t          t          j                            |||          d           t          j                            |||          }t          t          j	        ||
d         z            |dz   dz             d S )Nr   r   r  r   r   r   r   r   rS  rS  r   r   )r   d._MT
@BKg?r   r   )r   r<  r;  r   r   rf   r{   r   r{   rS  gĖy	@gdv*?g,mj%V?rk  )ri   r   r  r8   r  rp   r   rh   r   r  r   r   )rr   r/  r0  xvalsxmidcdfssfspdfsexpected_cdfsexpected_sfsexpected_pdfspvalsppfsexpected_ppfsrh   s                  r2   test_gh_9403_nontail_valuesz)TestTruncnorm.test_gh_9403_nontail_values  s   a&2r(+  	M  	MICHrvgsD"&9::EHc>D?&&uc488D/$$UC66C?&&uc488DH\\\22M8$8$8$899LH%A%A%ABBMQww ")E)E)E F Fm444\222m444}Q'7a8H'H I I #c	+ + +H]]]++E?&&uc488DHc273<<	+A4%HIIMm444Qww#EO$6$6tS$$G$G$68 8 8#EO$7$7c4$H$H$68 8 8 8 $EO$7$7c4$H$H$68 8 8#EO$6$6tS$$G$G$68 8 8/%%dC66Cs=+;'; < <tDy!mLLLLA 	M  	Mr4   c           	         ddgddgfD ]F\  }}t          j        t           j         ||t           j        g          }||z   dz  }t          j                            |||          }t          j                            |||          }t          j                            |||          }t          j        g d          }t          j        g d          }	t          j        g d          }
|d	k     rt          j        g d
          }
t          ||           t          ||	           t          ||
           t          t          j	        |
d         |
d         z            |dz              t          j        g d          }t          j        
                    |||          }t          j        |t          j        |          dz  |g          }t          ||           t          j                            |||          }t          ||           |d	k     r_t          t          j                            |||          d           t          t          j                            |||          d           n^t          t          j                            |||          d           t          t          j                            |||          d           t          j                            |||          }t          t          j	        ||
d         z            |dz   dz             t          j        ||d          }|d d d          }t          t          j                            |||          t          j                            || |           d d d                    t          t          j                            |||          t          j                            || |           d d d                    t          t          j                            |||          t          j                            || |           d d d                    Hd S )N'   r  ir   r9  r:  )r   pGC@Ff<r   r   )r   rN  rM  r   r   rf   r{   r=  gEC@g i?gspXio)>rk  r+  r   )ri   r   r  r8   r  rp   r   rh   r   r  r   r   rX  )rr   r/  r0  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rh   xvals2s                   r2   test_gh_9403_medium_tail_valuesz-TestTruncnorm.test_gh_9403_medium_tail_values  s   r(S#J/ ,	P ,	PICHrvgsD"&9::EHc>D?&&uc488D/$$UC66C?&&uc488DH\\\22M8$8$8$899LH%K%K%KLLMQww " *= *= *= !> !>m444\222m444}Q'7a8H'H I I #c	+ + +H]]]++E?&&uc488DHc273<<+CT%JKKMm444?&&tS$77De,,,Qww#EO$6$6tS$$G$G$68 8 8#EO$7$7c4$H$H$9; ; ; ; $EO$7$7c4$H$H$68 8 8#EO$6$6tS$$G$G$9; ; ;/%%dC66Cs=+;'; < <tDy!mLLLKT2..EDDbDk\F 3 3E3 E E % 2 26D53$ G G" MO O O 2 25#t D D % 3 3FTEC4 H H2 NP P P 3 3E3 E E % 3 3FTEC4 H H2 NP P P PW,	P ,	Pr4   c                     t          t          j        dd                              d          d           t          t          j        dt          j                                      d          d           d S )Ng      *@g      .@      ,@g T?rD  g @gR?)r   r8   r  rp   ri   r  rw   s    r2   test_cdf_tail_15110_14753z'TestTruncnorm.test_cdf_tail_15110_14753  sr    
 	S1155c::*	, 	, 	,262266s;;*	, 	, 	, 	, 	,r4   )r9  r   rS  r   r   )r  r_   r   rS  r   gLFu)r8  r   r   gMFmz%?r   gſ)r   rf   r   ghI}?r   gHNMr   gQ63E?gnl$A?gr1"D?gK8L?gQ63Egr1"D)r   r   gU*? bn?gnA??c3TXʿ)r8  r   gU*ҿrU  gnArV  )r  g"$7"gOxr?gp7`g'>K@casec                     |\  }}}}}}t           j                             ||d          \  }}	}
}t          ||	|
|g||||gd           d S )Nr\  r]  FFg<r   )r8   r  r   )rr   rX  r0   r1   m0v0s0k0mvrN   r[   s               r2   test_momentszTestTruncnorm.test_moments>  sd    #1b"b"_**1a*@@
1aAq!r2r2&6UCCCCCCr4   c                     t           j                             dt          j        d          \  }}t	          |d           t	          |d           d S )Nr   mvr]  g e3E?g:&A?)r8   r  ri   r  r   )rr   r_  r`  s      r2   test_9902_momentszTestTruncnorm.test_9902_momentsD  sJ    $$Q$==1Az***Az*****r4   c                     d\  }}t           j                            ||ddd          }t          ||                                cxk     o|                                cxk     o|k     nc            d S )N)r_   r>  r   r   r_   r:  r,  r.  s       r2   test_gh_1489_trac_962_rvsz'TestTruncnorm.test_gh_1489_trac_962_rvsI  sy    	TOT1ab99aeegg........$..../////r4   c                 P   ddt           j         dt           j         t           j         dddddg}dddt           j        ddddd	t           j        t           j        g}t          j                            ||dt          |          f
          }t          j        |          dt          |          fk    sJ t          t          j        ||	                    d          k                         t          t          j        |
                    d          |k                         d S )Nr  r_   rC  ir  r+  r   rL  -   r:  r   )axis)ri   r  r8   r  r   r  rA  r	   r   r-  ro  r.  s       r2   test_gh_11299_rvszTestTruncnorm.test_gh_11299_rvsO  s     BbfWrvgsCS"MB262sBRHOTCHH>>x{{q#c((m++++saeeemm+,,---quu!u}},--.....r4   c                     t          t          j        d          rAt          j                            dddt          j                                                   d S d S )Nr   r  rC  r   r   )r/   ri   r   r8   r  r   r   rw   s    r2   test_rvs_Generatorz TestTruncnorm.test_rvs_GeneratorY  sh    29m,, 	FORa-/Y-B-B-D-D   F F F F F	F 	Fr4   c                    t          j        t           j         t           j         dt           j         dg          }t          j        t           j        t           j        ddt           j        g          }t          j        g d          }g d}t          t	          j        ||                              |          |           t          t	          j        | |                               |           |           d S )Nr_   rD  )r_         @ro  	   r
  )gOul"gځ=!gL!g>EG	f g^K[X)ri   r   r  r   r8   r  r  r|  )rr   r0   r1   r^   rW   s        r2   test_logcdf_gh17064z!TestTruncnorm.test_logcdf_gh17064_  s    HrvgwRVGR899HbfbfaRV455H***+++ + + 	1--44Q77BBBQB//55qb998DDDDDr4   c                 z    t          j        dd                              d          }d}t          ||           d S )Nr   r   r   gl).0S?)r8   r  r  r   )rr   r   r  s      r2   test_moments_gh18634z"TestTruncnorm.test_moments_gh18634j  s@     ob!$$++A..  S!!!!!r4   N)r   r   r   r6  r   r   r   rp  r  r&  r)  r1  r6  rI  rP  rS  ri   r  _truncnorm_stats_datar   ra  rd  rf  rj  rl  rq  rs  r:   r4   r2   r  r  f  su          [[B B BC CH H	C CH  [[D D DE E
H HE E
H2 2 22 2 20 0 00 0 0&!M !M !MF-P -P -P^, , ,	 	 		1 	1 	1	= 	= 	=	< 	< 	<	
BF						
 &!						
	 	 	
	 	 	
	 	 	;"F %BH%:;;[V%:;;D D <;D
+ + +
0 0 0/ / /F F F	E 	E 	E" " " " "r4   r  c                      e Zd Zej                            dg d          d             Zej                            dg d          d             Zej                            ddd	g          d
             Zej                            dddg          d             Z	ej                            dddg          d             Z
ej                            dddg          d             ZdS )TestGenLogisticx, expected))ig4`n)ig4	ncg)r   gX
=)r`   gh@X)r   gh<c                 n    d}t           j                            ||          }t          ||d           d S )Nr  r   r   )r8   genlogisticr   r   )rr   r^   rW   r  logps        r2   test_logpdfzTestGenLogistic.test_logpdfw  s<      ''1--hU333333r4   r  ))r  gTKEl@)r  gJk$@)r   gsF<?)r  7~F<?c                 d    t          t          j                            |          |d           d S r8  )r   r8   ry  rG   r  s      r2   rp  zTestGenLogistic.test_entropy  s0    
 	)11!44cFFFFFFr4   r  )r  r_   g8.)  r
  gpT	oc                 f    t          t          j                            ||          |d           d S r  )r   r8   ry  r   r  s       r2   r  zTestGenLogistic.test_sf  s2     	),,Q22CeDDDDDDr4   	q, c, ref)r}   r  g^ #@)rd  rf   gGFf@c                 f    t          t          j                            ||          |d           d S NV瞯<r   )r   r8   ry  r  rr   r~  r  r  s       r2   r  zTestGenLogistic.test_isf  2     	)--a33SuEEEEEEr4   )r{   r  gİ@)r!  r
  g1a@c                 f    t          t          j                            ||          |d           d S r  )r   r8   ry  r   r  s       r2   re  zTestGenLogistic.test_ppf  r  r4   )r`   {Gz?g(?)r<  r
  g'Tn7c                 f    t          t          j                            ||          |d           d S r   )r   r8   ry  r  r  s       r2   test_logcdfzTestGenLogistic.test_logcdf  s2     	)00A66%HHHHHHr4   N)r   r   r   r   r   r   r{  rp  r  r  re  r  r:   r4   r2   rv  rv  t  s        [] -I -I -I J J
4 4J J
4 [X (E (E (E F FG G	F FG& [[+L+L+N O OE EO OE [[+I+H+J K KF FK KF [[+I+H+J K KF FK KF [[+N+K+M N NI IN NI I Ir4   rv  c                   t    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zej        j        d             ZdS )TestHypergeomc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestHypergeom.setup_method  r7  r4   c                 L   t           j                            dddd          }t          j        |dk              t          j        |dk              z  sJ t          j        |          dk    sJ |j        j        t          d         v sJ t           j                            ddd          }t          |t                    sJ t          j        ddd                              d          }t          |t          j                  sJ |j        j        t          d         v sJ d S )Nr
  r_   r   r;  r:  r   r=  )r8   	hypergeomr   ri   r   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestHypergeom.test_rvs  s   ""2r17";;vdai  26$!)#4#44444x~~((((z)L"99999o!!"a,,#s#####ob!R((,,Q//#rz*****y~<!8888888r4   c                     d}d}d}|}|}t           j                            d|||          }t          |dd           d S )Ni	  r<  r~  rf   gkㅒP?r+  )r8   r  rO  r   )rr   Mrt  Ntotgoodhgpmfs          r2   test_precisionzTestHypergeom.test_precision  sO    ##AsD!44E#8"=====r4   c                    t          t          j                            dddd          dd           t          t          j                            dddd          dd           t          t          j                            dddd          dd           t          t          j                            dddd          dd           d S )Nr   rf   r   rS  r+  r   )r   r8   r  rO  rw   s    r2   	test_argszTestHypergeom.test_args  s     	EO//1a;;S"EEEEO//1a;;S"EEEEO//1a;;S"EEEEO//1a;;S"EEEEEr4   c           	          t          dt          j                            dddd          cxk    odk    nc            d S )Nr   r9  io i  if0  rS  )r	   r8   r  rp   rw   s    r2   test_cdf_above_onez TestHypergeom.test_cdf_above_one  sH    U_((XtUCCJJJJsJJJJKKKKKr4   c                 <  	 ddt          j        g d          dz  }d		fd|D             }t          j        g d          }t          ||dd	
           g d}t          j                            |z   d          }g d}t          ||dd	
           d S )Ng    +@g     @)r   ffffff@333333@r   gffffff@@r        @     @c                 Z    g | ]'}t           j                            z   |          (S r:   )r8   r  r   )r@   eatenorangespearsquantiles     r2   rB   z1TestHypergeom.test_precision2.<locals>.<listcomp>  sC     * * * !!(GeOWeLL * * *r4   )r   gpR(g㘍R2gJޱ p9g?Mf=
G?r   r   gƠ>r  )g     @r  g     @g     @g     @)r   r  g)9g"1)ri   r   r   r8   r  r   )
rr   fruits_eatenr   rW   	quantilesres2	expected2r  r  r  s
          @@@r2   test_precision2zTestHypergeom.test_precision2  s     x = = =>>D* * * * * *(* * *8 9 9 9 : :XAD9999 0//	!!)Wu_guMM>>>	iad;;;;;;r4   c                 `   t          j        ddd          }|                                }t          j        ddg          }t          j        t          ||                     }t          ||           t          j        ddd          }|                                }t          |d           d S )Nr   r   r   rk  r   )	r8   r  rG   ri   r   rl  r   r   r   )rr   hgro  rm  rn  s        r2   rp  zTestHypergeom.test_entropy  s    _Q1%%JJLLXtTl++
fU:z::;;;
:&&&_Q1%%JJLLQr4   c                     d}d}d}d}t           j                            ||||          }d}t          ||d           d}d	}d
}d}t           j                            ||||          }d}t          ||d           d S )Nr      cA    .A     j@gor   rV  r   @  X  r  g_7	j$r>  )r8   r  r|  r   rr   r[   r  rt  r  resultrW   s          r2   r  zTestHypergeom.test_logsf  s     &&q!Q22FHa8888&&q!Q22 FHb999999r4   c                 D   d}d}d}d}t           j                            ||||          }d}t          ||d           d}d	}d
}d}t           j                            ||||          }d}t          ||d           d}d	}d}d}t           j                            ||||          }d}t          ||d           t	          j        g d          }d	}d
}d}t           j                            ||||          }t	          j        dd          }t          ||d           d S )Nr   r  r  r  g)\Ur   rV  r  r  r<  r  g*@Vr>  }      r~  gר)r  r  r  )r8   r  r  r   ri   r   fullr  s          r2   r  zTestHypergeom.test_logcdf  sM    ''1a33FHa8888 ''1a33&FHb9999''1a33 FHb9999
 H\\\""''1a3371122FHb999999r4   c                     d}d}d}t           j                            |||          }||z  |z  }t          ||           d S )Nip iP i.  )r8   r  r   r   )rr   r  rt  r  hmrms         r2   test_mean_gh18511zTestHypergeom.test_mean_gh18511?  sO     _!!!Q**UQYBr4   c                    d}d}t          j        dd          }d|z  }t          j                            |dz
  |||          }t          j        |dk              sJ t          j        t          j        |          dk               sJ d S )Nr_   r   r   r>        $@r   r   )ri   r  r8   r  r   r   diff)rr   rt  r  r  population_sizeru  s         r2   test_sf_gh18506zTestHypergeom.test_sf_gh18506J  s     Iaq&Oq1uoq!<<va!e}}vbgajj1n%%%%%%%r4   N)r   r   r   r6  rI  r  r  r  r  rp  r  r  r  r   r   r   r  r:   r4   r2   r  r    s          	9 	9 	9> > >F F FL L L< < <&
 
 
: : :0,: ,: ,:\	  	  	  [	& 	& 	& 	& 	&r4   r  c                   J   e Zd Zej                            dg d          d             Zej                            dg d          d             Zd Zd Z	ej                            d	d
dg          d             Z
ej                            dg d          d             ZdS )TestLoggammaz	x, c, cdf))r   rf   g;Y%?)r      gRٲa6_<)gHrd  gi|e?)rd  g6l?)i+r\   g֬CCf9)ir   g ֺlc                     t           j                            ||          }t          ||d           t           j                            ||          }t          ||d           d S r   )r8   loggammarp   r   r   )rr   r^   r  rp   ru  ys         r2   r  zTestLoggamma.test_cdf_ppf^  sb     Nq!$$3U++++NsA&&15))))))r4   zx, c, sf))r   r  gQOu3;)   r`   g\Z{0)r  rd  geɐ?)ig{Gzd?gr0T?c                     t           j                            ||          }t          ||d           t           j                            ||          }t          ||d           d S r   )r8   r  r   r   r  )rr   r^   r  r   rN   r  s         r2   r  zTestLoggamma.test_sf_isfp  sb     Na##2E****Nr1%%15))))))r4   c                 j    t           j                            dd          }t          |dd           d S )Nrf   g     @r  r   )r8   r  r   r   )rr   lps     r2   r{  zTestLoggamma.test_logpdf{  s6    
 ^""4++G%000000r4   c                     t          j        g d                              dd          }|D ]?\  }}}}}t          j                            |d          }t          |||||gd           @d S )N)r{   g"~jg46<@g oŏ      @rS  g	h"lxgQ?gZd;333333@g      (@g{/L@g??gгYҿgh|?5?r   r   msvkr]  r   rV  )ri   r   reshaper8   r  r   )rr   tabler  r   varskewkurtcomputeds           r2   ra  zTestLoggamma.test_stats  s          
 wr1~~ 	 ). 	1 	1$AtS$~++Av+>>H%hsD$0G./1 1 1 1 1	1 	1r4   r  r\   rd  c                    t           j                            |d          }t          j        |                                          sJ t           j                            |          }t          j        t          j        ||k               t          |                    }|
                    d          }|j        dcxk     r|j        k     sn J d S )Nr   r:  r  )confidence_levelr{   )r8   r  r   ri   isfiniter   median	binomtestcount_nonzeror  proportion_cir/  r0  )rr   r  r^   medbtestcis         r2   rI  zTestLoggamma.test_rvs  s     Nqv.. {1~~!!##### n##A&& 0S 9 93q66BB  % 88v%%%%bg%%%%%%%%r4   r  ))r  g3H໱k3@)r   r|  )r  g8,[H^}	)r  g90$)r  gtum\c                 d    t          t          j                            |          |d           d S r  )r   r8   r  rG   r  s      r2   rp  zTestLoggamma.test_entropy  s/     	..q113UCCCCCCr4   N)r   r   r   r   r   r   r  r  r{  ra  rI  rp  r:   r4   r2   r  r  W  s:        [[E E EF F* *F F* [ZB B BC C
* *C C
*1 1 11 1 1 [S3,//& & 0/& [X< < <= =	D 	D= =	D 	D 	Dr4   r  c                   ^    e Zd Zg dZej                            de          d             ZdS )TestJohnsonsu))r  r   r   g?r  )r   r   r   gH';vIh%,=)r   r   r   g?x7r  rX  c                     |\  }}}}}t          t          j                            |||          |d           t          t          j                            |||          ||           d S Nr  r   )r   r8   	johnsonsur   r  rr   rX  r^   r0   r1   r   tols          r2   r  zTestJohnsonsu.test_sf_isf  j    1aS**1a33ReDDDD++B155qsCCCCCCr4   Nr   r   r   casesr   r   r   r  r:   r4   r2   r  r    sX        ; ; ;E [VU++D D ,+D D Dr4   r  c                   ^    e Zd Zg dZej                            de          d             ZdS )TestJohnsonb))r  r   r   g?Hz>)r!  r   r   g0jA:r  )g!?r   r   gQbF5r  rX  c                     |\  }}}}}t          t          j                            |||          |d           t          t          j                            |||          ||           d S )Nr  r   r   )r   r8   r$  r   r  r  s          r2   r  zTestJohnsonb.test_sf_isf  r  r4   Nr  r:   r4   r2   r  r    sX        = = =E [VU++D D ,+D D Dr4   r  c                       e Zd Zd Zd Zd Zd Zd Zej	        
                    dddg          d	             Zd
 Zej	        
                    dddg          d             Zd ZdS )TestLogisticc                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S Nr  r
  )ri   rX  r8   logisticrp   r   r   rr   r^   r  r  s       r2   r  zTestLogistic.test_cdf_ppf  sS    KR  Nq!!^""2r4   c                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S r  )ri   rX  r8   r  r   r  r   r  s       r2   r  zTestLogistic.test_sf_isf  sS    KR  Na  ^""2r4   c                     d}d}t          t          j                            d|z
            |           t          t          j                            |          |           d S )Ng      <gg|EA@r   )r   r8   r  r   r  )rr   ru  desireds      r2   test_extreme_valuesz TestLogistic.test_extreme_values  sV    !#**1q5117;;;**1--w77777r4   c                 t    t           j                            g d          }g d}t          ||d           d S )N)r  r   r_   )gm\  .g9B.gO& $r   r   )r8   r  r   r   )rr   rz  rW   s      r2   test_logpdf_basiczTestLogistic.test_logpdf_basic  sI    ~$$\\\22) ) ) 	hU333333r4   c                 l    t           j                            ddg          }t          |ddg           d S )Nrz   r  )r8   r  r   r   rr   rz  s     r2   test_logpdf_extreme_valuesz'TestLogistic.test_logpdf_extreme_values  s7    ~$$c4[11 	TD$<(((((r4   zloc_rvs,scale_rvs)g9x&?gi '?)gB"?gs^&?c                    t           j                            d||          }d }t          |t           j                            |          |f          j        }t           j                            |          }t          ||d           d S )Nr`   r   rd   re   c                    | \  }}t          |          }t          j        t          j        ||z
  |z            dt          j        ||z
  |z            z   z            |dz  z
  }t          j        ||z
  |z  t          j        ||z
  |z            dz
  t          j        ||z
  |z            dz   z  z            |z
  }||fS Nr   rf   )r  ri   rl  r   )inputr   r0   r1   rt  x1x2s          r2   r   z#TestLogistic.test_fit.<locals>.func  s    DAqD		AqA~..RVTAXN3335 6 689A>B$(a&$(a0014&$(a001467 8 8:;<B r6Mr4   r  gKH9r   )r8   r  r   r$   	_fitstartr^   r   r   )rr   loc_rvs	scale_rvsr   r   expected_solution
fit_methods          r2   test_fitzTestLogistic.test_fit  s     ~!!sy!II	 	 	 !u~'?'?'E'EM    	^''--
 	
$5EBBBBBBr4   c                     t           j                            ddd          }t          t           j        |           t          t           j        |d           t          t           j        |d           d S )Nr`   r{   rf   r  r   r   r   )r8   r  r   r   rr   r   s     r2   test_fit_comp_optimizerz$TestLogistic.test_fit_comp_optimizer  sd    ~!!s1!==%end;;;%endCCCC%end1EEEEEEr4   
testlogcdfTFc                     t          j        g d          }|r t          j                            |          }n t          j                            |           }g d}t          ||d           d S )N)r5  r     r<  r~  )     g      g%h9fg?~T}%mgCx^&ْV瞯<r   )ri   r   r8   r  r  r|  r   )rr   r  r^   r  rW   s        r2   test_logcdfsf_tailsz TestLogistic.test_logcdfsf_tails  s     H00011 	)%%a((AA$$aR((AF F F8%000000r4   c                     t          j        g ddgdz  z   dgdz  z             }t          t          j        |           d S )N)	i5%   +   rh  rh  0   6   7   :   ;   r   =   rp  )ri   r   r   r8   r  r  s     r2   test_fit_gh_18176zTestLogistic.test_fit_gh_18176-  sT     x>>>$(#&(TAX. / / 	&end;;;;;r4   N)r   r   r   r  r  r  r  r   r   r   r   r  r  r  r!  r:   r4   r2   r  r    s            8 8 84 4 4) ) ) [03J3K3M N NC CN NC,F F F [\D%=991 1 :91< < < < <r4   r  c                   &    e Zd Zd Zd Zd Zd ZdS )
TestLogserc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestLogser.setup_method7  r7  r4   c                    t           j                            dd          }t          j        |dk              sJ t          j        |          dk    sJ |j        j        t          d         v sJ t           j                            d          }t          |t                    sJ t          j        d                              d          }t          |t          j                  sJ |j        j        t          d         v sJ d S )Nr   r;  r:  r   r=  r   )r8   logserr   ri   r   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestLogser.test_rvs:  s    |733vdai     x~~((((z)L"99999lt$$#s#####l4  $$Q''#rz*****y~<!8888888r4   c                 f    t           j                            dd          }t          |d           d S )Nr   r  g&Y3)r8   r&  rO  r   rr   r_  s     r2   test_pmf_small_pzTestLogser.test_pmf_small_pE  s1    LQ&& 	7#####r4   c                 d    t           j                            d          }t          |d           d S )Nr  gW  ?)r8   r&  r   r   r(  s     r2   test_mean_small_pzTestLogser.test_mean_small_pS  s/    Ld## 	;'''''r4   N)r   r   r   r6  rI  r)  r+  r:   r4   r2   r#  r#  6  sP          	9 	9 	9$ $ $( ( ( ( (r4   r#  c            	          e Zd Z ej        d          d             Zej                            dej	        ej
        g          ej                            dg d          ej                            dg d          ej                            d	d
dgdd
gf          d                                                 Zej                            dej	        dfej
        dfg          d             ZdS )TestGumbel_r_lfunctionscopec                 @    t           j                            d          S r4  ri   r   r   rw   s    r2   r   zTestGumbel_r_l.rng_      y$$T***r4   rA   r	  r   r   r   r
  r\   r   r   zfix_loc, fix_scaleTFc                     |                     d|||          }t                      }|r|dz  |d<   |r|dz  |d<   t          ||fi | d S )Nr`   r   rd   re   r   rf   r   r   )r   r  r   )	rr   rA   r	  r
  r   r  r   r   r   s	            r2   r  z&TestGumbel_r_l.test_fit_comp_optimizerc  s|     xxSgY%(  * * vv  	'"Q;DL 	+&]DN 	&dD99D99999r4   z	dist, sgnr   r   c                     |t          j        g d          z  }|                    |          \  }}t          ||dz             t          |dd           d S )N)r   r   r   r   r   r   r   gW  @g   @g3qtw>r  r   )ri   r   r   r   )rr   rA   sgnzrd   re   s         r2   r  zTestGumbel_r_l.test_fitx  sf     :::;;;XXa[[
U 	S!334445DAAAAAAr4   N)r   r   r   r   fixturer   r   r   r8   gumbel_rgumbel_lr  r  r:   r4   r2   r-  r-  ^  s=       V^*%%%+ + &%+ [Venen%EFF[Y


33[[***55[1#UmeT];= =: := = 65 43 GF
:  [[ENA+>,1NB+?+A B BB BB BB B Br4   r-  c                      e Zd Zd Zd Z ej        d          d             Zej        	                    d          ej        
                    ddd	g          ej        
                    d
dd	g          ej        
                    dddg          d                                                 Zej        
                    ddd	g          ej        
                    d
dd	g          ej        
                    dddg          ej        
                    dd  eddgd          D                        ej        d          d                                                             Z ej        d          d             Zd Zd ZdS )
TestParetoc                 	   t          j                    5  t          j        dt                     t          j                            dd          \  }}}}t          |t          j                   t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |t          j                   t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |t          j                   t          |t          j	                   t          |t          j	                   t          j                            d	d          \  }}}}t          |d
           t          |d           t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |t          j	                   t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |dt          j        d          z             t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |dt          j        d          z             t          |t          j	                   t          j                            dd          \  }}}}t          |d           t          |d           t          |dt          j        d          z             t          |d           d d d            d S # 1 swxY w Y   d S )Nrr  r{   r\  r]  rS  r  r[  r   r  g?grq@r         @gffffff?gK~?g      2@g۶m۶m?r  UUUUUU?gqq?r        @g%I$I?gQ?gUUUUUU@grq?g88Nb@)rv  rw  rx  ry  r8   paretor   ri   r  r  r   r%  rr   r_  r`  rN   r[   s        r2   ra  zTestPareto.test_stats  sk    $&& 7	N 7	N!'>:::++C+@@JAq!QBF###BF###BF###BF###++C+@@JAq!QBF###BF###BF###BF###++C+@@JAq!QC   BF###BF###BF###++C+@@JAq!QC   BF###BF###BF###++C+@@JAq!QAy)))A2333BF###BF###++C+@@JAq!QAs###At$$$BF###BF###++C+@@JAq!QAy)))A2333A	277+;+;;<<<BF###++C+@@JAq!QAy)))Az***A027;3G3GGHHHBF###++C+@@JAq!QAy)))A2333A	RWW-=-==>>>ALMMMo7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	N 7	Ns   R8SS Sc                     d}d}d}t           j                            ||d|          }||z  |z  }t          ||           d S )Ng    eArf   r  r   rc   )r8   rD  r   r   )rr   r^   r1   re   ru  rW   s         r2   r  zTestPareto.test_sf  sO    LOOAqauO55!Ga<8$$$$$r4   r.  r/  c                 @    t           j                            d          S r4  r2  rw   s    r2   r   zTestPareto.rng  r3  r4   z2ignore:invalid value encountered in double_scalarsr   r   rf   r   r   r  r   c                 ,   t           j                            d||||          }t           j                            |dd          d         }t           j                            |dd          d         }t           j                            |dd          d         }||cxk    r|cxk    rdk    sn J t           j                            d|||dz   |          }t           j                            |d	          \  }	}
}t	          |dz   |                                           |dz
  }|j        d         }t	          |	|t          j        t          j	        ||                                z                      z             t	          |
d           d S )
Nr`   r   r1   re   rd   r   r   p=
ף?)r   r   )r   fix_b)r   fbrf   r   )
r8   rD  r   r   r   r-  rA  ri   rl  r  )rr   r   r   r  r   r   shape_mle_analytical1shape_mle_analytical2shape_mle_analytical3shape_mle_a	loc_mle_ascale_mle_a
data_shiftndatas                 r2   r  zTestPareto.test_fit  s    |SIY$+#   ? ? !& 0 0A$ 0 G G J % 0 0AT 0 J J1 M % 0 0A$ 0 G G J%)> . . . .%. . . .)-. . . . . . |SIY%,q[   E E.3l.>.>t!.>.L.L+Y[1_dhhjj111AX
 #[RVBF:jnn6F6F+F$G$GHHH	J 	J 	JY"""""r4   r\   fix_shape, fix_loc, fix_scalec                     g | ]}d |v |	S Fr:   r@   ru  s     r2   rB   zTestPareto.<listcomp>  (     - - -A!&!  !+r4   TFr   repeatignoreinvalidc                     t           j                            d||||          }i }	|r||	d<   |r||	d<   |r||	d<   t          t           j        |fi |	 d S )Nr`   rI  r   r   r   )r8   rD  r   r   
rr   r   r   r  r   r   r  r   r   r   s
             r2   r   z&TestPareto.test_fit_MLE_comp_optimizer  s     |SIY$+#   ? ?  	#"DJ 	#"DL 	'&DN%elDAADAAAAAr4   c           	          d\  }}}t           j                            |||dt          j                            d                    }t          t           j        |           d S )N)r   r   r   r`   ið& r   )r8   rD  r   ri   r   r   r   )rr   rA  locationre   r   s        r2   test_fit_known_bad_seedz"TestPareto.test_fit_known_bad_seed  sa    
 ")x|xS-/Y-B-B7-K-K   M M%elD99999r4   c                     t          t          j                   t          t          t          j        j        g dd           t          t          t          j        j        g ddd           d S )Nr
  rf   r   )r   rf   r   r   r   r  )r  r8   rD  r  r"   r   rw   s    r2   test_fit_warningszTestPareto.test_fit_warnings	  sg    EL)))lEL$4iiiaHHHHlEL$4iiia	  	  	  	  	  	 r4   c                     t           j                            ddd|          }t          |d           t           j                            |          }d S )Ni~r   r`   )rd   r1   r   r   r   )r8   rD  r   r   r   )rr   r   r   r   s       r2   test_negative_datazTestPareto.test_negative_data	  sK    |DACcJJ$"""
 LT""r4   N)r   r   r   ra  r  r   r;  r   r   filterwarningsr   r  r'   ri   errstater   rc  re  rg  r:   r4   r2   r?  r?    s%       :N :N :Nx% % % V^*%%%+ + &%+ [ !1 2 2[[1a&11[YA//[[1a&11# # 21 0/ 212 2
#. [[2q'22[YA//[[1a&11[<- -$q)I)I)I - - -. . R["""B B #". . 21 0/ 32B R[""": : #":     # # # # #r4   r?  c                      e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zej                            d
dg dfdddd ej        d          z  ej        gfdddd ej        d          z  dgfdg dfg          d             Zd ZdS )TestGenparetoc                 r   dD ]i}t          j        |          }t          j                            |          \  }}t          |d           t          t          j        |                     jt          j        d          }t          j                            |          \  }}t          ||gddg           d S )NrS  r   r          r{   )	ri   r   r8   	genpareto_get_supportr   r	   isposinfr   )rr   r  r0   r1   s       r2   test_abzTestGenpareto.test_ab	  s     	$ 	$A
1A?//22DAqBBKNN#### JsOO++A..1AS	*****r4   c                    t          j        d          }t          j        ddd          }t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t          j        ddd          }t	          |	                    |          t           j        	                    |                     d S )Nr   r  r   r  r9  rS  r_   )
r8   ro  ri   rX  r   rh   r  rp   r   r   rr   rvr^   r~  s       r2   test_c0zTestGenpareto.test_c0(	  s     _r"""K3##q		5;??1#5#5666q		5;??1#5#5666a%+.."3"3444KB##q		5;??1#5#566666r4   c                    t          j        d          }t          j        ddd          }t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t	          |                    |          t           j                            |                     t          j        ddd          }t	          |	                    |          t           j        	                    |                     t	          |
                    d	          d           d S )
Nr"  rt  r   r  r9  r   rS  r_   r   )r8   ro  ri   rX  r   rh   uniformrp   r   r   r   ru  s       r2   test_cm1zTestGenpareto.test_cm14	  s   _s###K3##q		5=#4#4Q#7#7888q		5=#4#4Q#7#7888a%-"2"21"5"5666KB##q		5=#4#4Q#7#7888 			!a(((((r4   c                    t          j        d          }t          |                    t          j                  |                    t          j                  gddg           t          t	          j        |	                    t          j                                       t          j        d          }t          |                    t          j                  |                    t          j                  gddg           t          t	          j        |	                    t          j                                       t          j        d          }t          |                    t          j                  |                    t          j                  gddg           t          t	          j        |	                    t          j                                       d S )Nr\   rt  r   rS  r"  )
r8   ro  r   rh   ri   r  rp   r	   isneginfr   rr   rv  s     r2   
test_x_infzTestGenpareto.test_x_infB	  sC   _s###82r(CCCBIIbf--..///_r"""82r(CCCBIIbf--..///_s###82r(CCCBIIbf--../////r4   c                    t          j        ddd          }dD ]}t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8d S )	Nr   r_   r9  r   r   r  g+r  r   )r  r  )ri   rX  r8   ro  rh   r   rp   )rr   r^   r  pdf0dcpdfccdf0cdfcs           r2   test_c_continuityzTestGenpareto.test_c_continuityP	  s    K2r"" 		8 		8A?&&q!,,D% 8 8**1a"f55d77777?&&q!,,D$ 8 8**1a"f55d777778		8 		8r4   c           	      t   t           j        t          j        ddd          t          j        dddd          d	t          j        ddd          z
  f         }d
D ]\}t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8]d S Nr  r}   r\   baser   r9  FendpointrS  )r   r"  r  r   )ri   rM  r  rX  r8   ro  r   r   )rr   r~  r  ppf0r  ppfcs         r2   test_c_continuity_ppfz#TestGenpareto.test_c_continuity_ppf^	      E"+eT444+dArE:::r{5$S9999: ;  	8 	8A?&&q!,,D% 8 8**1a"f55d777778	8 	8r4   c           	      t   t           j        t          j        ddd          t          j        dddd          d	t          j        ddd          z
  f         }d
D ]\}t          j                            ||          }dD ]7}t          j                            |||z             }t          ||d           8]d S r  )ri   rM  r  rX  r8   ro  r  r   )rr   r~  r  isf0r  isfcs         r2   test_c_continuity_isfz#TestGenpareto.test_c_continuity_isfh	  r  r4   c           	      \   t           j        t          j        ddd          t          j        dddd          d	t          j        ddd          z
  f         }d
D ]P}t	          t
          j                            t
          j                            ||          |          |d           Qd S )Nr  r}   r\   r  r   r9  Fr  rS  )r  gC]r2r   gV瞯Ҽr   r   )	ri   rM  r  rX  r   r8   ro  rp   r   )rr   r~  r  s      r2   test_cdf_ppf_roundtripz$TestGenpareto.test_cdf_ppf_roundtripr	  s    E"+eT444+dArE:::r{5$S9999: ; / 	+ 	+AEO//0C0CAq0I0I1MME+ + + + +	+ 	+r4   c                 j    t           j                            dddd          }t          |d           d S )Nr  r}   r   r   gpEȜ)r8   ro  r|  r   r  s     r2   r  zTestGenpareto.test_logsf{	  s4    $$T3155122222r4   zc, expected_statsr   )r   r   rf   r  rk  rB  gqq@r_   rf   gqq?g      ?g$I$	?rq?r#  gll0@r   )r{   UUUUUU?r   333333c                 n    t           j                             |d          }t          ||dd           d S )Nr\  r]  r   r   re  )r8   ro  r   )rr   r  expected_statsr  s       r2   ra  zTestGenpareto.test_stats	  s;     &&q&&99UGGGGGGr4   c                 h    t           j                            d          }t          |dd           d S )Nr  gvǼ
  ?r   r   )r8   ro  r  r   )rr   r`  s     r2   test_varzTestGenpareto.test_var	  s3    O%%,5999999r4   N)r   r   r   rr  rw  rz  r~  r  r  r  r  r  r   r   r   ri   r%  r  ra  r  r:   r4   r2   rk  rk  	  sA       + + +
7 
7 
7) ) )0 0 08 8 88 8 88 8 8+ + +3 3 3 [
\\\	
T2gbgajj="&1	2
]T7271::$5v>	?
"""	#	%& &H H& &H: : : : :r4   rk  c                   >    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	S )
TestPearson3c                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestPearson3.setup_method	  r7  r4   c                    t           j                            dd          }t          j        |          dk    sJ |j        j        t          d         v sJ t           j                            d          }t          |t                    sJ t          j        d                              d          }t          |t          j
                  sJ |j        j        t          d         v sJ t          |          dk    sJ d S )Nr\   r;  r:  AllFloatr{   r   )r8   r+   r   ri   rA  r   rB  r   rC  r   rc  r  rF  s      r2   rI  zTestPearson3.test_rvs	  s    ~!!#G!44x~~((((z)J"77777n  %%#u%%%%%nS!!%%a((#rz*****y~:!666663xx1}}}}}}r4   c                    t           j                            dg d          }t          |t	          j        g d          d           t           j                            dd          }t          |t	          j        dg          d           t           j                            g d	d          }t          |t	          j        g d
          d           d S )Nrf   r   r\   r  )gtT?g+q?g?r  r   r8  r\   ND}i?r8  r   r   r   r   )r  gj?gdC?gs?g'M?)r8   r+   rh   r   ri   r   rr  s     r2   rQ  zTestPearson3.test_pdf	  s    ~!!!___55bh'K'K'KLL!	# 	# 	# 	#~!!"c**bh
|444@@@@~!!"4"4"4c::bh (@ (@ (@ A AGK	M 	M 	M 	M 	M 	Mr4   c                 h   t           j                            dg d          }t          |t	          j        g d          d           t           j                            dd          }t          |dgd           t           j                            g d	d          }t          |g d
d           d S )Nrf   r  )grE?gTp]0?g~?r  r   r8  r\   g E&"J?r  )giZ*J?gh+8w?gcK?g|<x6?gG?)r8   r+   rp   r   ri   r   rr  s     r2   r[  zTestPearson3.test_cdf	  s    ~!!!___55bh'K'K'KLL!	# 	# 	# 	#~!!"c**zl6666~!!"4"4"4c:: ? ? ?EI	K 	K 	K 	K 	K 	Kr4   c                     g d}ddt           j                            |          }fd|D             }t          ||           d S )Nr8  r   r   r{   r{   rT  c                 l    g | ]0}t          t          j        |          j                  d          1S r>   )r   r8   r+   rh   )r@   r  neg_infx_evals     r2   rB   z<TestPearson3.test_negative_cdf_bug_11186.<locals>.<listcomp>	  sG     ' ' ' --17FCCAF ' ' 'r4   )r8   r+   rp   r   )rr   skewsr@  int_pdfsr  r  s       @@r2   test_negative_cdf_bug_11186z(TestPearson3.test_negative_cdf_bug_11186	  su     !  ~!!&%00' ' ' ' ' %' ' 'h'''''r4   c                 6   t           j                            dd          }t          |d           t	          |t
          j                  sJ t           j                            dd          }t          |d           t	          |t
          j                  sJ d S )Nr   rf   r   r  )r8   r+   r  r   rC  ri   number)rr   r  s     r2   test_return_array_bug_11746z(TestPearson3.test_return_array_bug_11746	  s     &&q!,,VQ&"),,,,,&&q(33VQ&"),,,,,,,r4   c                    g d}d}t           j                            t           j                            ||          |          }t	          ||           t          j        dgdgg          }t          j        dd          }t	          t           j                            ||          t           j                            | |                      t	          t           j                            ||          t           j        	                    | |                      t	          t           j                            ||          t           j        
                    ||                       d S )Nr  r{   r   r  r   rf   )r8   r+   r   rp   r   ri   r   rX  rh   r   r  )rr   r  r  r   r  r^   s         r2   test_ppf_bug_17050zTestPearson3.test_ppf_bug_17050	  s?    !  n  !3!3FE!B!BEJJV$$$ x$#((KA**1d33**A2u55	7 	7 	7**1d33))1"te44	6 	6 	6**1d33++Au555	7 	7 	7 	7 	7r4   c                    g d}g d}g d}t          t          j                            ||          |d           t          t          j                            |d          t          j                            |          d           d S )N)r\   r{   rS  皙)rT  r  g      I@       @)g7>g~׼=gp'+7g;r  r   r   )r   r8   r+   r   r  )rr   r  r^   r  s       r2   r  zTestPearson3.test_sf	  s     %$$"""> > >))!T22CeDDDD))!Q//q1A1ANNNNNNr4   N)r   r   r   r6  rI  rQ  r[  r  r  r  r  r:   r4   r2   r  r  	  s          	 	 	M M MK K K	( 	( 	(	- 	- 	-7 7 7&	O 	O 	O 	O 	Or4   r  c                   8    e Zd Zd Zd Zd Zd Zd Zd Zd Z	dS )	
TestKappa4c                     g d}d}dD ]T}t           j                            |||          }t           j                            ||           }t	          ||           Ud S )N)r   r\   r  r{   rS  )
gffffffr"  r   皙ɿr  r\   r  r{   rS  ffffff?)r8   kappa4rp   ro  r   rr   r^   ro  r[   rG  	vals_comps         r2   test_cdf_genparetozTestKappa4.test_cdf_genpareto	  sr        	- 	-A<##Aq!,,D++Ar22ID),,,,	- 	-r4   c                    t          j        ddd          }d}t          j        ddd          }t          j                            |||          }t          j                            ||          }t          ||           d S )NrC  r   r_   r   r8  r   )ri   rX  r8   r  rp   
genextremer   r  s         r2   test_cdf_genextremezTestKappa4.test_cdf_genextreme	  st    KAr""KAr""|1a(($((A..	i(((((r4   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )Nr   r_   rS  r   )ri   rX  r8   r  rp   r  r   r  s         r2   test_cdf_exponzTestKappa4.test_cdf_expon	  sa    K2r""|1a((KOOA&&	i(((((r4   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )NrC  r   r_   r   )ri   rX  r8   r  rp   r<  r   r  s         r2   test_cdf_gumbel_rzTestKappa4.test_cdf_gumbel_r
  sc    KAr""|1a((N&&q))	i(((((r4   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )NrC  r   r_   r"  r   )ri   rX  r8   r  rp   r  r   r  s         r2   test_cdf_logisticzTestKappa4.test_cdf_logistic
  sc    KAr""|1a((N&&q))	i(((((r4   c                     t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           d S )NrC  r   r_   rS  )ri   rX  r8   r  rp   ry  r   r  s         r2   test_cdf_uniformzTestKappa4.test_cdf_uniform
  sc    KAr""|1a((M%%a((	i(((((r4   c                 0    t          j        dd           d S r  )r8   r  rw   s    r2   test_integers_ctorzTestKappa4.test_integers_ctor"
  s     	Qr4   N)
r   r   r   r  r  r  r  r  r  r  r:   r4   r2   r  r  	  s}        	- 	- 	-) ) )) ) )) ) )) ) )) ) )    r4   r  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestPoissonc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestPoisson.setup_method)
  r7  r4   c                     t          j        d          }t          j                            g d|          }d|dz  |dz  dz  g}t          ||           d S )Nrf   r   r   rf   r{   r   )ri   r  r8   r  rO  r   )rr   ln2rG  rW   s       r2   test_pmf_basiczTestPoisson.test_pmf_basic,
  sX    fQii}  C00QQq)h'''''r4   c                     t           j                            g dd          }g d}t          ||           t           j                            dd          }t          |d           d S )Nr  r   )r   r   r   ffffff?r   r   )r8   r  rO  r   intervalr   )rr   rG  rW   r  s       r2   test_mu0zTestPoisson.test_mu03
  sc    }  A..994***=))$22Xv&&&&&r4   c                    t           j                            dd          }t          j        |dk              sJ t          j        |          dk    sJ |j        j        t          d         v sJ t           j                            d          }t          |t                    sJ t          j        d                              d          }t          |t          j                  sJ |j        j        t          d         v sJ d S )Nr{   r;  r:  r   r=  r   )r8   r  r   ri   r   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestPoisson.test_rvs<
  s    }  7 33vdai     x~~((((z)L"99999m$$#s#####mC  $$Q''#rz*****y~<!8888888r4   c           	         d}t           j                             |d          }t          |||t          j        d|z            d|z  g           t          j        g d          }t           j                             |d          }||t          j        ddt          j        d          z  gt          j        ddgf}t          ||           d S )	Ng      0@r\  r]  rS  )r   rS  r   r   rf   r{   )r8   r  r   ri   r%  r   r  )rr   r  r  rW   s       r2   ra  zTestPoisson.test_statsG
  s    $$R$88RR#b& ABBBXooo&&$$R$88RVQ"'!**537GH)))))r4   N)r   r   r   r6  r  r  rI  ra  r:   r4   r2   r  r  (
  s_          ( ( (' ' '	9 	9 	9* * * * *r4   r  c                   V    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd ZdS )	TestKSTwoc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestKSTwo.setup_methodS
  r7  r4   c                    dD ]}t          j        dd|z  d|z  ddd|z  z
  dg          }d|z  |z  }t          j                            |dz             }|dk    rt          j        |          nd}t          j        dd||z  ddt          j                            d|          z  z
  t          dd|z  z
  d          dg          }t          j
                            ||          }t          ||           d S )Nr   rf   r   r_   r`   r   r   r{   r   rS  rf   r   )ri   r   r7   r   gammalnr   r8   ksoner   ro  kstworp   r   )rr   rt  r^   v1lgelgrW   rI  s           r2   r[  zTestKSTwo.test_cdfV
  s   ) 	0 	0A !SUAaCaAgq9::Aa%!B&&qs++B!#q26":::aCxArCx!"Qu{~~c1'='=%=!=!$Q2Xs!3!3!$!& ' 'H {q!,,HHh////#	0 	0r4   c                    t          j        ddd          }dD ]}t          j        dd|z  d|z  ddd|z  z
  dg          }d|z  |z  }t          j                            |dz             }|dk    rt          j        |          nd}t          j        ddd||z  z
  dt          j        	                    d|          z  t          d|z  d          dg          }t          j        	                    ||          }t          ||           d S )Nr   r   r+  r  r{   rS  rf   )ri   rX  r   r7   r   r  r   r8   r  r   r-  r  r   )rr   r^   rt  r  r  r  rW   ry  s           r2   r  zTestKSTwo.test_sfj
  s   K1b!!) 	/ 	/A!SUAaCaAgq9::Aa%!B&&qs++B!#q26":::aCxc!"R#X!"5;>>#q#9#9!9!$QrT3!4 5 5H knnQ**GGX....	/ 	/r4   c                 
   t          j        ddd          dd          }g d}|D ]]}|t          j        |          z  }t          j                            ||          }t          j        |          }t          |d           ^d S )Nr   rf   r+  r   )r<  r`   r  i  r   r   r  )ri   rX  r%  r8   r  rp   r  r   )rr   r^   ns_xxnprobsdiffss          r2   test_cdf_sqrtnzTestKSTwo.test_cdf_sqrtny
  s    
 K1b!!!""%,,, 	+ 	+Bbgbkk!BKOOB++EGENNEeT****		+ 	+r4   c                     t          j        ddd          }dD ]U}t          j                            ||          }t          j                            ||          }t          |d|z
             Vd S Nr   r   r+  r  )ri   rX  r8   r  rp   r   r   )rr   r^   rt  rI  ry  s        r2   rz  zTestKSTwo.test_cdf_sf
  so    K1b!!) 	= 	=A{q!,,HknnQ**G%hG<<<<	= 	=r4   c                    t          j        ddd          }dD ]l}|t          j        |          z  }t          j                            ||          }t          j                            ||          }t          |d|z
             md S r  )ri   rX  r%  r8   r  rp   r   r   )rr   r^   rt  r  rI  ry  s         r2   test_cdf_sf_sqrtnzTestKSTwo.test_cdf_sf_sqrtn
  s    K1b!!) 	= 	=ARWQZZB{r1--HknnR++G%hG<<<<		= 	=r4   c                 0   t          j        ddd          }dD ]|}||d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||         d           }d S )	Nr   r   r+  r  r{   r!  r  r   )ri   rX  r8   r  rp   r   r   rr   r^   rt  r  rI  condrG  s          r2   test_ppf_of_cdfzTestKSTwo.test_ppf_of_cdf
  s    K1b!!) 	= 	=A1s1u9B{r1--HLX_5D;??8Q//DDJ4t<<<<<	= 	=r4   c                 0   t          j        ddd          }dD ]|}||d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||         d           }d S )	Nr   r   r+  r  r{   rS  r  r   )ri   rX  r8   r  r  r   r   )rr   r^   rt  r  vals_isfr  rG  s          r2   test_isf_of_sfzTestKSTwo.test_isf_of_sf
  s    K1b!!) 	= 	=A1s1u9B{r1--HLX^4D;>>(A..DDJ4t<<<<<	= 	=r4   c                 V   t          j        ddd          }dD ]}|t          j        |          z  |d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||                    d S )Nr   r   r+  r  r{   rS  )ri   rX  r%  r8   r  rp   r   r   r  s          r2   test_ppf_of_cdf_sqrtnzTestKSTwo.test_ppf_of_cdf_sqrtn
  s    K1b!!) 	2 	2Abgajj.!c!e),B{r1--HLX^4D;??8Q//DDJ41111	2 	2r4   c                 V   t          j        ddd          }dD ]}|t          j        |          z  |d|z  k             }t          j                            ||          }d|k     |dk     z  }t          j                            ||          }t          ||         ||                    d S )Nr   r   r+  r  r{   r  )ri   rX  r%  r8   r  r   r  r   )rr   r^   rt  r  ry  r  rG  s          r2   test_isf_of_sf_sqrtnzTestKSTwo.test_isf_of_sf_sqrtn
  s    K1b!!) 	2 	2Abgajj.!c!e),BknnR++GKGdN3D;??7A..DDJ41111	2 	2r4   c                     t          j        ddd          dd          }dD ]R}t          j                            ||          }t          j                            ||          }t          ||           Sd S r  )ri   rX  r8   r  r   rp   r   )rr   r  rt  r  rI  s        r2   re  zTestKSTwo.test_ppf
  st    Aq"%%abb)) 	- 	-A**B{r1--HHe,,,,	- 	-r4   c           	         g d}t          j        g d          }t          j        g dg dg dg dg dg dg          }t          |          D ]y\  }}|t          j        d	          z  t          j        t           j        d	z  |z            z  }t          j                            ||          }t          |||         d
           zd S )N)r_   r<  r`   r  r~  r   )rk  gUUUUUU?r{   r   rf   r   )gRT>gr	?gK5
?gn
"5?gU
?gk?)g&6#>gb
E>gI5?g\?g;?g%1?)g6>gL>g<?g䓀^?gO|6$?g qO?)g}+: >gwQ9>gH{?g]qv(?g)~/v?gmJ?)gV27J=gGk(>gWX?gY?g{0`?gZ
H?)g_R=g4>g̪?gT_@?g<e?g2?rf   r  r   )
ri   r   	enumerater  r%  rj   r8   r  rp   r   )rr   r  ratiosrW   idxrt  r^   rI  s           r2   test_simard_lecuyer_table1z$TestKSTwo.test_simard_lecuyer_table1
  s    +**888998- - -- - -- - -- - -- - -- - -
    mm 	@ 	@FC"RWRU1WQY%7%77A{q!,,HHhsm$?????	@ 	@r4   N)r   r   r   r6  r[  r  r  rz  r  r  r  r  r  re  r  r:   r4   r2   r  r  R
  s          0 0 0(/ / /+ + += = == = == = == = =2 2 22 2 2- - -@ @ @ @ @r4   r  c                        e Zd Zd Zd Zd ZdS )TestZipfc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestZipf.setup_method
  r7  r4   c                    t           j                            dd          }t          j        |dk              sJ t          j        |          dk    sJ |j        j        t          d         v sJ t           j                            d          }t          |t                    sJ t          j        d                              d          }t          |t          j                  sJ |j        j        t          d         v sJ d S )Nr  r;  r:  r   r=  r   )r8   zipfr   ri   r   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestZipf.test_rvs
  s    z~~c~00vdai     x~~((((z)L"99999jnnS!!#s#####joo!!!$$#rz*****y~<!8888888r4   c                 v   t           j                             d          \  }}t          t          j        |                     t          |t          j                   t           j                             dd          \  }}t          t          j        ||g                                                      d S )Nffffff@r0   r  skr0   r^  )r8   r
  r	   ri   r  r   r  r   rE  s        r2   ra  zTestZipf.test_moments
  s    z#&&1AQz#t441BKA''++---.....r4   N)r   r   r   r6  rI  ra  r:   r4   r2   r  r  
  sA          	9 	9 	9/ / / / /r4   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestDLaplacec                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestDLaplace.setup_method
  r7  r4   c                    t           j                            dd          }t          j        |          dk    sJ |j        j        t          d         v sJ t           j                            d          }t          |t                    sJ t          j        d                              d          }t          |t          j
                  sJ |j        j        t          d         v sJ t           j                            d          J d S )Nr  r;  r:  r=  r   r   )r8   dlaplacer   ri   rA  r   rB  r   rC  rb  rc  rF  s      r2   rI  zTestDLaplace.test_rvs  s    ~!!#G!44x~~((((z)L"99999n  %%#s#####nS!!%%a((#rz*****y~<!88888~!!#&&22222r4   c                    d}t          j        |          }|                     d          \  }}}}d}t          j        | |dz             }|                    |          }	t          j        |	|dz  z            t          j        |	|dz  z            }}
t          ||fd           t          ||f|
||
dz  z  dz
  fd	d
           d S )NrS  r\  r  r   rf   r   r  r[  r  r  r  )r8   r  ri   r  rO  rl  r   r   )rr   r0   dlr_  r`  rN   r[   r  r  ppm2m4s               r2   ra  zTestDLaplace.test_stats  s    ^AXXf%%
1aYr1Q3VVBZZ2q5!!26"RU(#3#3BaVV$$$ARAX] 3%dKKKKKKr4   c                     t          j        d          }t          j        |          }|                    d          \  }}}}t	          ||fd           t          ||fd           d S )Nr   r\  )r   r   )r        
@)ri   r  r8   r  r   r   )rr   r0   r  r_  r`  rN   r[   s          r2   test_stats2zTestDLaplace.test_stats2  se    F2JJ^AXXf%%
1aaVX&&&A
+++++r4   N)r   r   r   r6  rI  ra  r  r:   r4   r2   r  r  
  sS          	3 	3 	3L L L, , , , ,r4   r  c                       e Zd Zd Zej                            dddg          d             Zej                            dddg           fd            Zd Z	d	 Z
d
 Zej                            dg d          d             Z xZS )TestInvgaussc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestInvgauss.setup_method"  r7  r4   zrvs_mu,rvs_loc,rvs_scale)rf   r   r   )g
ףp=@g r@gʡE6@c                    t           j                            d|||          }t           j                            ||          \  }}}||z
  }t	          j        |          }t          |          t	          j        |dz  |dz  z
            z  }	||	z  }
t          |
|dd           t          |	|dd           t          ||           t           j                            d|||          }t           j                            ||dz
  |dz             \  }}}t          |dz   |           t          |dz
  |           t           j                            |d	
          d         }t           j                            |d	          d         }t           j                            |d	          d         }||cxk    r|cxk    rd	k    sn J d S )Nr`   )r   r  rd   re   r   r   r   r  r   r  rJ  )fmur   )fix_mur   )
r8   r"  r   r   ri   r   r  rl  r   r   )rr   rvs_mur   r  r   r  rd   re   mu_temp	scale_mlemu_mle
shape_mle1
shape_mle2
shape_mle3s                 r2   r  zTestInvgauss.test_fit%  s    ~!!sv&-Y " @ @ ++Dw+??Cg~'$--IIr
Wr](B!C!CD	" 	U;;;;	5u5AAAAS'"""~!!sv&-Y " @ @ ++Dw{3<q= , B BCY]E***Wq[#&&& ^''$'77:
^''T'::1=
^'''66q9
Z====:============r4   )gX9v>@g	@gGz@c                 \   t           j                            d          }t          j                            d||||          }t          t          t          j                  t          j                  j        } ||          }t          j                            |          }t          ||            ||dd          }t          j                            |dd          }t          ||           t          t          j        ||           t          j        ||dz
  z
  dk              sJ t          t          j        ||dz
             t          t          j        |d           t          t          j        ||t           j                            d          d         	           d S )
Nr   r`   )r   r  rd   re   r   r   rf   )r   r!  r   r   r  )ri   r   RandomStater8   r"  r   r   r   r   r   r   r   rand)
rr   r$  r   r  r   r   	super_fitsuper_fittedinvgauss_fit	__class__s
            r2   r   z(TestInvgauss.test_fit_MLE_comp_optimizerD  s    i##D))~!!sv&-YS " R R $u~..??C	 y~))$//\<000 !yA1555~))$QA)>>\<000 	&endIIII vtw{+q011111%end1MMMM 	&endCCCC 	&end-/Y^^A->->q-A	C 	C 	C 	C 	C 	Cr4   c                     t          t          j                   t          j        t
                    5  t          j                            g dd           d d d            d S # 1 swxY w Y   d S r  )r  r8   r"  r   r   r"   r   rw   s    r2   test_fit_raise_errorsz"TestInvgauss.test_fit_raise_errorsh  s    EN+++]<(( 	2 	2Nyyyq111	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2s   $A$$A(+A(c                    g d}g d}t           j                            d|          }t          ||           t           j                            dd          }t	          |d           t           j                            dd          }t	          |d	           t           j                            d
d          }t	          |d           t           j                            dd          }t	          |d           d S )N)g4wT;?gjdV&}?g{i\0>gDV_h?gqacX?)r   r   r   r   r   皙?r  rd  ?gfFn   gr^:g9̗?r  gx_;:g!?gٷ
??)r8   r"  rp   r   r   r   )rr   r  rW   rS   
cdf_actual	sf_actuals         r2   rz  zTestInvgauss.test_cdf_sfn  s    . . ."??##CB#//Xv&&& ^''$'77

$9:::N%%cd%33		#7888 ##GV44 3444 ##Hf55 122222r4   c                    t           j                            dd          }t          |d           t           j                            dd          }t          |d           t           j                            dd          }t          |d           t           j                            dd          }t          |d	           d S )
Nr  r7  r6  giJ.r8  gr^ߺrd  gpgFgpQ^L)r8   r"  r  r   r|  )rr   r  r|  s      r2   r~  zTestInvgauss.test_logcdf_logsf  s     &&v$&77 1222&&sD11 5666$$Ut$445666$$S$//011111r4   zmu, ref))g:0yU>g,9)rd  g%!)r}   g40)r   gK'
@)r  g`p
@c                 d    t          t          j                            |          |d           d S r  )r   r8   r"  rG   )rr   r  r  s      r2   rp  zTestInvgauss.test_entropy  s/     	..r22CeDDDDDDr4   )r   r   r   r6  r   r   r   r  r   r3  rz  r~  rp  __classcell__r1  s   @r2   r  r  !  s;          [7')>?A A> >A A>: [7')>?A A C  C  C  CA A CD2 2 2!3 !3 !3F2 2 2. [Y )D )D )D E E
E EE E
E E E E Er4   r  c                       e Zd Zej                            dg d          ej                            dg d          d                         Zej                            dg d           fd            Zd	 Zd
 Z	d Z
d Z xZS )TestLaplacer   )rC  r   r   rf   r  )r   rf   r   r_   c                    t           j                            d          }t          j                            d|||          }t          j        |          }t          j        t          j        ||z
                      t          |          z  }t          j        
                    |          \  }}t          ||dd           t          ||dd           t          j        
                    ||          \  }}t          ||dd           t          j        
                    ||          \  }}t          ||           |dz  }t          j        t          j        ||z
                      t          |          z  }t          j        
                    ||          \  }}t          ||           t          j        
                    ||          \  }}t          ||           t          t          t          j        j
        |||	           t          t          t          j        j
        t           j        g           t          t          t          j        j
        t           j        g           d S )
Nr   r`   r7  r   r  r   r  rf   r  )ri   r   r,  r8   r.  r   r  rl  r   r  r   r   r   r  r  r  r  r  )	rr   r   r  r   r   loc_mler&  rd   re   s	            r2   r  zTestLaplace.test_fit  s   
 i##D))}  cwi.1 ! 3 3 )D//F26$.1122SYY>	 ]&&t,,
UW5u====yu5AAAA ]&&t'&::
Uyu5AAAA]&&tI&>>
UW%%% kF26$*--..T:	 ]&&t#&66
UY&&& ]&&tI&>>
UWc""" 	lEM$5t'&	( 	( 	( 	( 	j%-"3bfX>>>j%-"3bfX>>>>>r4   rvs_loc,rvs_scale))rC  r_   r_   r   )r{   r  c                    t           j                            d          }t          j                            d|||          }d }t          j                            |          \  }}t          t          t          j                  t          j                                      |          \  }}	 ||||          }
 |||	|          }|
|k     st          j	        |
|dd          sJ d S d S )Nr   r   r7  c           	          dt          |           t          j        d|z            z  d|z  t          j        t          j        || z
                      z  z
  z  S )Nr   rf   r   )r  ri   r  rl  r   )rd   re   r   s      r2   llz3TestLaplace.test_fit_MLE_comp_optimizer.<locals>.ll  sS    CII%8E'26"&*<*<#=#==> ? ?r4   r   r  )
ri   r   r,  r8   r.  r   r   r   r   r   )rr   r   r  r   r   rG  rd   re   loc_opt	scale_optll_mlell_optr1  s               r2   r   z'TestLaplace.test_fit_MLE_comp_optimizer  s     i##D))}  dy.1 ! 3 3	? 	? 	? ]&&t,,
U"4#6#6#(=2 225#d)) 	C%%GY--"+ff38u#F #F #Fr4   c                    t          j        g d          }t          j                            |d          \  }}t          |ddd           t          j                            |d          \  }}t          |ddd           d S )N)rS  rS  r[  rT  r  rR  r  r   r   r   r  r  )ri   r   r8   r.  r   r   )rr   r   rd   re   s       r2   test_fit_simple_non_random_dataz+TestLaplace.test_fit_simple_non_random_data  s    x77788]&&t!&44
Uqu59999]&&tA&66
UQU777777r4   c                 F   d}t           j                            |           }|dk    sJ t           j                            |          }|dk    sJ t           j                            |          }|dk    sJ t           j                            |           }|dk    sJ d S )Nr   r   rS  )r8   r.  rp   r   )rr   r^   p0p1s       r2   test_sf_cdf_extremesz TestLaplace.test_sf_cdf_extremes  s    ]r"" Syyyy ]q!!Syyyy]a   Syyyy ]qb!!Syyyyyyr4   c                     d}t           j                            |          }t          |t	          j        |           dz  d           d S )Nr  rf   r   r   )r8   r.  r   r   ri   r   )rr   r^   ru  s      r2   r  zTestLaplace.test_sf  sE    MQ261"::a<e444444r4   c                     d}t           j                            |          }t          |t	          j        d|z             d           d S )Ng}:rf   r   r   )r8   r.  r  r   ri   r  )rr   ru  r^   s      r2   r  zTestLaplace.test_isf  sE    Ma  BF1Q3KK<e444444r4   )r   r   r   r   r   r   r  r   rM  rQ  r  r  r=  r>  s   @r2   r@  r@    s       [Y66[[---88+? +? 98 76+?Z [0 3? 3? 3? @ @F F F F@ @F(8 8 8  *5 5 5
5 5 5 5 5 5 5r4   r@  c                      e Zd Zd Zd Zej                            dg d          d             Zej                            dg d          ej                            dd	g          ej                            d
ddg          ej                            dddg          d                                                 Z	dS )TestLogLaplacec                     t          j        g d          }t          j        g d          }g d}t          t          j                            ||          |d           d S )N)r   r[  rT  )r  r    4&kC)g ?gKH9gXrL0r   r   )ri   r   r   r8   
loglaplacer   )rr   r  r^   r  s       r2   r  zTestLogLaplace.test_sf#  sf     H___%%H'''((+++(++Aq113UCCCCCCr4   c                 z    d}g d}g d}t          t          j                            ||          |d           d S )Nr  )r   r\   r  r  r  )gHhlh#?gH]9@?g"fj#@g11Ags!8wBr  r   )r   r8   rX  r  )rr   r  r~  r  s       r2   r  zTestLogLaplace.test_isf+  sS     +++6 6 6(,,Q22CeDDDDDDr4   r  r   rf   r   r   c                 L   d|dz
           }t          j        d|dz   d          }t          t          j                            ||          t           j                   t          j        t          j        t          j                            ||                              rJ d S )Nr\  r   r{   r]  )	ri   r  r   r8   rX  r  r  r   r  )rr   r  momr  s       r2   test_moments_statsz!TestLogLaplace.test_moments_stats4  s    QUmIc1s7C(( 	(//155rv>>> 6"+e&6&<&<Q&<&L&LMMNNNNNNNr4   r  )r{   rS  r   z
loc, scale)r  g@fix_cTFr  c                    t           j                            d          }t          j                            |||d|          }d|i}|r||d<   |r||d<   dt          |          z
  }	|	dk    rUd	}
t          j        t          t          f|

          5  t          j        j        |fi | d d d            n# 1 swxY w Y   d S t          t          j        |fi | d S )Nr   r`   r  r   fcr   r   r   r  r  )ri   r   r   r8   rX  r   r  r   r   r  r  r   r   )rr   r  rd   re   r^  r  r   r   r   nfreer  s              r2   test_fit_analytic_mlez$TestLogLaplace.test_fit_analytic_mle?  s=    i##$788##A3e#14 $ 6 6 } 	DJ 	#"DNCIIA::MIj9KKK 3 3 $T22T2223 3 3 3 3 3 3 3 3 3 3 3 3 3 3F%e&6EEEEEEEs   B66B:=B:N)
r   r   r   r  r  r   r   r   r]  rb  r:   r4   r2   rU  rU  !  s       D D DE E E [S,,,//O O 0/O [S///22[\L>::[WtUm44[[4-88F F 98 54 ;: 32F F Fr4   rU  c                      e Zd Zej                            dddg          d             Z ej        d          d             Zej                            dg d	          ej                            d
g d          ej                            dg d          ej                            dd  e	ddgd          D                       d                                                 Z
d Zd Zd ZdS )TestPowerlawzx, a, sf)rk  r   g      ?)g     ?g      p?gSQ>c                 f    t          t          j                            ||          |d           d S r   )r   r8   powerlawr   )rr   r^   r0   r   s       r2   r  zTestPowerlaw.test_sf^  s1     	))!Q//%@@@@@@r4   r.  r/  c                 @    t           j                            d          S r4  r2  rw   s    r2   r   zTestPowerlaw.rngd  r3  r4   r   )r\   r{   r   r   rf   r   r4  r  r5  rU  c                     g | ]}d |v |	S rW  r:   rX  s     r2   rB   zTestPowerlaw.<listcomp>l  rY  r4   TFr   rZ  c                 ,   t           j                            d||||          }t                      }	|r||	d<   |r5t	          j        |                                t          j                   |	d<   |r||	d<   t          t           j        |fi |	ddi d S )Nr  )r   r0   rd   re   r   r   r   r   r  T)	r8   rf  r   r  ri   	nextafterr-  r  r   r`  s
             r2   r   z(TestPowerlaw.test_fit_MLE_comp_optimizerh  s     ~!!siW(1 " E E vv 	#"DJ 	=<

RVG<<DL 	'&DN 	&end 	< 	<d 	< 	<6:	< 	< 	< 	< 	< 	<r4   c           	          d}d}d}t           j                            |||dt          j                            d                    }dt          j        |          dz  i}t          t           j        |fi | d S )	Ng`- @r   grߟA@r`   r   )r0   rd   re   r   r   r   rf   )r8   rf  r   ri   r   r   ptpr   )rr   r0   rb  re   r   r   s         r2   test_problem_casezTestPowerlaw.test_problem_case  s     #"~!!A85s/1y/D/DQ/G/G " I I "&,,*+%endCCdCCCCCr4   c                 z   t          t          j                   d}t          t          |          5  t          j                            g ddd           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j                            g dd           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j                            g dd	           d d d            n# 1 swxY w Y   d
}t          t          |          5  t          j                            g dd           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j                            g dd           d d d            d S # 1 swxY w Y   d S )Nz7 Maximum likelihood estimation with 'powerlaw' requiresr  r   rf   r   r   r   r  rf   r   r   z$Negative or zero `fscale` is outsider8  r  z0`fscale` must be greater than the range of data.)r  r8   rf  r  r"   r   r  r  s     r2   re  zTestPowerlaw.test_fit_warnings  s   EN+++H<s333 	< 	<Nyyyq;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< I<s333 	2 	2Nyyyq111	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 I<s333 	2 	2Nyyyq111	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 	2 6:S111 	5 	5Nyyy444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 B:S111 	4 	4Nyyy333	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4sY   %A##A'*A'$B66B:=B:$D		DD,$EE #E ?$F00F47F4c                     g d}t           j        }t          j        d          5  t	          ||           d d d            d S # 1 swxY w Y   d S )N)r   r   rf   rf   r   r   r   r   r   r   r   r  r\  over)r8   rf  ri   ri  r   )rr   r   rA   s      r2   test_minimum_data_zero_gh17801z+TestPowerlaw.test_minimum_data_zero_gh17801  s     433~[h''' 	6 	6)$555	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6s   AAAN)r   r   r   r   r   r   r  r;  r   r'   r   rm  re  rs  r:   r4   r2   rd  rd  [  s{        [Z1HJK KA AK KA V^*%%%+ + &%+ [[*=*=*=>>[Y


33[[***55[<- -$q)I)I)I - - -. .< <. . 65 43 ?><$D D D4 4 466 6 6 6 6r4   rd  c                   >   e Zd Zej                            dg d          d             Zej                            dddg          d             Zej                            dg d          d	             Zej                            dg d
          d             Z	dS )TestPowerLogNormzx, c, s, ref))r`   r
  r   ga!R()rd  r
  r   g;?)rd  r  r   gE?)MDr  r   g=c                 h    t          t          j                            |||          |d           d S r   )r   r8   r)  r   rr   r^   r  rN   r  s        r2   r  zTestPowerLogNorm.test_sf  s4     	*--aA66%HHHHHHr4   zq, c, s, ref)g?r  r   r}   )gR4-r
  r   r   c                 h    t          t          j                            |||          |d           d S )Ng|=r   )r   r8   r)  r  )rr   r~  r  rN   r  s        r2   r  zTestPowerLogNorm.test_isf  s4     	*..q!Q775IIIIIIr4   ))(,* Er  r   g?)r  r  r   gv6)r  r  r   g+	94|7)r}  r  r   g?c                 h    t          t          j                            |||          |d           d S )Ngt =r   )r   r8   r)  rp   rx  s        r2   r[  zTestPowerLogNorm.test_cdf  s4     	*..q!Q775IIIIIIr4   ))rv  r  r   gS^Ռe9)@xDrd  r   g0g;)g\)c=Hrd  r   g7H7c                 h    t          t          j                            |||          |d           d S )NgAfc=r   )r   r8   r)  rh   rx  s        r2   rQ  zTestPowerLogNorm.test_pdf  s4    
 	*..q!Q775IIIIIIr4   N)
r   r   r   r   r   r   r  r  r[  rQ  r:   r4   r2   ru  ru    s<       " [^E E EF F
I IF F
I
 [^ACEF FJ JF FJ [^A A AB B
J JB B
J [^G G GH HJ J	H HJ J Jr4   ru  c                       e Zd Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zd	S )
TestPowerNormr  ))rp  r   g| <)r
  rf   ge()r`   r  g%!@6)r  r}   gT;-c                 f    t          t          j                            ||          |d           d S r   )r   r8   	powernormr   r  s       r2   r  zTestPowerNorm.test_sf  s1     	**1a00#EBBBBBBr4   r  ))r  r
  gĿ)gwJ?r`   g!X)r!  r  g缂U)r  r  gͫ1@)r  rf   gD@)Jz5r   gU!zYr@c                 f    t          t          j                            ||          |d           d S Nr  r   )r   r8   r  r  r  s       r2   r  zTestPowerNorm.test_isf  s1     	++Aq113UCCCCCCr4   ))irp  g.u	T9)rf   rp  ?)r  rp  gsK-)rC  r  gk8>)r  r  g^u1-c                 f    t          t          j                            ||          |d           d S r  )r   r8   r  rp   r  s       r2   r[  zTestPowerNorm.test_cdf  s1     	++Aq113UCCCCCCr4   N)	r   r   r   r   r   r   r  r  r[  r:   r4   r2   r  r    s         [[C C CD D
C CD D
C [[= = => >D D> >D [[B B BC CD DC CD D Dr4   r  c                   l    e Zd Zd Zd Zd Zej                            dddg          d             Z	dS )	TestInvGammac                    t          j                    5  t          j        dt                     t          j                            dd          }g d}t          ||           g d}t          j                            |d          }g dt          j        dd	gt          j	        d
dgt          j	        t          j	        dgf}t          ||          D ]\  }}t          ||           	 d d d            d S # 1 swxY w Y   d S )Nrr  g(\O3@r\  r  )g~?gCX&?g*7gS?gBqFq @)皙?@gffffff@)r  gEy?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@)rv  rw  rx  ry  r8   r!  r   ri   r  r  r  r   )rr   r\  rW   r0   r^   r  s         r2   test_invgamma_inf_gh_1866z&TestInvGamma.test_invgamma_inf_gh_1866"  sU    $&& 	* 	*!'>:::>''%'@@D% % %HD(+++A>''!V'<<D888}=k:57H D(++ * *1#Aq))))*	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	*s   CC66C:=C:c                     t          j        dd          }t          j                            |d          }t          j                            |d          }t          ||           d S )Ngr   r   )ri   r  r8   r!  rp   r   r   r  s       r2   r  zTestInvGamma.test_cdf_ppf5  sW    Ka  Nq!$$^1%%2r4   c                     t           j        dk    rt          j        dd          }nt          j        dd          }t          j                            |d          }t          j                            |d          }t          ||d           d S )N        rf   r`      r   rS  r   )	sysmaxsizeri   r  r8   r!  r   r  r   r  s       r2   r  zTestInvGamma.test_sf_isf<  s~    ;As##AA Ar""ANa##^1%%2C((((((r4   a, ref)r   g70K6:)r  gVMOuc                 d    t          t          j                            |          |d           d S r   )r   r8   r!  rG   rr   r0   r  s      r2   test_large_entropyzTestInvGamma.test_large_entropyI  s/     	..q113UCCCCCCr4   N)
r   r   r   r  r  r  r   r   r   r  r:   r4   r2   r  r  !  s        * * *&  ) ) ) [X?:<= =	D 	D= =	D 	D 	Dr4   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestFc                     t           j        ddgg}|D ]\  }}} |j        |j        g|R  }d |D             }d |D             }t	          ||           d S )N)rf   r   rS  c                 <    g | ]\  }}} |j         |j        g|R  S r:   rh   r0   r@   _f_argsr   s       r2   rB   z(TestF.test_endpoints.<locals>.<listcomp>_  4    ===E1vrvbd#U###===r4   c                     g | ]\  }}}|	S r:   r:   r@   r  r  	_correct_s       r2   rB   z(TestF.test_endpoints.<locals>.<listcomp>`      >>>!5UI9>>>r4   )r8   frh   r0   r   )rr   r   r  r  _correctanscorrects          r2   r  zTestF.test_endpointsY  s    &#&'#' 	' 	'Bx"&&&&&CC=====>>>>>!#w/////r4   c                 ^   t           j                             ddd          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                      d S )Nr+        @r\  r]  )r8   r  r	   ri   r  rE  s        r2   test_f_momentszTestF.test_f_momentsc  s    W]]2sF];;
1aAAABKNN"#####r4   c                     t          j                    5  t          j        dt                     t          j                            dgdz  g dd           d d d            d S # 1 swxY w Y   d S )Nrr  r+  r   )rf   r   r  rD  r\  dfndfdr^  )rv  rw  rx  ry  r8   r  rw   s    r2   test_moments_warningszTestF.test_moments_warningsk  s    $&& 	H 	H!'>:::GMMrd1f,,,MGGG	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	Hs   AA$$A(+A(c                    t          j        dgdgg          }t          j        ddg          }t          j                            ||d          \  }}}}||dz
  z  gdz  }t	          ||           d|dz  z  ||z   dz
  z  |z  |dz
  dz  z  |dz
  z  }t	          ||           d|z  |z   dz
  t          j        d|dz
  z            z  |d	z
  t          j        |||z   dz
  z            z  z  }	t	          ||	           d|d
|z  dz
  z  ||z   dz
  z  |dz
  |dz
  dz  z  z   z  }
||d	z
  z  |dz
  z  ||z   dz
  z  }|
|z  }t	          ||           d S )Nr   r+  rU  r\  r  rf   r   rD  r  r      )ri   r   r8   r  r   r%  )rr   r  r  r_  r`  rN   r[   r  v2s2k2numk2denk2s                r2   test_stats_broadcastzTestF.test_stats_broadcastq  s   hbT{##hBx  W]]sV]DD
1aS1Woq 2aZ39q=)C/37Q,>#'J2us{Q"'!S1W+"6"66a273c	A#677792cQsURZ(C#IM:Qw37Q,./ 0sQw37+sSy1}=U]2r4   N)r   r   r   r  r  r  r  r:   r4   r2   r  r  X  sS        0 0 0$ $ $H H H    r4   r  c                      e Zd Zd Zd Zd Zej                            dddg          d             Z	ej                            dg d	          ej                            d
ddgddgddgg dg dgddgddggdgdggg          d                         Z
ej                            d
ddgddgddgg dg dgddgddggdgdggg          d             Zd ZdS )TestStudentTc                 h    t          t          j                            ddg          ddg           d S )Nr   r  g?g?)r   r8   r'  rz  rw   s    r2   test_rvgeneric_stdzTestStudentT.test_rvgeneric_std  s/    !%'++q!f"5"5
J7OPPPPPr4   c                 b   t          t          j                            dd          t          j        t          j        t          j        t          j        f           t          t          j                            dd          dt          j        t          j        t          j        f           t          t          j                            dd          dt          j        t          j        t          j        f           t          t          j                            dd          ddt          j        t          j        f           t          t          j                            d	d
          t          j        t          j        f           t          t          j                            dd
          dt          j        f           t          t          j                            dd
          dt          j        f           t          t          j                            dd
          d           d S )Nr   r\  )r  r^  )\(?r   rf   gGz @g     i@r   r  gGz@r   g
ףp=
@)r   gq    @)r   r8   r'  ri   r  r  rw   s    r2   test_moments_tzTestStudentT.test_moments_t  s   UW]]a]88VRVRVRV4	6 	6 	6UW]]dF];;"&"&"&1	3 	3 	3UW]]a]88"&"&"&1	3 	3 	3UW]]dF];;/2626:	< 	< 	<UW]]a]668HIIIUW]]dD]99C=IIIUW]]a]66bfFFFUW]]dD]99;RSSSSSr4   c                 t    g d}g d}t          t          j                            |          |d           d S )N)r   rf   r  r`   )g?@gTM]?ggY?U?r   r   r   r8   r'  rG   )rr   r  rW   s      r2   test_t_entropyzTestStudentT.test_t_entropy  sE    __; ; ;++XEBBBBBBr4   zv, ref)r`   r  )r  r  c                 d    t          t          j                            |          |d           d S r  r  )rr   r`  r  s      r2   test_t_extreme_entropyz#TestStudentT.test_t_extreme_entropy  s-     	**Ce<<<<<<r4   methname)rh   r   rp   r   r   r  
df_infmaskr   r   )r   r   r   )r   r   r   c                    t           j                            d           t          j        |t                    }t           j                            dd|j                  }t          j        j        |j         }t           j        ||<   t          j
        |dd          }t          j
        ||          dd          }t          j        dd          }t          ||          }t          ||          }	t          ||          }
 ||          }t          ||          |
||                              t          ||           |	||                               d S )	Nr   r   r_   r:  r   r   r  rd   re   rc   )ri   r   r   r   boolry  rA  randnr  r8   r'  r  r-  r   )rr   r  r  r  r^   t_dist
t_dist_ref	norm_distt_meth
t_meth_ref	norm_methr   s               r2   test_t_inf_dfzTestStudentT.test_t_inf_df  s6    		qZ
$777
Yq":+;<<IOZ-.:BAQ///WJ;Qa@@@
J1A...	**Z22
Ix00	fQiiS_ii*&>&>???S*%zz!ZK.'A'ABBBBBr4   c                    t           j                            d           t          j        |t                    }t           j                            dd|j                  }t           j        ||<   t          j	                            |ddd          }t          j
                            ddd	          }t          j	                            ||          ddd          }t          d
          D ]G}t          ||         |         ||                    t          ||         |          ||                    Ht          j	                            |dd          }t          j
                            dd          }t          j	                            ||          dd          }t          ||         |           t          ||          |           d S )Nr   r  r_   r:  r   r   r\  )r  rd   re   r^  rd   re   r^  r   r  rc   )ri   r   r   r   r  ry  rA  r  r8   r'  r  r  r   rG   )rr   r  r  r   
res_ex_infres_ex_noinfr  s          r2   test_t_inf_df_stats_entropyz(TestStudentT.test_t_inf_df_stats_entropy  s   
 		qZ
$777
Yq":+;<<:gmmrq6mBBZ%%!1f%EE
w}}J;Qa,2 % 4 4q 	? 	?AQ
+Z];;;Q,l1o>>>>goo!o44Z''AQ'77
w"j[/qJJS_j111S*%|44444r4   c                     g d}g d}g d}g d}t          t          j                            ||          |d           t          t          j                            ||          |d           d S )N)r   r  r_   r   )r  d~QJr|  r   )gZ_2g9g!ǟuIgdg)g73?r   gմFhAW;gm0_?r  r   )r   r8   r'  r   rh   )rr   r^   r  
logpdf_refpdf_refs        r2   test_logpdf_pdfzTestStudentT.test_logpdf_pdf  s     OO###@ @ @
> > >q"--zFFFFAr**G%@@@@@@r4   N)r   r   r   r  r  r  r   r   r   r  r  r  r  r:   r4   r2   r  r    s       Q Q QT T TC C C [X68:; ;= =; ;= [Z *< *< *< = =[\QFQFQF-6YY			,B./VaV,<./S1#J,8 9 9C C	9 9= =C  [\QFQFQF-6YY			,B./VaV,<./S1#J,8 9 95 5	9 95&
A 
A 
A 
A 
Ar4   r  c                   V    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd ZdS )TestRvDiscretec                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestRvDiscrete.setup_method  r7  r4   c                    g d}g d}d}t          j        d||f          }|                    |          }t          |t          j                  sJ t          ||          D ]>\  }}t          t          ||k              t          |          z  |z
            dk     sJ ?|                                }t	          j
        t          |          t          j                  sJ d S )N)r   r   r   rf   r   r   )r   r}  r5  r   r}  r   r   sample)namevaluesr:  r  )r8   rD   r   rC  ri   rc  r  r   rl  r   r   r   integer)rr   statesprobabilitysamplesr  r^   rN   ru  s           r2   rI  zTestRvDiscrete.test_rvs  s    $$$4448V[4IJJJEEwE!RZ(((((,, 	> 	>DAqs16{{5>>1A566=====EEGG}T!WWbj1111111r4   c                 f   t          j        g d          }t          j        g d|f          }t	          t          ||                     }|                                }t          ||           t          j        g dg df          }|                                }t          |d           d S )N)rk  r  r}  r  r  )rS  r   r   r   )	ri   r   r8   rD   rl  r   rG   r   r   )rr   rF  ru  rn  ro  s        r2   rp  zTestRvDiscrete.test_entropy  s    ***++iii%7888%u--...
IIKK:&&&iii%=>>>IIKKQr4   c                     g d}g d}t          j        ||f          }ddgddgg}t          |                    |          dd	gd
dggd           d S )Nro  r{   r}  r  r  rS  r  r[  rf   r{   r  r   r}  r  r   )r8   rD   r   rO  )rr   xkpkrv  r^   s        r2   ri  zTestRvDiscrete.test_pmf  s    YY__r2h///"X!Wq		sc$*/	1 	1 	1 	1 	1 	1r4   c                     g d}g d}t          j        ||f          g d}g d}t                              |          |d           t          fd|D             |d           d S )	Nro  r  r  )r   rS  r  r  r   r[  r   r   )r   r{   r{   r{   r   r   r   r   r  r   c                 :    g | ]}                     |          S r:   )rp   )r@   r  rv  s     r2   rB   z+TestRvDiscrete.test_cdf.<locals>.<listcomp>  s#    777777r4   )r8   rD   r   rp   )rr   r  r  x_valuesrW   rv  s        @r2   r[  zTestRvDiscrete.test_cdf  s    YY__r2h///555555x(((???? 	7777h777 u	. 	. 	. 	. 	. 	.r4   c                     g d}g d}t          j        ||f          g d}g d}t                              |          |d           t          fd|D             |d           d S )	Nro  r  r  )r\   r{   r  r   r   rS  )r   r   rf   rf   r   r   r  r   c                 :    g | ]}                     |          S r:   )r   )r@   r~  rv  s     r2   rB   z+TestRvDiscrete.test_ppf.<locals>.<listcomp>)  s#    555q555r4   )r8   rD   r   r   )rr   r  r  q_valuesrW   rv  s        @r2   re  zTestRvDiscrete.test_ppf  s    YY__r2h///000%%%x(((???? 	5555H555 u	. 	. 	. 	. 	. 	.r4   c           	          g dg df}t          j        |          }t          |                    |                    |j        d d                   dz             |j        dd                     d S )N)r   rf   r   r#  rD  )r\   r  r}  r}  r\   r  r   r  r   )r8   rD   r   r   rp   r  )rr   rG  rv  s      r2   test_cdf_ppf_nextz TestRvDiscrete.test_cdf_ppf_next,  s|    !:!:!:;d+++266"&&ss"4"4t";<<59	& 	& 	& 	& 	&r4   c                 B   t          j        d                              d          }t          j        g dg dg dg          }t	          j        ||f          }t          |                                t          j        |j	        |j
        z            d           d S )NrU  )r   r   )r\   r\   r  r  )r\   r\   r  r  r  r  r   )ri   r  r  r   r8   rD   r   r   rl  r  r  rr   r  r  rv  s       r2   test_multidimensionz"TestRvDiscrete.test_multidimension4  s    Yr]]""6**X---------/ 0 0 r2h///		RVBEBEM%:%:GGGGGGr4   c                    g d}ddg}t          t          t          j        fi t	          ||f           g d}t          t          t          j        fi t	          ||f           g d}g d}t          t          t          j        fi t	          ||f           g d}g d}t          t          t          j        fi t	          ||f           ddg}ddg}t          t          t          j        fi t	          ||f           d S )Nr
  r{   r  )r{   333333?gffffff濩r   rf   r   r   r   )r}  r}  r}  r}  r  r   )r  r  r8   rD   r  rr   r  r  s      r2   test_bad_inputzTestRvDiscrete.test_bad_input=  s/   YY3Zj%"3MMtB87L7L7LMMMYYj%"3MMtB87L7L7LMMMYYj%"3MMtB87L7L7LMMM__'''j%"3MMtB87L7L7LMMMV3Zj%"3MMtB87L7L7LMMMMMr4   c                    t          j        d                              d          t          j        dd          }}t	          t
          t          j        fi t          ||f           t          j        d                              d          t          j        dd          }}t	          t
          t          j        fi t          ||f           t          j        d                              d          t          j        dd          }}t          t          j        ||f          
                    d          d           d S )	Nr   rf   rf   rf   r   gUUUUUU?r  r  r   rf   r   )ri   r  r  r  r  r  r8   rD   r  r   rO  r  s      r2   test_shape_rv_samplez#TestRvDiscrete.test_shape_rv_sampleQ  s    1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM 1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM 1%%f--rwvs/C/CBU&r2h777;;A>>DDDDDr4   c                     g d}g d}t          j        ||f          }t          |                                t	          j        |j        |j        z            d           d S )N)r   rf   r   r  r#  r+  )r\   r  r  r  r  r\   r  r  r   )r8   rD   r   r   ri   rl  r  r  r  s       r2   test_expect1zTestRvDiscrete.test_expect1`  sd       +++r2h///		RVBEBEM%:%:GGGGGGr4   c           
         g d}g d}t          j        ||f          }t          |                                |                                d           t          |                                t          d t          ||          D                       d           t          |                    d           t          d t          ||          D                       d           d S )	N)/g      i@g     r@g      y@g     @@g     @g     @      @g      @r  g     0@g     @g     P@g     @g     p@g      @g     @g      @g     @r  g     h@g     0@g     @g     @g     @g     P@g     @g     @g     @r  g     8@g      @g     ȩ@g     @g     X@g      @g     @g     @g     x@g     @@g     @g     h@g     ̰@g     0@g     @g     @g     \@g     @)/g-C6:?r   gF%uk?g:vz?r   r   g.nr?g|гY?r   r   r   g @6*? 4U0*C?g@+?gC6z?g nr?g ?gOjM?g n?g1w-!?g:pΈ?gףp=
?g _Le?r   g^)p?g~jtx?gJ4q?gGzt?g J4q?g Mb@?g@Psׂ?g@^)ˀ?r   r   g N@s?g 1w-!_?r  gൄ|г?r   gH}}?r   g
F%u?r   r   g ^)ˀ?g v?r   r  r  r   c              3   &   K   | ]\  }}||z  V  d S ru   r:   r@   r`  ws      r2   	<genexpr>z.TestRvDiscrete.test_expect2.<locals>.<genexpr>  s*      99daAE999999r4   c                     | dz  S Nrf   r:   r   s    r2   rO   z-TestRvDiscrete.test_expect2.<locals>.<lambda>  
    AqD r4   c              3   ,   K   | ]\  }}|d z  |z  V  dS )rf   Nr:   r	  s      r2   r  z.TestRvDiscrete.test_expect2.<locals>.<genexpr>  s.      <<AAqD1H<<<<<<r4   )r8   rD   r   r   r   rl  r  )rr   r  pyrv  s       r2   test_expect2zTestRvDiscrete.test_expect2g  s
   = = =? ? ?  q"g... 			RWWYYU;;;;		99c!Rjj99999	G 	G 	G 	G 			..11<<Q<<<<<5	J 	J 	J 	J 	J 	Jr4   N)r   r   r   r6  rI  rp  ri  r[  re  r  r  r  r  r  r  r:   r4   r2   r  r    s          2 2 2
 
 
	1 	1 	1. . .. . .& & &H H HN N N(E E EH H H#J #J #J #J #Jr4   r  c                       e Zd Zd Zd ZdS )TestSkewCauchyc                    t          j        ddd          }t          t          j                            |d          t          j                            |                     t          t          j                            |d          t          j                            |                     t          t          j                            |d          t          j                            |                     d S NrC  r   r`   r   r  )	ri   rX  r   r8   
skewcauchyrh   r*  rp   r   r  s     r2   test_cauchyzTestSkewCauchy.test_cauchy  s    KAs##!%"2"6"6qA"6">">"',"2"21"5"5	7 	7 	7!%"2"6"6qA"6">">"',"2"21"5"5	7 	7 	7!%"2"6"6qA"6">">"',"2"21"5"5	7 	7 	7 	7 	7r4   c                    t           j                            d           t           j                            d          dz  dz
  }t           j                            d          dz  dz
  }g d}g d}t	          t
          j                            ||          |           t	          t
          j                            ||          |           t	          t
          j        	                    ||          |           d S )Nr   r_   rf   r   r   )
g& 45?gQʶ?g-4<??gJ?gw@v?gJ%?g>[u?g
a2?g	Rn?gѦ}cي?)
gN@Q?gPPz@	?g?g;
7?glg?g!?%?gQҙ?gC"?go?g@Sg?)
ri   r   r   r-  r   r8   r  rh   rp   r   )rr   r0   r^   rh   rp   s        r2   test_skewcauchy_Rz TestSkewCauchy.test_skewcauchy_R  s    & 		qINN2"Q&INN2#a'% % %$ $ $ 	(,,Q22C888(,,Q22C888(,,S!44a88888r4   N)r   r   r   r  r  r:   r4   r2   r  r    s2        7 7 7 9  9  9  9  9r4   r  c                       e Zd Zd Zej        d             Zej                            dg d          d             Z	dS )TestJFSkewTc                 *   dx}}|dz  }g d}g d}t          j        ||          }t          j        |          }t          |                    |          |                    |                     t          |                    |          |                    |                     t          |                    |          |                    |                     t          |                     d          |                     d                     d S )Nr   rf   )r"  r   rS  r   )r   r\   rk  r   r   rS  r\  )r8   	jf_skew_tr'  r   rh   rp   r   )rr   r0   r1   r  r^   r~  jfr'  s           r2   test_compare_tzTestJFSkewT.test_compare_t  s     	AU!!!---_Q""GBKKq		15588,,,q		15588,,,q		15588,,,((!''&//:::::r4   c                     t          j        t          t                    j        dz            }t           j                            |d          S )a  Sample data points computed using the `ST5` distribution from the
        GAMLSS package in R. The pdf has been calculated for (a,b)=(2,3),
        (a,b)=(8,4), and (a,b)=(12,13) for x in `np.linspace(-10, 10, 41)`.

        N.B. the `ST5` distribution in R uses an alternative parameterization
        in terms of nu and tau, where:
            - nu = (a - b) / (a * b * (a + b)) ** 0.5
            - tau = 2 / (a + b)
        z"data/jf_skew_t_gamlss_pdf_data.npyz	x,pdf,a,bnames)ri   loadr   __file__parentrec
fromarraysr  s     r2   gamlss_pdf_datazTestJFSkewT.gamlss_pdf_data  sD     wNN!$HH
 
 v  [ 999r4   za,b)r   )rD  r   )rU     c                     ||d         |k    |d         |k    z           }|d         |d         }}t          |t          j        ||                              |          d           dS )zCompare the pdf with a table of reference values. The table of
        reference values was produced using R, where the Jones and Faddy skew
        t distribution is available in the GAMLSS package as `ST5`.
        r0   r1   r^   rh   r  r   N)r   r8   r  rh   )rr   r(  r0   r1   r   r^   rh   s          r2   test_compare_with_gamlss_rz&TestJFSkewT.test_compare_with_gamlss_r  sr     S!Q&?3+?1+DE
 cDK3U_Q2266q99FFFFFFr4   N)
r   r   r   r  r   r;  r(  r   r   r+  r:   r4   r2   r  r    s{        ; ; ;  ^: : ^: [U$>$>$>??	G 	G @?	G 	G 	Gr4   r  rf   r   g@r   gףp=
1@r>  gRZ@i   gS㥛Ԋ@r\   r]   g&@iQ i'  i0ybi l   HO1Z i3r8  ir_   ir`   ikr  i1r   i  i4i N  i(  lEI. @ i c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	e
j                            de          d	             Zd
 Zd Zd ZdS )TestSkewNormc                 .    t          d          | _        d S r4  )r   r   rw   s    r2   r6  zTestSkewNorm.setup_method  s    %d++r4   c                     t          j        ddd          }t          t          j                            |d          t          j                            |                     d S r  )ri   rX  r   r8   skewnormrh   r  r  s     r2   test_normalzTestSkewNorm.test_normal  sY    KAs##!%."4"4Q!"4"<"<"'*.."3"3	5 	5 	5 	5 	5r4   c                     d}t           j                            d|| j                  }t	          ||j                   t           j                            d|| j                  }t	          ||j                   d S )N)r   r   r   r   )r0   r   r   r8  )r8   r2  r   r   r   rA  )rr   rA  r^   s      r2   rI  zTestSkewNorm.test_rvs  sm    NEIIUAG$$$N%dhGGUAG$$$$$r4   c                    t           j                            dt          d          dd| j                  }t          j        |          t          j        |          t          j        |          t          j	        |          g}t           j                             dddd          }t          ||d           t           j                            d	t          d          dd| j                  }t          j        |          t          j        |          t          j        |          t          j	        |          g}t           j                             d	ddd          }t          ||d           d S )
Nr   r  r   rf   )r0   r   rd   re   r   r\  )r0   rd   re   r^  rV  r  )r8   r2  r   rb  r   ri   r   r  r  kurtosisr   )rr   XrW   r  s       r2   ra  zTestSkewNorm.test_moments%  s,   NSq,0H  6 6GAJJq		5:a==%.:K:KL>''!!V'LL!(Ha@@@@N#c((,0H  6 6GAJJq		5:a==%.:K:KL>''"!1f'MM!(Ha@@@@@@r4   c                     g dg dg dg dg dg dg dg}|D ]8\  }}}t           j                            ||          }t          ||d	           9d S )
N)r  r   gEAV)r  r   gV|@$a)r  r   g0rY)r  r{   Zk)rL  r   r9  )r   r  ļ)rf   g    cr:  r  r   )r8   r2  r   r   )rr   
logpdfvalsr^   r0   	logpdfvalrz  s         r2   test_pdf_large_xzTestSkewNorm.test_pdf_large_x2  s     211333000222444555555

  * 	8 	8OAq)>((A..DD)$77777	8 	8r4   c                     t           j                            g dd          }t          |t	          j        d          d           t           j                            dd          }t          |dd           d S )	N)r_   r
  r9  r   r   r  r   r  r  rS  )r8   r2  rp   r   ri   onesr  s     r2   test_cdf_large_xzTestSkewNorm.test_cdf_large_xB  sn     N|||R00271::E2222Nr3''3U++++++r4   c                    g dg dg dg dg dg}|D ]l\  }}}t           j                            ||          }t          ||d           t           j                            | |           }t          ||d           md S )N)rn  r   gzbLe9)r  rf   gn'/2;)r   r   g::)rW  r   g|<)r  r  r  r  r   )r8   r2  rp   r   r   )rr   cdfvalsr^   r0   cdfvalru  s         r2   test_cdf_sf_small_valuesz%TestSkewNorm.test_cdf_sf_small_valuesK  s     .--+++,,,...///
 $ 	2 	2LAq&""1a((AAvD1111!!1"qb))AAvD11111	2 	2r4   z
a, momentsc                     t          |d          D ]7\  }}t          j                            ||          }t	          ||d           8d S )Nr   )startr  r   )r  r8   r2  r  r   )rr   r0   r^  orderrW   r\  s         r2   test_noncentral_momentsz$TestSkewNorm.test_noncentral_moments\  s[    (::: 	7 	7OE8.''q11CC66666	7 	7r4   c           	      t   t           j                            d          }d\  }}}t          j        |||          }|                    d|          }t          j                            |dd          \  }}}	t          j                            |dd          \  }
}}||cxk    rdk    sn J ||
k    sJ t          j                            |ddd	
          \  }}}|dk    sJ t          j        |||          }|                    d          }t          j        |          t          j        |          f}t          ||           t          j
                            dd|          }t          j                            |          }t          j        t          j        |                    sJ t          j                            |d	          \  }}}t          j        |          sJ t          j        |          t          j        |          }}t          |||t          j        dt           j        z            z  z              t          ||dz  ddt           j        z  z
  z             t          j                            |d          \  }}}t          j                            | d          \  }}}t          |||g| | |g           t          j                            |d	          \  }} }!t          j                            | d	          \  }"}#}$t          |"|#|$g| |  |!g           d S )Nl   #ke )r   rA  r{   r`   r   r  r   r   gmmr   methodmsr]  r   rL  rf   mle)ri   r   r   r8   r2  r   r   r   r  r   rD  r   r  isinfr  r%  rj   )%rr   r   r0   rd   re   rA   r   a2loc2scale2a3loc3scale3a4loc4scale4dist4r   r  r   a5loc5scale5r_  r`  a6ploc6pscale6pa6mloc6mscale6ma7ploc7pscale7pa7mloc7mscale7ms%                                        r2   r  zTestSkewNorm.test_fitb  s   i##$788$3~ae,,hhCch22 !>--c4a-@@D& >--c4a-@@D&t    q      Rxxxx !>--c1Qt-LLD&{{{{r400kk$k''gcllEJsOO+S!!! |#>> n  &&vbk#&&''''' !>--d4-@@D&x|| wt}}bfTll14&271RU7+;+;";;<<<619AI6777 $n00U0CCUG#n00#e0DDUGeW-ufg/FGGG#n00T0BBUG#n00#d0CCUGeW-ufg/FGGGGGr4   c                 F  	 t          j        g dddgz  z   dgz             }t          j                            |          }t          j                            ||          }t          j                            |d          }t          j                            ||          }||dz
  k     sJ t           j                            d          	d	d
dd}	fd}t          j        t          j        |||          }t           j        	                    ||j
        d           d S )N)rC  r   r  rU  r   r   T)superfitr{   l   y
ND )rC  r   )r  r_   )r  r_   r0   rd   re   c                 (    t          | |          S )N)r   )r&   )funr   r   s     r2   	optimizerz0TestSkewNorm.test_fit_gh19332.<locals>.optimizer  s    )#vC@@@@r4   )ro  r  r   )ri   r   r8   r2  r   r   r   r   testingr   params)
rr   r^   rq  r   params_superr  r   ro  
fit_resultr   s
            @r2   test_fit_gh19332zTestSkewNorm.test_fit_gh19332  s$   
 H***R1#X5;<<##A&&n!!&!,,
 ~))!d);;n!!,22S3Y i##$788y;GG	A 	A 	A 	A 	A Yu~q&INNN


""6:+<4"HHHHHr4   c                 f    t          t          j                            dd          dd           d S )Nr}   r~  gi}#%?r   r   )r   r8   r2  r   rw   s    r2   re  zTestSkewNorm.test_ppf  s2     	**4557HuUUUUUUr4   N)r   r   r   r6  r3  rI  ra  r=  r@  rD  r   r   r   _skewnorm_noncentral_momentsrH  r  rt  re  r:   r4   r2   r/  r/    s        , , ,5 5 5% % %A A A8 8 8 , , ,2 2 2" [\+GHH7 7 IH7
.H .H .H`I I I6V V V V Vr4   r/  c                   &    e Zd Zd Zd Zd Zd ZdS )	TestExponc                 `    t          t          j                            d          d           d S r  )r   r8   r  rh   rw   s    r2   	test_zerozTestExpon.test_zero  s&    U[__Q''+++++r4   c                     t          t          j                            d          d           t          t          j                            t          j                            d                    d           d S )Nr  r  )r   r8   r  rp   r  r   rw   s    r2   	test_tailzTestExpon.test_tail  sR    U[__U++U333U[__U[^^B%7%788"=====r4   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S No_?46@yX5ͻ@j+?UX@)ri   r   r  r  r  r8   r  r   r  s     r2   test_nan_raises_errorzTestExpon.test_nan_raises_error  <    HfffffbfEFFj%+/155555r4   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r~  )ri   r   r  r  r  r8   r  r   r  s     r2   test_inf_raises_errorzTestExpon.test_inf_raises_error  r  r4   N)r   r   r   rz  r|  r  r  r:   r4   r2   rx  rx    sP        , , ,> > >6 6 6
6 6 6 6 6r4   rx  c                   l    e Zd Zd Zd Zd Zej                            dddg          d             Z	dS )	TestNormc                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r~  )ri   r   r  r  r  r8   r  r   r  s     r2   r  zTestNorm.test_nan_raises_error  <    HfffffbfEFFj%*.!44444r4   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r~  )ri   r   r  r  r  r8   r  r   r  s     r2   r  zTestNorm.test_inf_raises_error  r  r4   c                 \    g d}t          t          t          j        j        |d           d S )Nr
  shrimp)plate)r  r  r8   r  r   r  s     r2   test_bad_keyword_argzTestNorm.test_bad_keyword_arg  s,    IIi(CCCCCCr4   rd   r   r   c                     d}t           j                            d|z   d|z   |          }t          ||d           t           j                            d|z    d|z    |           }t          ||d           d S )Ngg	{F.:r+  rU  rd   r   r   )r8   r  
_delta_cdfr   )rr   rd   rW   r  s       r2   test_delta_cdfzTestNorm.test_delta_cdf  s     )
%%bfbf#%>>xe4444
%%3i2c6%EExe444444r4   N)
r   r   r   r  r  r  r   r   r   r  r:   r4   r2   r  r    sv        5 5 5
5 5 5
D D D [UQF++
5 
5 ,+
5 
5 
5r4   r  c                       e Zd ZdZd Zd ZdS )TestUniformgh-10300c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r~  )ri   r   r  r  r  r8   ry  r   r  s     r2   r  z!TestUniform.test_nan_raises_error  =    HfffffbfEFFj%-"3Q77777r4   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |           d S r~  )ri   r   r  r  r  r8   ry  r   r  s     r2   r  z!TestUniform.test_inf_raises_error  r  r4   N)r   r   r   __doc__r  r  r:   r4   r2   r  r    s7        N8 8 8
8 8 8 8 8r4   r  c            
       D   e Zd Zd Zd Zd Zd Zej        	                    dg d          d             Z
ej        	                    dg d	g d
g dg dg dg          d             Zej        	                    dg dg dg dg dg dg dg          d             ZdS )TestExponNormc                 l   d }d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d\  }}}d||z  z  }t           j                             |||d          }t          | ||||                     d S )	Nc                     dd| |z  dz  z  z   }d| |z  dz  z  |dz  z  }dd| |z  dz  z   dz  z  }|d| z  z   ||z  d| | z  z  z   ||gS )NrS  r   rf   r   r        @r   r:   )lamsigr  opK2exp_skewexp_kurts         r2   get_momsz,TestExponNorm.test_moments.<locals>.get_moms  sz     c#g\))DC#I>)D4L8Ha39q.0B77H3JC#s3w- 78LLr4   )r   r   r   rS  r\  r  )r8  rf   r\   )r   r   r   )rC  r+  rA  )r8   	exponnormr   )rr   r  r  r  r  Kstss          r2   ra  zTestExponNorm.test_moments  sp   	M 	M 	M C39o##A2S&#IIC#sB!7!7888!C39o##A2S&#IIC#sB!7!7888C39o##A2S&#IIC#sB!7!7888"C39o##A2S&#IIC#sB!7!788888r4   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |dd           d S 	Nr  r  r  r  r  r   r   r  )ri   r   r  r  r  r8   r  r   r  s     r2   r  z#TestExponNorm.test_nan_raises_error  D    HfffffbfEFFj%/"5qqKKKKKKr4   c                     t          j        dddddt           j        g          }t          t          t
          j        j        |dd           d S r  )ri   r   r  r  r  r8   r  r   r  s     r2   r  z#TestExponNorm.test_inf_raises_error  r  r4   c                 v   t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           d S )Ni|r   r     r}   )r   r8   r  rh   rw   s    r2   test_extremes_xzTestExponNorm.test_extremes_x  s    EO//a88#>>>EO//a88#>>>EO//d;;SAAAEO//d;;SAAAAAr4   zx, K, expected))r
  r}   g6
N-)r   r}   g՜n+H?)r   r}   gi?)r  r}   gbJI-)r_   r   gI8?)r_   r4  gQ3|-0?c                 f    t          t          j                            ||          |d           d S r  )r   r8   r  rh   )rr   r^   r  rW   s       r2   test_std_pdfzTestExponNorm.test_std_pdf)  s1     	++Aq118%HHHHHHr4   zx, K, scale, expected)r   r}   r   gVAҤ?)rC  {Gzt?r   g'^>)r  r}   r`   r   )r  r}   r   gbr ;)r   rd  r   gVMe?c                     t           j                            |||          }|dk    r
|dk    sJ d S t          ||d           d S )Nr  r   r   r   )r8   r  rp   r   rr   r^   r  re   rW   ru  s         r2   test_cdf_small_KzTestExponNorm.test_cdf_small_K?  sU     O1E22s??888888Axe444444r4   )r_   r}   r   ghG}$;)rf   r  r   g]fJ?)r   r  r{   g31"g#;)r_   r  r{   gf
+-)r
  r  r{   r   )r8  rd  r   ga9S?c                     t           j                            |||          }|dk    r
|dk    sJ d S t          ||d           d S )Nr  r   -a=r   )r8   r  r   r   r  s         r2   test_sf_small_KzTestExponNorm.test_sf_small_KX  sU     Oq!511s??888888Axe444444r4   N)r   r   r   ra  r  r  r  r   r   r   r  r  r  r:   r4   r2   r  r    s       9 9 96L L L
L L L
B B B$ [-B B BC CI IC CI [4>>>DDD444GGG???	AB B5 5B B5& [4BBB@@@DDDFFF333@@@BC C5 5C C5 5 5r4   r  c                       e Zd Zd Zd Zej                            dg d          d             Zej                            dg d          d             Z	dS )	TestGenExponc                     ddl m} t          j                            t          j        ddd          ddd          }t           ||d          dd           d S )	Nr   )simpsonr_   r}   r{   r   )dxr   )scipy.integrater  r8   genexponrh   ri   r  r   )rr   r  ru  s      r2   test_pdf_unity_areaz TestGenExpon.test_pdf_unity_areah  sd    ++++++NryB55sCEEGGA$///A66666r4   c                     t           j                            t          j        ddd          ddd          }t          j        d|k    |dk    z            sJ d S )Nr   r_   r}   r{   r   r   )r8   r  rp   ri   r  r   )rr   rp   s     r2   test_cdf_boundszTestGenExpon.test_cdf_boundsn  sT    n  1b$!7!7c3GGvqCxC1H-.......r4   zx, p, a, b, c))r>  gM <r   rf   r  )rk  g%DYY?r{   rf   r   )rk  gS4z?      #@rf   r{   )r}   ga^5?r  rk  r{   )r  gs%)?r  rk  r{   )r  gdm?rk  r   r{   c                     t           j                            ||||          }t          ||d           t           j                            ||||          }t          ||d           d S r  )r8   r  r   r   r  )rr   r^   ru  r0   r1   r  r   r  s           r2   r  zTestGenExpon.test_sf_isf~  sj     ^q!Q**AE****n  Aq!,,QU++++++r4   ))rk  g;\i?r{   rf   r   )rk  gu0?r  rf   r{   )r}   g-%I?r  rk  r{   )r  g]d?r  rk  r{   )r  g泩'?rk  r   r{   c                     t           j                            ||||          }t          ||d           t           j                            ||||          }t          ||d           d S r  )r8   r  rp   r   r   )rr   r^   ru  r0   r1   r  rp   r   s           r2   r  zTestGenExpon.test_cdf_ppf  sj     n  Aq!,,QU++++n  Aq!,,QU++++++r4   N)
r   r   r   r  r  r   r   r   r  r  r:   r4   r2   r  r  g  s        7 7 7/ / /  [_I I IJ J, ,J J, [_J J JK K, ,K K, , ,r4   r  c                       e Zd Zd ZdS )TestTruncexponc                     ddg}ddg}ddg}t          t          j                            ||          |d           t          t          j                            ||          |d	           d S )
Nr
  r`   g_93@gBX@g,M<gǃ@֫5gLa㧝=r   r  )r   r8   
truncexponr   r  )rr   r1   r^   r  s       r2   r  zTestTruncexpon.test_sf_isf  sx     I	"%'=>(++Aq113WEEEE(,,S!44aeDDDDDDr4   N)r   r   r   r  r:   r4   r2   r  r    s(        E E E E Er4   r  c                       e Zd Zd ZdS )TestExponpowc                     t          t          j                            dd          d           t          t          j                            t          j                            dd          d          d           d S )Nr  r   r  r   r   )r   r8   exponpowrp   r  r   rw   s    r2   r|  zTestExponpow.test_tail  si    EN..ub995AAAEN..u~/@/@B/G/GLL	 	 	 	 	r4   N)r   r   r   r|  r:   r4   r2   r  r    s#            r4   r  c                        e Zd Zd Zd Zd ZdS )TestSkellamc                     t          j        dd          }d\  }}t          j        g d          }t          t          j                            |||          |d           d S )Nr  r>  rD  )gYjP'?g$S?gQ`s2?gC/qF?gD<]Y?g/Xj?g86y?g]a¨?g:?g?gQ>?g?g:?g]a¨?g96?g0X?gA<]?gB/q?gQ`s?g$S?gYjP'?gX_?g+rx?gfSr?gJXx~?rV  )ri   r  r   r   r8   skellamrO  )rr   r[   mu1mu2skpmfRs        r2   ri  zTestSkellam.test_pmf  sm    Ic2S- - -. . 	EM--ac::FBOOOOOOr4   c                     t          j        dd          }d\  }}t          j        g d          }t          t          j                            |||          |d           d S )Nr  r>  rD  )gƃQ?gS`X'?gVy)>?g:	 S?gei.f?gȼJ]x?g)?g{^'+i?gLIg>?gnZ?g?rvͪ?gA?g0?g#J?gqSm
.?g~B?gd?gFBD?gQ9?gmF^?gcMy?gGJq?gC^c?g.){?gñݸ?r   rV  )ri   r  r   r   r8   r  rp   )rr   r[   r  r  skcdfRs        r2   r[  zTestSkellam.test_cdf  sm    Ic2S- - -. . 	EM--ac::FANNNNNNr4   c                     d\  }}}t          t          j                            |||          dd           t          t          j                            |||          dd           d S )N)r   r   gs1Cr   r  r   r   )r   r8   r  rO  rp   )rr   r^   r  r  s       r2   test_extreme_mu2zTestSkellam.test_extreme_mu2  se    .3))!S#66FFFF))!S#66FFFFFFr4   N)r   r   r   ri  r[  r  r:   r4   r2   r  r    sL        P P P*O O O*G G G G Gr4   r  c                      e Zd Zd Zd Z ej        d          d             Zej        	                    dddg          ej        	                    d	g d
          ej        	                    dg d          ej        	                    dd  e
dd          D                        ej        d          d                                                             Zd ZdS )TestLognormc                     t          j                    5  t          j        dt                     t          j                            g dd          }t          |g d           d d d            d S # 1 swxY w Y   d S )Nrr  r   r{   r   r   )r   g~r?g e3E?)rv  rw  rx  ry  r8   r'  rh   r   rr   rh   s     r2   rQ  zTestLognorm.test_pdf  s     $&& 	J 	J!'>:::-##KKK33C%c+H+H+HIII	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	J 	Js   AA00A47A4c           	         d\  }}}t          t          j                            ||z
  |          t          j                            t          j        ||z
            |z                       t          t          j                            ||z
  |          t          j                            t          j        ||z
            |z                       d S )N)g(\5i@   gOn?rM   )r   r8   r'  r   r  ri   r  r|  )rr   r  r  sigmas       r2   r  zTestLognorm.test_logcdf  s    *B((B%(88
bfRUmmE&9::	< 	< 	<++BrEU+;;
((2u)<==	? 	? 	? 	? 	?r4   r.  r/  c                 @    t           j                            d          S r4  r2  rw   s    r2   r   zTestLognorm.rng  r3  r4   r   r\   rf   r   )r   r   rf   r  )r  r   r   rU  c                     g | ]}d |v |	S rW  r:   )r@   es     r2   rB   zTestLognorm.<listcomp>  rY  r4   )FTr   rZ  r\  r]  c                     t           j                            d||||          }i }	|r||	d<   |r||	d<   |r||	d<   t          t           j        |fi |	ddi d S )Nr`   )r   rN   re   rd   r   r   r   r   r  T)r8   r'  r   r   r`  s
             r2   r   z'TestLognorm.test_fit_MLE_comp_optimizer  s     }  cYi%,3 ! @ @  	#"DJ 	#"DL 	'&DN 	&emT 	< 	<T 	< 	<6:	< 	< 	< 	< 	< 	<r4   c                 z    d}g d}g d}t          t          j                            ||          |d           d S )NgI+?)r\   g|=gҶOɃ;gk3;9"7)g?y+@g~K8ax@gƶ@g9]Ar  r   )r   r8   r'  r  )rr   rN   r~  r  s       r2   r  zTestLognorm.test_isf  sR    
 &&&# # #))!Q//5AAAAAAr4   N)r   r   r   rQ  r  r   r;  r   r   r   r'   ri   ri  r   r  r:   r4   r2   r  r    sP       J J J? ? ? V^*%%%+ + &%+ [[2q'22[Y


33[[***55[<- -q)I)I)I - - -. . R["""< < #". . 65 43 32<$	B 	B 	B 	B 	Br4   r  c                      e Zd Zd Zd Zd Zd Zej        	                    e
d          d             Zej        	                    e
d          d             Zej        	                    e
d          d	             Zd
 Zej                            ed          d             Zej                            dej        j        ej        j        g          ej                            dddg          d                         Zej                            dg d          d             Zej                            dg d          d             ZdS )TestBetac                     t           j                            ddd          }t          |d           t           j                            ddd          }t          |t          j                   d S )Nr   r   r{   g;B.)r8   r  r   r   ri   r  rr   r   s     r2   r{  zTestBeta.test_logpdf  s\    ""1a--FN333""1c1--FBF+++++r4   c                 `   d\  }}t          j        g d          }t          j        ||          }t	          |                    |                                          d           t	          |                    |          t          j        |                    |                               d S )Ni  i  r  r{   r  gƒ)	ri   r   r8   r  r   r   rl  rh   r   rr   r  r  r^   r1   s        r2   test_logpdf_ticket_1866z TestBeta.test_logpdf_ticket_1866   s    tH___%%Jud##))+=>>>a"&!"5"566666r4   c                 `    g d}t          t          t          j        j        |ddd           d S )Nr\   r{   r  r   r   r  )r   r   r  )r  r  r8   r  r   r  s     r2   test_fit_bad_keyword_argsz"TestBeta.test_fit_bad_keyword_args'  s=    OOi1$	& 	& 	& 	& 	& 	&r4   c                 ^    g d}t          t          t          j        j        |dd           d S )Nr  r{   )fafix_a)r  r  r8   r  r   r  s     r2   #test_fit_duplicated_fixed_parameterz,TestBeta.test_fit_duplicated_fixed_parameter,  s0     OOj%*.!3GGGGGGr4   zOverflow, see gh-14901reasonc                 p    d\  }}}t          t          j                            |||          d           d S )N)g?g     R@g   0xAgx)>)r   r8   r  r   )rr   ru  r0   r1   s       r2   test_issue_12635zTestBeta.test_issue_126352  s8     71a
q!Q//1FGGGGGr4   c                 >   t          j        g d          }t          j        g d          }d}t          j                            ||dz   d|z
            }t          ||           t          j                            ||dz   d|z
            }t          ||           d S )N)g@3@?g^?gNC?)r_   r`   r   r-  r   r   )ri   r   r8   r  r  r   r   )rr   inv_R
count_listru  invr   s         r2   test_issue_12794zTestBeta.test_issue_12794>  s      1 1 1 2 2 Xooo..
jnnQ
Q0CDDU###jmmCa*1DEEQr4   c                     d}t          j        dd          }d}d|z
  |dz   ||z
  }}}t          j                            |||          }t          j                            |||          }t          |d|z
             d S )Nh㈵>r   r
  r   )ri   r  r8   r  r   rp   r   )	rr   alpha_2count_nobsr~  r0   r1   r  r   s	            r2   test_issue_12796zTestBeta.test_issue_12796P  s     1b!!g+vz4&=a1jnnQ1%%jnnS!Q''Q[)))))r4   c                    d\  }}t          t          j                            d||          t          j                   d\  }}t          t          j                            d||          t          j                   d\  }}t          t          j                            d||          d           t          t          j                            d||          d           d\  }}t          t          j                            d||          d           t          t          j                            d	||          d           d S )
NrZ  r   )r  r   r   )r   r   r   +ph  )r   r   rS  )r   r8   r  rh   ri   r  )rr   r0   r1   s      r2   r  zTestBeta.test_endpoints\  s    1UZ^^Aq!,,bf555 1UZ^^Aq!,,bf555 1UZ^^Aq!,,a000UZ^^FAq111555 1UZ^^Aq!,,a000UZ^^Ha33Q77777r4   zDoes not convert boost warningc                     d\  }}}t          j        t                    5  t          j                            |||           d d d            d S # 1 swxY w Y   d S )N)gףp=
?g   vH7B  @0B)r   warnsry  r8   r  r   )rr   r~  r0   r1   s       r2   test_boost_eval_issue_14606z$TestBeta.test_boost_eval_issue_14606s  s    '1a\.)) 	$ 	$JNN1a###	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$ 	$s   "AAArL  a, b)r        )@)r  r  c                 H    d}	  ||||           d S # t           $ r Y d S w xY w)Nr   )OverflowError)rr   rL  r0   r1   ru  s        r2    test_beta_ppf_with_subnormal_a_bz)TestBeta.test_beta_ppf_with_subnormal_a_by  sG    
 
	F1aOOOOO 	 	 	 DD	s    
!!r  ))r{   r{   gο)rd  r   g )r   r4  g&׾k )r   r   g*)Mc                 p    t          t          j        ||                                          |           d S ru   r   r8   r  rG   r  s       r2   rp  zTestBeta.test_entropy  s2     	
1a((0022C88888r4   za, b, ref, tol))r   r_   gCpr  )r_   r
  g8EOr   )g    NAg    NAg(4FrF  )g    SAg   SAg8TAUr  )r  g   _Bg[VVuD&r-  )r  r  gR#Lr   )rf   r  g?r5r-  )rf   r|  <Fr  )rf   r  guRTc\r  )r   r  gL4r  )r   r|  6Er  )r   r  g.fq>\r  )r_   r  gnQc}4rF  )r_   r|  g{C Er  )r_   r  %\r  )r|  rf   r  r  )r|  r   r  r  )r  r_   r  r  c                 t    t          t          j        ||                                          ||           d S rQ  r  )rr   r0   r1   r  r  s        r2   r  zTestBeta.test_extreme_entropy  s8    H 	
1a((0022CcBBBBBBr4   N)r   r   r   r{  r  r  r  r   r   skipifMACOS_INTELr  r  r  r  xfailr   r  r   r8   r  r   r  r  rp  r  r:   r4   r2   r  r    s        , , ,7 7 7& & &
H H H [,DEE	H 	H FE	H [,DEE    FE " [,DEE	* 	* FE	*8 8 8. [w'GHH$ $ IH$
 [X

'GHH[Vnn%EFF  GF IH@ [[D D DE E
9 9E E
9 [	
 	
 	
 .C C/ .C C Cr4   r  c                   f   e Zd Zg dZd Zd Zej                            dg d          d             Z	ej                            de          d             Z
ej                            d	eg d
z             d             Zej                            d	ddg          d             Zd Zd Zd ZdS )TestBetaPrime))rv        Y@r  D>?)r  r  r  m嗽?)r   r  r\   gPK?)r   r  r  g%p?)r  r  r\   g#|/?)r  r  r  gsM
<)r  r  r  $5Є*?)^ 9^;r  r\   gompP?)r   r  r  g7j"!9)r   r  r  z^J?)r  r  r\   gܷ"+>)r  r  r  grNs: )r  r  r  gK>c                    d\  }}t          j        g d          }t          j        ||          }t	          t          j        |                    |                                                               t          |	                    |          t          j
        |                    |                               d S )Nr  r  )ri   r   r8   r  r	   r  r   r   r   rh   r   r  s        r2   r{  zTestBetaPrime.test_logpdf  s    tH___%%OE4((AHHQKK((,,..///a"&!"5"566666r4   c                    t           j                            ddd          }t          |d           d\  t	          j        g d          }t           j                            |          }t          t	          j        |                                                     t           j	        j
        fd|D             }t          ||dd	           d S )
Nr   r  r}  r   r  r  c                 @    g | ]} t           j        |          S r:   )r8   r  )r@   rH  r  r  gen_cdfs     r2   rB   z*TestBetaPrime.test_cdf.<locals>.<listcomp>  s+    JJJ''%/3t<<JJJr4   -=r  )r8   r  rp   r   ri   r   r	   r  r   rE   _cdf_singler   )rr   r^   r@  cdfs_gr  r  r%  s       @@@r2   r[  zTestBetaPrime.test_cdf  s     O3,,QtH___%%""1eT22D!!%%''((( %1JJJJJJJJJf15999999r4   zp, a, b, expected))r}         ?r  gV)?)r  r)  r  gWJB9*=)r  r)  r  gOG J<)rZ  rk        @gΣ01)      ?rk  r*  g8ǘ`?)>q?r  r\   gMDc                 l    t           j                            |||          }t          ||d           d S r  )r8   r  r   r   )rr   ru  r0   r1   rW   r^   s         r2   re  zTestBetaPrime.test_ppf  s8     O1a((8%000000r4   z
x, a, b, pc                 h    t          t          j                            |||          |d           d S r  )r   r8   r  r   )rr   r^   r0   r1   ru  s        r2   test_ppf_gh_17631zTestBetaPrime.test_ppf_gh_17631  s1    ++Aq!44aeDDDDDDr4   zx, a, b, expected))r  r  r  r  )r  r  r\   gV[?)rv  r  r\   r,  c                 h    t          t          j                            |||          |d           d S r  )r   r8   r  rp   )rr   r^   r0   r1   rW   s        r2   test_cdf_gh_17631zTestBetaPrime.test_cdf_gh_17631  s3     	++Aq!44hUKKKKKKr4   )r  r  r\   g%?)r  r  r  goXr?c                 |    t           j                            |||          }|dk     sJ t          ||d           d S )NrS  gh㈵>r   )r8   r  rp   r   )rr   r^   r0   r1   rW   r  s         r2   test_cdf_extreme_tailsz$TestBetaPrime.test_cdf_extreme_tails(  sE     O1a((3wwww8$//////r4   c                     g d}g d}g d}g d}t           j                            |||          }t          ||d           d S )N)r   r   rf   r  r  r  r  r  r  r  r  r  r  r  )r   rf   r   r\   r\   r\   r\   r  r  r  r  r  r  r  )r  r|  ꌠ9Y>)Frv  r  r   r  rv  r  r  r   r  r  r  )g/:g  U/7gKH9g<![a?gw 4?g)J?g5?r!  r  r  r  g%?gsM
<r  r  r   )r8   r  r   r   )rr   r0   r1   r^   r  	sf_valuess         r2   r  zTestBetaPrime.test_sf3  s|        0 0 0; ; ;
 O&&q!Q//		3U333333r4   c                     t           j                            g ddd           t          j        dd                               d           d S )N)r\   rk  r}  r  皙?r   r   r  rE  r\  )r8   r  r   rw   s    r2   test_fit_stats_gh18274z$TestBetaPrime.test_fit_stats_gh18274H  sQ     	666QqIII!q!!!''/////r4   c                     t           j        dg}t          j        dddg                              d          }t          ||           d S )NgooB?rf   r  gffffff@r   )ri   r  r8   r  r  r   )rr   r  r   s      r2   test_moment_gh18634z!TestBetaPrime.test_moment_gh18634O  sJ     v()oa#s,,33A66S!!!!!r4   N)r   r   r   cdf_valsr{  r[  r   r   r   re  r/  r1  r3  r  r9  r;  r:   r4   r2   r  r    sq         H 7 7 7: : :> [	B 	B 	B 1 1 1 [\844E E 54E [ 
 
 
 	
 L L L [	.	/	12 20 0	2 204 4 4*0 0 0	" 	" 	" 	" 	"r4   r  c            
       h   e Zd Zd Zd Zd Zd Zej        	                    dddg          d             Z
ej        	                    d	g d
          d             Zej        	                    dg d          ej        	                    dg d          ej        	                    dg d          ej        	                    dddg          ej        	                    dddg          ej        	                    dddg          d                                                                         ZdS )	TestGammac                     t           j                            ddd          }t          |d           t           j                            ddd          }t          |d           d S )	NZ   i  r  r  g
CTb?r   r_   gBΖ?)r8   r_  rh   r   r  s     r2   rQ  zTestGamma.test_pdf\  sZ    koob#To22C---kooa4o00C+++++r4   c                 f    t           j                            dd          }t          |d           d S r  )r8   r_  r   r   r  s     r2   r{  zTestGamma.test_logpdfd  s1     ##Aq))FA&&&&&r4   c                 ^    g d}t          t          t          j        j        |dd           d S )Nr  r   r  )r   r  )r  r  r8   r_  r   r  s     r2   r  z#TestGamma.test_fit_bad_keyword_argsj  s.    OOi!!8LLLLLLr4   c                     t          j        t          j                            dd          dd          sJ t          j        t          j                            dd          dd	          sJ d S )
NrZ  r   gplC@r  r   r  r`   g1}t@r   )ri   iscloser8   r_  r  rw   s    r2   r  zTestGamma.test_isfn  s    " z%+//%33+%9 9 9 	9 	9 	9z%+//%55+%9 9 9 	9 	9 	9 	9 	9r4   re   rS  rT  c                 |    t           j                            |dz  |dz  d|          }t          |dd           d S )N   r  r   r  g>S*r   r   )r8   r_  r  r   rr   re   r  s      r2   r  zTestGamma.test_delta_cdf  sF     &&uSy%)Qe&LL6UCCCCCCr4   za, ref, rtol))r  gt.r   )rf   r|  r   )r`   gX>k-־@r   )r  gwM7@r   )g NgmCg%og$6@r   )r  oܘ#]@r   c                 d    t          t          j                            |          ||           d S rQ  )r   r8   r_  rG   )rr   r0   r  r   s       r2   rp  zTestGamma.test_entropy  s/     	++A..$??????r4   r0   )r}   r   r  rd   )r}   r   r  r  TFr   r  c                 H   t           j                            d          }t          j                            |||d|          }i }	|r||	d<   |r||	d<   |r||	d<   dt          |	          z
  }
|
dk    rPd	}t          j        t          |
          5  t          j        j
        |fddi|	 d d d            n# 1 swxY w Y   d S t          j        j
        |fddi|	}t          j        | }|
dk    r4t          |                                t          j        |                     |
dk    r8t          |                    d          t          j        |dz                       |
dk    r:t          |                    d          t          j        |dz                       d S d S )Nr   r`   r  r  r   r   r   r   r  r  rL  rJ  r   rf   )ri   r   r   r8   r_  r   r  r   r   r  r   r   r   r  )rr   r0   rd   re   r  r   r  r   r   r   ra  r  thetarA   s                 r2   test_fit_mmzTestGamma.test_fit_mm  s    i##$788{qcS,/  1 1  	DJ 	DL 	#"DNCIIA::MIz;;; ; ;::T:T:::; ; ; ; ; ; ; ; ; ; ; ; ; ; ;F::T:T::{E"A::DIIKK777A::DKKNNBGD!G,<,<===A::DKKNNBGD!G,<,<===== :s   B66B:=B:N)r   r   r   rQ  r{  r  r  r   r   r   r  rp  rM  r:   r4   r2   r>  r>  [  s       , , ,' ' 'M M M9 9 9, [WsCj11D D 21D [^B B BC C@ @C C@ [S...11[UNNN33[Wnnn55[WtUm44[Yu66[[4-88> > 98 76 54 65 43 21> > >r4   r>  c                      d} t          j        d| dz  z  d| dz  z  dd          }t          |                    d          d           d S )	Nrd  g;f?rf   r   r   rc   rS  gV{q@)r8   r3  r   rh   )jitterZs     r2   test_pdf_overflow_gh19616rQ    sT     F6FAI-q619}!1MMMAAEE#JJ 122222r4   c                       e Zd Zd Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d	             Z	d
 Z
dS )
TestDgammac                    t           j                            d          }d}|                    d|          }|                    d|          }t
          j                            ||          }t
          j                            t          j	        |          |          dz  }t          ||           t          j        |          }t          |                    |          |d           d S )Nl   OP($ r_   r  )r0  r   rf   r  r   )ri   r   r   normalry  r8   dgammarh   r_  r   r   )rr   r   r   r^   r0   r   r  rA   s           r2   rQ  zTestDgamma.test_pdf  s    i##$788JJRdJ++KKRdK++lq!$$koobfQii++a/S!!!|ASu555555r4   zx, a, expected))r  r   ggrU>)rL  r   g$IC<)ir   g2Wj<)r  g~)A.=)r   r   gf?c                    t           j                            ||          }t          ||d           t           j                            ||          }t          ||d           t           j                            | |          }t          ||d           t           j                            ||          }t          || d           d S r8  )r8   rV  rp   r   r   r   r  )rr   r^   r0   rW   rp   r   r   r  s           r2   test_cdf_ppf_sf_isf_tailz#TestDgamma.test_cdf_ppf_sf_isf_tail  s     lq!$$XE2222lx++QU++++\__aR##H51111lx++aRe,,,,,,r4   r  ))r  gmqn @)?g?)r  gx?c                 d    t          t          j                            |          |d           d S r  r   r8   rV  rG   r  s      r2   rp  zTestDgamma.test_entropy  s/      	,,Q//5AAAAAAr4   ))r  r  )r  g>_)r  g5i)r  go@)rW  g4Fa3@)r  grO]@c                 d    t          t          j                            |          |d           d S r  r\  r  s      r2   test_entropy_entreme_valuesz&TestDgamma.test_entropy_entreme_values  s/    " 	,,Q//5AAAAAAr4   c                    t          j        g d          }t          j                            |          }t          t          |                    D ]3}||         t          j                            ||                   k    sJ 4d S )N)r   r   r|  r  )ri   r   r8   rV  rG   r  r  )rr   r^   r  r  s       r2   test_entropy_array_inputz#TestDgamma.test_entropy_array_input  s~    H'''((L  ##s1vv 	6 	6AQ45<//!5555555	6 	6r4   N)r   r   r   rQ  r   r   r   rY  rp  r^  r`  r:   r4   r2   rS  rS    s        6 6 6, [-: : :; ;- -; ;- [X8 8 89 9B B	9 9B [X: : :; ;
B 
B; ;
B6 6 6 6 6r4   rS  c                   f    e Zd Zd Zd Zej                            dg d          d             ZdS )TestChi2c                     t          t          j                            dd          dd           t          t          j                            dd          dd           d S )Nr   gޞw1D?r  rV  r`   g6:֜?r   r8   chi2rh   rw   s    r2   r  zTestChi2.test_precision(  sj    EJNN4668N$&	( 	( 	( 	(EJNN3446J$&	( 	( 	( 	( 	( 	(r4   c                    d}t           j                            d|          }t          |dd           t           j                            d|          }t          |dd           d}t           j                            d	|          }t          |d
d           t           j                            d|          }t          |dd           d S )Nr  gλm:=6g'bd5 <r  r   r{   gQ8@r)  gܐ؆0guu[9=r\   g8-*@)r8   re  r   r   )rr   r  r^   s      r2   re  zTestChi2.test_ppf.  s    JNN5"%%<5IIIIJNN3##7eDDDDJNN5"%%:GGGGJNN3##8uEEEEEEr4   r  ))r  gܫ>)r   gƯʉ?)r`   gn>@)   g͔v0@)rW  g9:3@c                 r    t          t          j        |                                          |d           d S r   )r   r8   re  rG   r  s      r2   rp  zTestChi2.test_entropyF  s3     	
2..00#EBBBBBBr4   N)	r   r   r   r  re  r   r   r   rp  r:   r4   r2   rb  rb  &  s{        ( ( (F F F0 [Y: : :; ;C C; ;C C Cr4   rb  c                   l    e Zd Zd Zd Zd Zej                            dddg          d             Z	dS )	TestGumbelLc                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S Nr2  r  )ri   rX  r8   r=  rp   r   r   r  s       r2   r  zTestGumbelL.test_cdf_ppfR  sS    Kb!!Nq!!^""2r4   c                    t          j        dd          }t          j                            |          }t          j                            |          }t          j        |          }t          j        |           }t          ||           d S rl  )
ri   rX  r8   r=  r  r|  r   r   expm1r   )rr   r^   r  r:  ur`  s         r2   r~  zTestGumbelL.test_logcdf_logsfX  sr    Kb!!N!!!$$N  ##F1II]11r4   c                     t          j        dd          }t          j                            |          }t          j                            |          }t          ||           d S )Nr  r   )ri   rX  r8   r=  r   r  r   r  s       r2   r  zTestGumbelL.test_sf_isf`  sS    KQNa  ^""2r4   rd   r   r   c                     t           j                            d|          }t           j                            ||          \  }}t	          ||           d S )Nr`   )r   rd   r   )r8   r=  r   r   r   )rr   rd   r   
fitted_locr   s        r2   test_fit_fixed_paramz TestGumbelL.test_fit_fixed_paramf  sR     ~!!s!44**4c*::
AZ%%%%%r4   N)
r   r   r   r  r~  r  r   r   r   rs  r:   r4   r2   rj  rj  P  ss               [URG,,& & -,& & &r4   rj  c                       e Zd Zd Zd ZdS )TestGumbelRc                 d    t          t          j                            d          dd           d S )Nr<  ?~T}%m;r  r   )r   r8   r<  r   rw   s    r2   r  zTestGumbelR.test_sfq  s=     	))"--/E"	$ 	$ 	$ 	$ 	$ 	$r4   c                 d    t          t          j                            d          dd           d S )NrZ  rD  r  r   )r   r8   r<  r  rw   s    r2   r  zTestGumbelR.test_isfz  s=     	**5113D"	$ 	$ 	$ 	$ 	$ 	$r4   N)r   r   r   r  r  r:   r4   r2   ru  ru  o  s2        $ $ $$ $ $ $ $r4   ru  c                   	   e Zd Z ej        d          d             Zej        d             Zej        d             Zej        d             Zej	        j
        ej	                            d ej        d           ej        d	ej	        j
        
          g          ej	                            dddg          ej	                            dg d          ej	                            dddg          d                                                             Zej	        j        ej	                            dddg          d                         Zd Zej	                            d          ej	                            dddg          ej	                            dddg          d                                     Zd  Zd! Zd" Zej	        j
        ej	                            d# ej        g d$g d%g d&           ej        g d'g d(g d)ej	        j
        
           ej        g d* ej        d+d,d-           ej        d.dd/          ej	        j        
          g          d0                         Zej	                            d# ej        g d$g d%g d&           ej        g d'g d(g d)ej	        j
        
           ej        g d* ej        d+d,d-           ej        d.dd/          ej	        j        
          g          d1             Zej	                            d2d3dg          ej	                            d4d5d6g          d7                         Zej	                            d8d9d:gd;d:gg          d<             Zej	                            d=d>d3ej        ej        ej        fgd?d@gg          dA             Zej	                            dBg dC          ej	                            dDej         j!        dE ej        dFd3dG          dHfej         j"        dE ej        dFd3dG          dHfej         j!        dI ej        d3dJdG          dEfej         j"        dI ej        d3dJdG          dHfg          dK                         Z#ej	                            dLg dM          dN             Z$ej	        j        ej	                            dLg dO          dP                         Z%dQS )RTestLevyStableT)autousec                     dt           j        _        dt           j        _        dt           j        _        t           j        j        t           j        _        dS )z2Setup default parameters for levy_stable generatorS1	piecewiseN)r8   levy_stableparameterizationcdf_default_methodpdf_default_method_levy_stable	_QUAD_EPSquad_epsrw   s    r2   reset_levy_stable_paramsz'TestLevyStable.reset_levy_stable_params  s<     .2*/:,/:,%*%7%A"""r4   c                     t          j        t          t                    j        dz            }t           j                            |j        d          }|S )a  Sample data points for pdf computed with Nolan's stablec

        See - http://fs2.american.edu/jpnolan/www/stable/stable.html

        There's a known limitation of Nolan's executable for alpha < 0.2.

        The data table loaded below is generated from Nolan's stablec
        with the following parameter space:

            alpha = 0.1, 0.2, ..., 2.0
            beta = -1.0, -0.9, ..., 1.0
            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,
        and the equivalent for the right tail

        Typically inputs for stablec:

            stablec.exe <<
            1 # pdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-pdf-sample-data.npyx,p,alpha,beta,pctr!  ri   r#  r   r$  r%  r&  r'  Tr  s     r2   nolan_pdf_sample_dataz$TestLevyStable.nolan_pdf_sample_data  sM    6 wNN!<=
 
 v  /C DDr4   c                     t          j        t          t                    j        dz            }t           j                            |j        d          }|S )a#  Sample data points for cdf computed with Nolan's stablec

        See - http://fs2.american.edu/jpnolan/www/stable/stable.html

        There's a known limitation of Nolan's executable for alpha < 0.2.

        The data table loaded below is generated from Nolan's stablec
        with the following parameter space:

            alpha = 0.1, 0.2, ..., 2.0
            beta = -1.0, -0.9, ..., 1.0
            p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5,

        and the equivalent for the right tail

        Ideally, Nolan's output for CDF values should match the percentile
        from where they have been sampled from. Even more so as we extract
        percentile x positions from stablec too. However, we note at places
        Nolan's stablec will produce absolute errors in order of 1e-5. We
        compare against his calculations here. In future, once we less
        reliant on Nolan's paper we might switch to comparing directly at
        percentiles (those x values being produced from some alternative
        means).

        Typically inputs for stablec:

            stablec.exe <<
            2 # cdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-cdf-sample-data.npyr  r!  r  r  s     r2   nolan_cdf_sample_dataz$TestLevyStable.nolan_cdf_sample_data  sN    J wNN!<=
 
 v  /C DDr4   c                 b    t          j        t          t                    j        dz            }|S )a&  Sample data where loc, scale are different from 0, 1

        Data extracted in similar way to pdf/cdf above using
        Nolan's stablec but set to an arbitrary location scale of
        (2, 3) for various important parameters alpha, beta and for
        parameterisations S0 and S1.
        z1data/levy_stable/stable-loc-scale-sample-data.npy)ri   r#  r   r$  r%  r  s     r2   nolan_loc_scale_sample_dataz*TestLevyStable.nolan_loc_scale_sample_data  s1     wNN!?@
 
 r4   sample_sizer<  r  marksr  S0r}  z
alpha,beta))rS  r   )rS  r   )r  r   )r  r{   zgamma,deltar   r   r  c                     |t           j        _        t          j        ||||          }t          j        |                    |d          |j                  \  }}	|	dk    sJ d S )N)r  r  re   rd   r   r   r  )r8   r  r  r  r   rp   )
rr   r  r  r  r_  r  r  lsr   ru  s
             r2   rI  zTestLevyStable.test_rvs  sp    ( .>*d%U
 
 
 |FF$F77
 
1 4xxxxxxr4   r  r{   r   c                     t           j                            d           d}d}d}t          j                            ||||d          }t          j        |d||||f          \  }}|d	k    sJ d
S )z3Additional test cases for rvs for alpha equal to 1.h:rS  r{   r  r  rd   re   r   r  r  r}   N)ri   r   r   r8   r  r   r  )rr   r  r  rd   re   r^   statru  s           r2   test_rvs_alpha1zTestLevyStable.test_rvs_alpha1  s     		y!!!!!%3e'+ " - -,q-%*D#u$=? ? ?a4xxxxxxr4   c                    g d}t           j                            |          \  }}}}t          |ddd           t	          |dd           t	          |dd	           t	          |d
d           |g dz   }t           j                            |          \  }}}	}
t          |d           t          |d           t	          |
dd	           t	          |	dd	           d S )N)wgr  r   r   r   r   羼 u?r  r  r  r  67',?r  r  r  r  tA}˜.?r  r  r  r  Gz?r   r}   re  )\(̿rf   gۧ1?r   g9]c?)r  r  r  r  r  r   gv?r  )r8   r  r  r   r   r   rr   r^   alpha1beta1loc1scale1r  alpha2beta2rR  rS  s              r2   r  zTestLevyStable.test_fit  s   
 
 

 ',&7&A&A!&D&D#tV148888E4+++FGQ///'1	
 	
 	

 9999&+&7&A&A"&E&E#tVVQUBFFA...D&!,,,,,r4   zUnknown problem with fitstart.r  zalpha,beta,delta,gamma)r  r5  rf   r   )rS  r5  rf   r   parametrizationc                     |t           j        _        t           j                            ||||dd          }t           j                            |          }|\  }}	}
}t          ||||g||	|
|gd           dS )z7Test that fit agrees with rvs for each parametrization.r4  r   r  r}   r   N)r8   r  r  r   r  r   )rr   r  r  r  r_  r  r   r   	alpha_obsbeta_obs	delta_obs	gamma_obss               r2   test_fit_rvszTestLevyStable.test_fit_rvs-  s     -<) $$4U%e$ % 
 
 ))$//471	8Y	D%')Y7	
 	
 	
 	
 	
 	
r4   c                 x   t          j        g d          }t          j                            |          \  }}}}t          j                            |           \  }}}}	t          |d           |dk    sJ t          ||           t          ||            t          ||            t          |	|           d S )Nr   r   r   r   r_   r_   r_   r9  r9  r`   r`   r   r   )ri   r   r8   r  r  r   r   )
rr   r^   r  r  r  r  r  r  rR  rS  s
             r2   test_fit_beta_flipz!TestLevyStable.test_fit_beta_flipF  s    H???@@&+&7&A&A!&D&D#tV&+&7&A&A1"&E&E#tVUAqyyyyFF+++EE6***D4%(((FF+++++r4   c                 V   d}t          j        g d          }t          j                            |           \  }}}}t          j                            | |z             \  }}}	}
t          ||           t          ||           t          |	||z              t          |
|           d S )Nr   r  )ri   r   r8   r  r  r   )rr   SHIFTr^   r  r  r  r  r  r  rR  rS  s              r2   test_fit_delta_shiftz#TestLevyStable.test_fit_delta_shiftR  s    H???@@&+&7&A&A1"&E&E#tV&+&7&A&A1"u*&M&M#tVFF+++E5)))D$,///FF+++++r4   c                    g d}t           j                            |          \  }}}}|dk     sJ d|             |t          |          k     sJ dt          |           d|             g d}t           j                            |          \  }}}	}
|dk    sJ d|             |	t	          |          k    sJ dt	          |           d|	             d S )	N)r   r   r   r   r_   r_   r_   r9  r9     r  r   zExpected alpha < 1, got zExpected loc < z, got )r   r   r   r   r_   r_   r_   r9  r9     r  zExpected alpha > 1, got zExpected loc > )r8   r  r  r-  ro  r  s              r2   test_fit_loc_extrapz"TestLevyStable.test_fit_loc_extrap]  s    666&+&7&A&A!&D&D#tVzzz>f>>zzzc!ff}}}DADDdDD}}}777&+&7&A&A"&E&E#tVzzz>f>>zzzc"gg~~~FRFFFF~~~~~r4   z pct_range,alpha_range,beta_range)r}   r{   r!  )r\   r   rf   )r   r   r   )r}   r  r{   r  r!  )r\   r{   r   r  rf   )gr   r   r}  r  r   )r}   r  r\   rk  ffffff?r{   ?r   r   r  r!  r\   rf   r
  r      c                 t   |}t          j                    }|j        dk    o
|j        dk    d                    |j        |j        |j        g          }ddfdgddfd	gddfd
gddfdgddfdgddfdgg}t          |          D ]\  }	\  }
}}|
t          j        _	        || ||                   n|}t                      5 }|                    t          d           t          j                            |d         |d         |d         dd          }t          j        d          5  t!          |g d|t          j        ||d         z
            t          j        ||d         z
            t          j        |d                   z  g          }ddd           n# 1 swxY w Y   ||d         |k    t          j        |          z           }d|	 d |
 d!| d"|j        j         d#| 
}t+          ||d         ||d$%           ddd           n# 1 swxY w Y   dS )&z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnir  c           	      r   t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    | d         dk    z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    t          j        | d         d	d
g          z  z  | d         dk    t          j        | d         ddg          z  z  | d         dk    t          j        | d         ddg          z  z  | d         dk    t          j        | d         ddg          z  t          j        t          j        | d                   g d          z  z  | d         dk    t          j        | d         dg          z  t          j        t          j        | d                   dg          z  z  | d         dk    t          j        | d         ddg          z  t          j        t          j        | d                   g d          z  z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    | d         dk    z  | d         dk    z  z  | d         dk    t          j        | d         dg          z  t          j        t          j        | d                   g d          z  z  | d         dk    t          j        | d         ddg          z  t          j        t          j        | d                   g d          z  z  | d         dk    t          j        | d         d	d
g          z  t          j        t          j        | d                   ddg          z  z  | d         dk    z   z  S )Npctr  r  r   r{   r   r8  r5  r}   r!  r}  r  r  r  r\   rk  r   )r{   r  r  r  r  )gٿ333333ӿr}  r5  r{   r  rS  r\   r  r}  r5  )r   r   rS  r  r  )ri   isinr   r  alpha_range
beta_range	pct_ranges    r2   rO   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s   GAeHi00GAgJ445GAfIz223
 vY!^uX_. vY#-wZ3.0uX_. wZ3.GAeHsCj99: wZ3.GAeHsCj99:$ wZ3.GAeHr2h778%, wZ3.GAeHsCj99:GBF1V9$5$5|||DDE-6 wZ3.GAeHrd334GBF1V9$5$5t<<=7@ wZ3.GAeHsCj99:GBF1V9$5$57M7M7MNNOA#J wZ3.vY#-/uX-/K(T wZ3.vY$.0uX-/U-^ wZ3.vY#-/uX-/_2h wZ2-GAeHrd334GBF1V9$5$57G7G7GHHIi7r wZ2-GAeHsCj99:GBF1V9$5$5|||DDEs<| wZ2-GAeHsCj99:GBF1V9$5$5RyAAB}AF 7s*GC,EH r4   r~  r-  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )Nr  r  r  r  rS  ri   r  r  s    r2   rO   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  sq    GAeHi00GAgJ445GAfIz223 wZ#%' wZ2%	' r4   c                     | d         dk     z  t          j        | d                   z  dv z  t          j        | d                   z  S )Nr  rS  r  r  r  )r  r  r  is_linux_32r  s    r2   rO   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s_    wZ2%$_&GAeHi001 ;&( GAfIz22	3 r4   g&.=c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  S )Nr  r  r  r  r  r  s    r2   rO   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s^    GAeHi00GAgJ445GAfIz223 wZ3&( r4   fft-simpsonr  c                     | d         dk    t          j        | d                   z  t          j        | d                   z  t          j        | d                   z  S )Nr  r  r  r  r  r  s    r2   rO   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  s^    wZ3&GAeHi001GAgJ445 GAfIz223 r4   r  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk     z  S )Nr  r  r  r   r  r  r  s    r2   rO   z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>  sp    GAeHi00GAgJ445GAfIz223 wZ!^% wZ#%	' r4   Nz2Density calculations experimental for FFT method.*r^   r  r  r   r   re   rd   r\  rq  calcabserrrelerrru  r  z	pdf test  failed with method 'z' [platform: z]

Ferr_msgverbose)platformunamesystemmachinejoin	processorr  r8   r  r  r   recordry  rh   ri   ri  r   r   isnanr   r"  r   )rr   r  r  r  r  r   r  platform_desctestsixdefault_methodr   filter_funcsubdatasupru  subdata2failuresmessager  s     ```              @r2   test_pdf_nolan_samplesz%TestLevyStable.test_pdf_nolan_samplesi  s   4 %   lg-I%-62I\5=%/:< < t J J J J J JL^ U % % % % % % U % % % % % % % W ' ' ' ' ' ' t & & & & & & t & & & & & &kC
L "+5!1!1*	 *	 B 3AE0 + 7 ;;t,,  =A "$$ %

"H   %))CLG$FO *   [h/// 	 	0444F1ws|#344F1ws|#344rvgcl7K7KK   H	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 $H%-(1++
W W W W W"/W W4<N4HW WLTW W   CL#!   ?% % % % % % % % % % % % % % %*	 *	s9   A'H+A(F8,H+8F<<H+?F< AH++H/	2H/	c                    |}ddfdgddfdgddfdgdd	fd
gddfdgddfdgg}t          |          D ]\  }\  }}	}
|t          j        _        |
| |
|                   n|}t	                      5 }|                    t          d           t          j                            |d         |d         |d         dd          }t          j	        d          5  t          |g d|t          j        ||d         z
            t          j        ||d         z
            t          j        |d                   z  g          }ddd           n# 1 swxY w Y   ||d         |	k    t          j        |          z           }d| d| d|j        j         d| }t          ||d         |	|d !           ddd           n# 1 swxY w Y   dS )"z4 Test cdf values against Nolan's stablec.exe output.r~  r&  c                    t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    t          j        | d         g d          z  | d         dk    z  | d         dk    t          j        | d         g d          z  | d         dk    z  z   z  S 	Nr  r  r  rS  )r  r  r  r}   r\   r  r}  r!  r  r  s    r2   rO   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>^  s    GAeHi00GAgJ445GAfIz223
 wZ2-GAfI/A/A/ABBCuX-/
 wZ2-GAfI??@uX-/	 r4   r  c                    t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    t          j        | d         g d          z  | d         dk    z  z  | d         dk    t          j        | d         g d          z  | d         dk    z  z  S r  r  r  s    r2   rO   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>s  s    GAeHi00GAgJ445GAfIz223 7r)&	+=+=+=>>?5T)+	 7r)&	???;;<5T)+ r4   r  r  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  S )Nr  r  r  333333?r  r  s    r2   rO   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  s^    GAeHi00GAgJ445GAfIz223 wZ#%' r4   r  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )Nr  r  r  r  r  r  r  s    r2   rO   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  q    GAeHi00GAgJ445GAfIz223 wZ#%' wZ3&	( r4   rd  c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )Nr  r  r  rZ  r  r  r  s    r2   rO   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  r  r4   r}   c                     t          j        | d                   t          j        | d                   z  t          j        | d                   z  | d         dk    z  | d         dk    z  S )Nr  r  r  rS  rZ  r  r  s    r2   rO   z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>  r  r4   Nz[Cumulative density calculations experimental for FFT method. Use piecewise method instead.*r^   r  r  r   r   r  r\  rq  r  ru  r  z	cdf test r  z'
r  Fr  )r  r8   r  r  r   r  ry  rp   ri   ri  r   r   r  r   r"  r   )rr   r  r  r  r  r   r  r  r  r   r  r  r  ru  r  r  r  s     ```            r2   test_cdf_nolan_samplesz%TestLevyStable.test_cdf_nolan_samplesA  s   2 % U % % % % % %, T $ $ $ $ $ $& t & & & & & & t & & & & & & t & & & & & & t & & & & & &GL
\ "+5!1!1(	 (	 B 3AE0 + 7 ;;t,,  =A "$$ #

"@  
 %))CLG$FO *   [h/// 	 	0444F1ws|#344F1ws|#344rvgcl7K7KK   H	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 $H%-(1++Ar A A A A&n2A A6>A ACL#!   ;# # # # # # # # # # # # # # #(	 (	s9   A'G2A(E&G&E**G-E*.AGG	G	r  r   rX  rh   rp   c                    t          j                    }|j        dk    odt          j                    d         v }|r|dk    rt	          j        d           |}dt          j        _        dt          j        _	        ||d         |k             }d| t          j        _
        |d	v sJ |dk    rt          j        j        nt          j        j        } ||d
         |d         |d         dd          }	t          |	||         d           dS )zGTests for pdf and cdf where loc, scale are different from 0, 1
        r  32bitr   rh   z4Test unstable on some platforms; see gh-17839, 17859r~  r  S)rh   rp   r^   r  r  rf   r   r  r  N)r  r  r  architecturer   r   r8   r  r  r  r  rh   rp   r   )
rr   r  r  rX  r  r  r   r  r.  r  s
             r2   test_location_scalez"TestLevyStable.test_location_scale  s      lg-W'X=R=T=TUV=W2W  	P45==KNOOO* 0;,/:,tG}-.-8[[*~%%%%%)U]]E!!8I8M 	 XCL''*GFO1!
 
 
 	GDM400000r4   zmethod,decimal_placesr  r   r~  c           	         t          j        g d          }t          j        g d          }t          j        g d          }t          j        d          5  t                      5 }|                    t
          d           |t          j        _        t          j        	                    |d|dd	
          }t          ||||           ddd           n# 1 swxY w Y   ddd           dS # 1 swxY w Y   dS )z sample points extracted from Tables and Graphs of Stable
        Probability Density Functions - Donald R Holt - 1973 - p 187.
        )r   r   r   r   r   r   r   r   rf   rf   rf   rf   r   r   r   r   r   r   r   r   )gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g?gDioɴ?g r?gH?g+?gHPs?gX ?g&?g0*?gv/?ga2U0*?)r   rk  r{   r   r   rk  r{   r   r   rk  r{   r   r   rk  r{   r   r   rk  r{   r   r\  r   zDensity calculation unstable.*)categoryr  r   r   r  N)ri   r   ri  r   rR   ry  r8   r  r  rh   r   )rr   rL  decimal_placesxsdensitybetasr  rh   s           r2   'test_pdf_alpha_equals_one_beta_non_zeroz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zero  s    XHHH
 
 (  
 
   
 
 [X&&& 
	 
	(9(;(; 
	sJJ'8     4:E0#''AuA1'EECWnf  
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	 
	s7   C/'A$CC/C	C/C	C//C36C3zparams,expected)r  r  r   r   )rf   r   r_   r  )r_   rC  r   r   c                     t           j                             |d         |d         |d         |d         d          }t          ||           d S )Nr   r   rf   r   r\  r  )r8   r  r   )rr   rq  rW   observeds       r2   ra  zTestLevyStable.test_stats  sU     $**1IvayfQivay + 
 
 	Hh/////r4   r  )rk  r{   r   zfunction,beta,points,expectedrS  rW  r_   r   r"  r  c                     d|cxk     rdk     sn J t           ||||          t          j        t          |          |                     dS )a\  Ensure the pdf/cdf routines do not return nan outside support.

        This distribution's support becomes truncated in a few special cases:
            support is [mu, infty) if alpha < 1 and beta = 1
            support is (-infty, mu] if alpha < 1 and beta = -1
        Otherwise, the support is all reals. Here, mu is zero by default.
        r   r   r  r  N)r   ri   r  r  )rr   r  r.  r  r  rW   s         r2   !test_distribution_outside_supportz0TestLevyStable.test_distribution_outside_support)  se    P 5}}}}1}}}}}}HV5t444GCKK**	
 	
 	
 	
 	
r4   zx,alpha,beta,expected))r   /iZ?s0?gz5F?)r   ~H?|/mg>m?)r   .d5?L,ٿg깃\?)r   >?ЀjoؿgA]4?)r   pa2?Յ пgqQ?c                     dt           j        _        t          t           j                            |||          |           dS )a  Test pdf for x equal to zeta.

        With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0
        will be close to zeta.

        When case "x equal zeta" is not handled properly and quad_eps is not
        low enough: - pdf may be less than 0 - logpdf is nan

        The points from the parametrize block are found randomly so that PDF is
        less than 0.

        Reference values taken from MATLAB
        https://www.mathworks.com/help/stats/stable-distribution.html
        Afc=r  Nr8   r  r  r   rh   rr   r^   r  r  rW   s        r2   test_x_equal_zetaz TestLevyStable.test_x_equal_zetaW  sJ    Z &-"!!!5t!<<	
 	
 	
 	
 	
r4   )
)r  r  r  gz¶?)r  r  r  gV?)r  r  r  gRE)3\?)r  r  r  gB?)r  r  r  g/^?)-C6r  r  gH?)r  r  r  gn?)r  r  r  gx\?)r  r  r  gVM%?)r  r  r  gm?c                     dt           j        _        t          t           j                            |||          |           dS )a  Test pdf for x near zeta.

        With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0
        will be close to zeta.

        When case "x near zeta" is not handled properly and quad_eps is not
        low enough: - pdf may be less than 0 - logpdf is nan

        The points from the parametrize block are found randomly so that PDF is
        less than 0.

        Reference values taken from MATLAB
        https://www.mathworks.com/help/stats/stable-distribution.html
        r  r  Nr  r  s        r2   test_x_near_zetazTestLevyStable.test_x_near_zeta  sJ    D &-"!!!5t!<<	
 	
 	
 	
 	
r4   N)&r   r   r   r   r;  r  r  r  r  r   r   r   r  rI  r   r  r  r  r  r  r  r  ri   rX  r  r  r  r	  r  r  ra  r8   r  rp   rh   r  r  r   r:   r4   r2   rz  rz    s       V^D!!!B B "!B ^  ^B ^) ) ^)V ^  ^ [[FLlfl4v{7GHHH
 
 [/$>>[CCC  []VV,<==  >=  ?>  $ [[Vc1X..
 
 /. 
- - -0 [>??[ 	
  [D$< 
 
   @?

, 
, 
,	, 	, 	,
G 
G 
G [[*FL

 
 FL(((###(((k&	   FLDDDCB''B2&&k'	  -
 *@ @+  ,@D [*FL

 
 FL(((###(((k&	   FLDDDCB''B2&&k'	  -
 *z z+ *zx [Wq!f--[VeU^441 1 54 .-1@ [AJ!	
   @ [!RVRVRV!<=/	
 0 0 0 [W&7&7&788[' !%CB''	 !%CB''	 !%Ar2&&	 !%Ar2&&	'	
 :
 
;  98<
  [&	
 	
 	
) 8
 
9 8
0 [[	
 	
 	
  
 
!  "
 
 
r4   rz  c                       e Zd Zd Zd ZdS )TestArrayArgumentc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestArrayArgument.setup_method  r7  r4   c                     t           j                            t          j        d          t          j        d          d          }t          |j        d           d S )Nr   rD  r  )r8   r  r   ri   r  r?  r   rA  rr   r   s     r2   test_noexceptionz"TestArrayArgument.test_noexception  sK    jnn")A,,rwqzz")  + +SY(((((r4   N)r   r   r   r6  r&  r:   r4   r2   r"  r"    s2          ) ) ) ) )r4   r"  c                       e Zd Zd Zd ZdS )TestDocstringc                    t           j        j        2t          dt           j        j                                        v            t           j        j        4t          dt           j        j                                        v            d S d S )Nr*  r  )r8   r*  r  r	   lowerr  rw   s    r2   test_docstringszTestDocstring.test_docstrings  sn    >!-J%."8">">"@"@@AAA?".K5?#:#@#@#B#BBCCCCC /.r4   c                 R    t          j                     t          j                     d S ru   )r8   rE   rD   rw   s    r2   test_no_name_argzTestDocstring.test_no_name_arg  s&    r4   N)r   r   r   r+  r-  r:   r4   r2   r(  r(    s5        D D D    r4   r(  c                     t          g d          } t          | dk    | d          \  }}t          |g d           t          |dg           t          ddk    | d          \  }}t          ||            t          |dgt          j        |           z             t          | dk    | d          \  }}t          ||            t          |dgt          j        |           z             d S )N)r   r   rf   r   rf   r   r   r   rf   )r   rf   rf   r   r   r   )r   r   r   ri   r   r0   r1   r  s      r2   test_args_reducer0    s    ###$$Aa!eQ""DAqq///***q1#a!eQ""DAqq!q1#

*+++a!eQ""DAqq!q1#

*+++++r4   c                   R   e Zd Zg dZd Zg dZej                            de	          d             Z
d Zd Zd Zd	 Zd
 Zd Zd Zej        j        ej                            dddg          d                         Zej                            dddg          d             ZdS )TestFitMethod)ncfr  r  	irwinhallc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestFitMethod.setup_method  r7  r4   )r  r  ry  r4  z	dist,argsc                 t   || j         v rt          j        d|z             t          j        dddddt          j        g          }t          j        dddddt          j        g          }t          t          |          }t          t          |j        |d           t          t          |j        |d           d	S )
r  z"%s fit known to fail or deprecatedr  r  r  r  r  r   r  N)fitSkipNonFiniter   r   ri   r   r  r  r-  r8   r  r  r   )rr   rA   r/  r^   r  distfuncs         r2   !test_fit_w_non_finite_data_valuesz/TestFitMethod.test_fit_w_non_finite_data_values  s     4(((K<tCDDDHfffffbfEFFHfffffbfEFF5$''j(,!<<<<j(,!<<<<<<r4   c           
         t           j                            d           t          j        d          5  t          j                            dddd          }t          j        t          j        |          t          j        d          z
  d	z  	                                          }t          t          j        t          j                            |d
d                    |d
dgd           d d d            d S # 1 swxY w Y   d S )Ni90  r\  r  rk  r         4@r
  r:  rf   r   r  r  r   )ri   r   r   ri  r8   r'  r   r%  r  r   r   r   r   )rr   r^   expected_shapes      r2   test_fix_fit_2args_lognormz(TestFitMethod.test_fix_fit_2args_lognorm  s>   
	u[X&&& 	@ 	@!!$Dr!::AWrvayy26"::'=&A%G%G%I%IJJNBHU]%6%6qq%6%L%LMM+Q3$@ @ @ @	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@s   B;C==DDc                    t          j        dd          }t          j                            |          \  }}t          |d           t          |t          j        d                     t          j                            |d          \  }}t          |d           t          |t          j        d                     t          j                            |d          \  }}t          |d           t          |d           d S )Nr   r  r   rf   r   r  )ri   r  r8   r  r   r   r%  r   rr   r^   rd   re   s       r2   test_fix_fit_normzTestFitMethod.test_fix_fit_norm  s    IaOOZ^^A&&
UC###E271::...Z^^AA^..
US!UBGAJJ'''Z^^Aa^00
UC###UAr4   c                    t          j        dd          }t          j        |                                          }d}t          j                            ||          \  }}}t          j        |                                          |z
  }t          t          j        |          t          j	        |          z
  |d           t          ||           t          ||                                |z  d           d}d}t          j                            |||          \  }}}t          ||           t          ||           t          ||                                |z  d           d	}d}t          j                            |||          \  }}}t          ||           t          ||           t          ||                                |z  d           d}d	}	t          j                            |||	
          \  }}}t          ||           t          ||	           |t          j        |	          z
  }
t          t          j	        |          |
           d S )Nr   r  r   r   r   rV  rD  r   r   rf   r  )ri   r  r  r   r8   r_  r   r   r   digammar   )rr   r^   meanlogr   r0   rd   re   rN   r   r   r  s              r2   test_fix_fit_gammaz TestFitMethod.test_fix_fit_gamma
  s   IaOO&)).."" 553F16688w&BF1II(:(::AqIIIIS$E16688A:q9999
 bt<<3QS$E16688A:q9999bt<<3QS$E16688A:q9999 VDD3S$UF###bfVnn$GOA..22222r4   c           	         d }t          j        g d          }t          j                            |dd          \  }}}}t          |d           t          |d           t           ||||          ddgd           t          j        g d          }t          j                            |ddd	          \  }}}}t          |d           t          |d           t          |d            ||||          \  }}t          |dd
           d|z
  }	t          j                            |	ddd          \  }
}}}t          |d           t          |d           t          |d            ||
||	          \  }}t          |dd
           t          |
|           t          t          t          j        j        |dd           t          j        g d          }t          t          t          j        j        |dd           t          t          t          j        j        |ddd           t          t          t          j        j        |ddd           t          t          t          j        j        |dddd           d S )Nc                 h   t          |          }t          j        |                                          }t          j        d|z
                                            }t	          j        | |z             }||| t	          j        |           z   z  z
  ||| t	          j        |          z   z  z
  g}|S r   )r  ri   r  rl  r   psi)r0   r1   r^   rt  s1r  psiabr   s           r2   mlefuncz0TestFitMethod.test_fix_fit_beta.<locals>.mlefunc3  s     AAB!""BKA&&Eufw{1~~566ufw{1~~5668DKr4   )r  rk  r{   r   r   r  r  r   rf   )r   r   r   r  )r  r   r   r{   r  )r   r   r   )r   r   r  r   )r   r  r   r   )
ri   r   r8   r  r   r   r   r   r  r  )rr   rK  r^   r0   r1   rd   re   dadbr  rQ  b2rR  rS  r  s                  r2   test_fix_fit_betazTestFitMethod.test_fix_fit_beta0  s   		 		 		 H'''(( :>>!!A>>>1c5S!UA1a((1a&t<<<< H'''(( :>>!!>DD1c5QS!UAAq!!BAD)))) U$z~~bQQq~IIBfRT1VQR$$BAD))))B""" 	j%*.!#aHHHHHZZZ  j%*.!!AFFFFj%*.!!A!LLLLj%*.!!A!LLLL 	j%*.!aQ	( 	( 	( 	( 	( 	(r4   c                    t          j        g d          }t          j                            |          \  }}t          |d           t          |d           t          j                            |d          \  }}t          |d           t          |d           t          j                            |d          \  }}t          |d           t          |d           d S )N)rf   rf   r   r   r   r   r   rD  rf   r   r  r   r   r   )ri   r   r8   r  r   r   r?  s       r2   test_expon_fitzTestFitMethod.test_expon_fitg  s    H---..[__Q''
US!UA[__Qq_11
US!UA[__QQ_//
US!UAr4   c           	         t          j        g d          }t          j        |dz
            }t          j                            |d          \  }}}t          ||                                d           t          |d           t          |t          j	        |
                                          d           t          j                            |dd          \  }}}t          |t          j        |t          j        d          z
  dz  
                                          d           t          |d           t          |d           t          j                            |dd	
          \  }}}t          |d	           t          |d           t          |t          j	        |
                                          d           d S )N)r  r   r_   r>     r  r   r   r  r   r  r  rf   r   )r   fix_s)ri   r   r  r8   r'  r   r   rz  r   r   r   r%  )rr   r^   lnxm1rA  rd   re   s         r2   test_lognorm_fitzTestFitMethod.test_lognorm_fitv  s   H---..q1u!M--aa-88sEuyy{{7777S!rvejjll33%@@@@!M--aa-BBsErw):Q(>'D'D'F'FGG"	$ 	$ 	$ 	$S!UA!M--aat-DDsEUD!!!S!rvejjll33%@@@@@@r4   c                    t          j        g d          }t          j                            |          \  }}t          ||                                           t          |t          j        |                     t          j                            |d          \  }}t          |d           t          ||                                           t          j                            |d          \  }}t          |d           t          |d           t          t          t          j        j        |d           t          t          t          j        j        |d           d S )N)rS  r  r        "@r   r   r_   r  r   rT  )ri   r   r8   ry  r   r   r-  rl  ro  r  r  r?  s       r2   test_uniform_fitzTestFitMethod.test_uniform_fit  s#   H)))**]&&q))
US!%%''"""UBF1II&&&]&&qq&11
US!UAEEGG$$$]&&q&44
US!UBj%-"3QSAAAAj%-"3QsCCCCCCr4   rL  MLEMMc           
      `   d\  }}t           j                            ||dd          }t           j                            |d|          }t           j                            |d|          }t	          ||dd	           t           j                            |d|
          }t	          ||dd	           t           j                            |d|          }t           j                            |d|          }t	          ||dd	           t           j                            |d|          }t	          ||dd	           t          t          t           j        j        |dd|           t          t          t           j        j        |dddd|           t           j                            |ddd|          }	|	\  }
}}}t          |
||gg d           d}t           j                            |d          }t           j                            |||          \  }
}}t          |
|           d S )N)r[  r  r`   r   r   r[  )r   rL  )r  rL  r  r  )r  rL  r  )r  rL  )rL  rL  )rK  rL  r   rf   )r  r   rL  r   r   )r  r  r   r   rL  )r  r   r   rL  )r[  r   r   r:  )	r8   r  r   r   r   r  r  r   r_  )rr   rL  r0   r1   r^   res_1res_2res_3res_4res_5aabbrG  ssr   s                  r2   test_fshapeszTestFitMethod.test_fshapes  s   
 1JNN1acN==
qR77
qR77u5u====
q6::u5u====
qR77
qR77u5u====
q6::u5u==== 	j%*.!aOOOO 	j%*.!aQv	7 	7 	7 	7
 
qRa&IIBBb"b\:::... {qs++[__Ta_??
BRr4   c                     t           j        }|                    dd          }t          d          }t	          t
          |j        |fi |d|i d S )Nrf   r`   )r  r   i)enikibenikirL  )r8   r  r   r  r  r  r   )rr   rL  rA   r   r.  s        r2   test_extra_paramszTestFitMethod.test_extra_params  s]     xx!#x&&t$$$i4FF3FFvFFFFFFr4   N)r   r   r   r   r6  r7  r   r   r   r   r9  r=  r@  rE  rO  rQ  rV  rY  r   re  rh  r:   r4   r2   r2  r2    sW       111D   A@@[[(33= = 43=@ @ @  $3 $3 $3L5( 5( 5(n  A A A(D D D$ [[Xt}55$ $ 65 $L [Xt}55G G 65G G Gr4   r2  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )
TestFrozenc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestFrozen.setup_method  r7  r4   c                    t           j        }t          j        dd          }|                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                    d          }|                    ddd          }t          ||           |                                }|                    dd          }t          ||           |	                                }|	                    dd          }t          ||           |
                                }|
                    dd          }t          ||           |                                }|                    dd          }t          ||           |                                }|                    dd          }t          ||           |                    d          }|                    ddd          }t          ||           t          |j        |j                   t          |j        |j                   d S )Nr  r[  rc   r;  rk  rf   )r8   r  rh   r   rp   r   r  r   r  r   r  rz  rG   r  r0   r1   )rr   rA   frozenresult_fr  s        r2   r  zTestFrozen.test_norm  s   zC000::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&99T??4s33Xv&&&==??S11Xv&&&;;==t3//Xv&&&::<<d#..Xv&&&::<<d#..Xv&&&>>##$c22Xv&&&==##QD44Xv&&&VXtv&&&VXtv&&&&&r4   c                    d}t           j        }t          j        |          }|                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                    d          }|                    d|          }t          ||           |                                }|                    |          }t          ||           |	                                }|	                    |          }t          ||           |
                                }|
                    |          }t          ||           |                                }|                    |          }t          ||           |                                }|                    |          }t          ||           |                    d          }|                    d|          }t          ||           t          |j        |j        j                   t          |j        |j        j                   d S )Nr   r;  rk  r  rf   )r8   r_  rh   r   rp   r   r  r   r  r   r  rz  rG   r  r0   rA   r1   )rr   r0   rA   rm  rn  r  s         r2   
test_gammazTestFrozen.test_gamma	  sa   {Q::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&99T??q!!Xv&&&==??QXv&&&;;==1Xv&&&::<<!Xv&&&::<<!Xv&&&>>##aXv&&&==##Q""Xv&&&VXv{}---VXv{}-----r4   c                     t          j        d          }|                    d          }|                     d           |                    d          }t          ||           d S )Nr   rf   r\  r]  )r8   r'  r  r   )rr   rm  m1r  s       r2   test_regression_ticket_1293z&TestFrozen.test_regression_ticket_1293=  sa    q!!]]1V$$$ ]]1 	Rr4   c                 l   d}t          j        |          }|j                            |          \  }}t	          ||gddg           d}t           j                            d|           t	          |j                            |          dt          j        g           d}t          j        |          }|j                            |          \  }}t	          ||gddg           d}t           j                            d|           t	          |j        j        |j        j	        ft           j                            |                     t          j        d          }t          |j        |j        u           dD ]}t          j        |          }t          j        |          }|j        |j	        }}t	          |d           t          t          j        |                     t          j        d          }t           j                            |          \  }}t          ||gdd	g           d S )
Nr  rt  r   r  r\   r   rm  rn  r{   )r8   ro  rA   rp  r   rh   ri   r  r0   r1   r	   r   rq  r   )rr   r  rv  r0   r1   rv1s         r2   rr  zTestFrozen.test_abL  s    _q!!!w##A&&1aVb#Y'''A###RW))!,,q"&k:::_q!!!w##A&&1aVb#Y'''Aq!!!bgi+U_-I-I!-L-LMMMo$$$'(((  
	/ 
	/A
1A1%%%B4qABBKNN### 
3A?//22DAqQFRI....
	/ 
	/r4   c                 T    t          t          t          j        d                     d S )N	rv_frozen)r	   r/   r8   r9   rw   s    r2   test_rv_frozen_in_namespacez&TestFrozen.test_rv_frozen_in_namespacex  s#    +[99:::::r4   c                    t          j                    }t          t          |d                     d|_        t          |j                                        t          j        	                    d                                                     t          j        	                    d          }|
                    d|           d S )Nr   *   r   rD  r   )r8   r  r	   r/   r   r   	get_stateri   r   r,  r   )rr   rm  rndms      r2   test_random_statezTestFrozen.test_random_state|  s    //000 !V(2244Y**2..88::	< 	< 	< y$$T**


-----r4   c                    t          j        dd          }t          j        d          }t          j        g dg df          }|||fD ]}d|_        |                    d	           t          j        |          }|                    d	          }t          j        |          }|                    d	          }t          ||           |
                    d
          |
                    d
          g}	t          |	d         |	d                    t          |                    |	d                   |                    |	d                              d S )Ngdsz@g@e?r[  )r   r   rf   r   r  r  r   rD  r:  r{   r   r   )r8   r  r  rD   r   r   pickledumpsloadsr   r   rp   )
rr   r  poissr  distfnrN   r0	unpickledr1medianss
             r2   test_picklingzTestFrozen.test_pickling  s[    z,.ABBb!!"<<<+?+?+?+A B B B UF+ 	4 	4F"&FJJAJV$$A##BQIA&&BR    zz#	c(:(:;GWQZ000GAJ//"wqz224 4 4 4	4 	4r4   c           
         d }t          j        ddd          }t          j        dd          5  |                    |ddd	
          }t           j                            |dddddd	          }d d d            n# 1 swxY w Y   t          ||           t          j        dd          }|                    |          }t           j                            |dd          }t          ||           d S )Nc                     | S ru   r:   r   s    r2   r   z$TestFrozen.test_expect.<locals>.func  s    Hr4   rf   r   r   rl  r\  )r^  divider   T)r   ubconditionalrf   r/  rd   re   r   r  r  r  )r   r/  rd   )r8   r_  ri   ri  r   r   r  )rr   r   gmgm_val	gamma_valru  p_valpoisson_vals           r2   test_expectzTestFrozen.test_expect  sQ   	 	 	 [1!1---[(;;; 	I 	IYYtaTYBBF**4d./A4 + I II	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 		***M!###m**4d*BB{+++++s   A A==BBN)r   r   r   r6  r  rp  rs  rr  rx  r}  r  r  r:   r4   r2   rj  rj    s          1' 1' 1'f2. 2. 2.h  */ */ */X; ; ;. . .4 4 40, , , , ,r4   rj  c                   b    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd ZdS )
TestExpectc                 @   t           j                            d dd          }t          |dd           t           j                            d dd          }t          |dd           t           j                            d	dd          }t           j                            d
dd          }t           j                            d dd||          }t          |dd           t           j                            d dd||d          }t          |dd           d S )Nc                     | dz
  | dz
  z  S )Nr   r:   r   s    r2   rO   z&TestExpect.test_norm.<locals>.<lambda>  s    1qs r4   r   rf   rc   r   r  rV  c                     | S ru   r:   r   s    r2   rO   z&TestExpect.test_norm.<locals>.<lambda>  s     r4   r  r  c                     dS r   r:   r   s    r2   rO   z&TestExpect.test_norm.<locals>.<lambda>      Q r4   rd   re   r   r  r   c                     dS r   r:   r   s    r2   rO   z&TestExpect.test_norm.<locals>.<lambda>      a r4   Trd   re   r   r  r  rS  )r8   r  r   r   r   )rr   r`  r_  r   r  prob90prob90cs          r2   r  zTestExpect.test_norm  s   J33!DDAq"----Jmm!<<Aq"----Z^^Daq^11Z^^Daq^11"";;AQ2""MMFC4444*##KKQaB204 $ 6 6GR444444r4   c           	      R   t           j                            d ddd          }t          |dd           t           j                            d	 dd
d          }t          |dd           t           j                            ddddd          }t           j                            ddddd          }t           j                            d dd
d||d          }t          |dd           t           j                            d ddd||d          }t          |dd           d S )Nc                     | dz
  | dz
  z  S )NUUUUUU@r:   r   s    r2   rO   z&TestExpect.test_beta.<locals>.<lambda>  s    51U7(; r4   rD  r   rf   )r/  rd   re   qq?r)  rV  c                     | S ru   r:   r   s    r2   rO   z&TestExpect.test_beta.<locals>.<lambda>  s     r4   rT  r   r  r  r_   rc   r  c                     dS )NrS  r:   r   s    r2   rO   z&TestExpect.test_beta.<locals>.<lambda>  s    R r4   )r_   r_   Fr  r   c                     dS r   r:   r   s    r2   rO   z&TestExpect.test_beta.<locals>.<lambda>  r  r4   TrS  )r8   r  r   r   r   )rr   r`  r_  r  r   r  r  s          r2   	test_betazTestExpect.test_beta  s=   J;;'"#1  . .Avr2222JkkRrJJAub1111Z^^D"baq^99Z^^D"baq^99""<<hB)+ru # N NFC4444*##KKhA*+rt $ M MGR444444r4   c                 T   t           j                             dddd          \  }}t           j                            d dd          }t          ||d	
           t           j                            d dd          }t          ||d
           t           j                            d dddd	          }t          ||d
           dt           j                            dd	gdddd                                          z
  }t           j                            d dddd          }t          ||d	
           t           j                            d ddddd          }t          |dd
           t           j                            d ddd          }	t          |	dd	
           d S )Nr
  r_   rD  rT  r  c                     | S ru   r:   r   s    r2   rO   z+TestExpect.test_hypergeom.<locals>.<lambda>  r  r4   )r
  r_   rD  r  r)  rV  c                     | dz
  dz  S NrX  rf   r:   r   s    r2   rO   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    adQY r4   r  c                     | dz
  dz  S r  r:   r   s    r2   rO   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    QrTAI r4   r   )r/  rd   r   r  r   c                     dS r   r:   r   s    r2   rO   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    q r4   r  rU  c                     dS r   r:   r   s    r2   rO   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    1 r4   T)r/  rd   r   r  r  c                     dS r   r:   r   s    r2   rO   z+TestExpect.test_hypergeom.<locals>.<lambda>  s    ! r4   r   )r/  r   r  )r8   r  r   r   rO  rl  )
rr   m_truev_truer_  r`  v_bounds	prob_trueprob_boundsprob_bcprob_bs
             r2   test_hypergeomzTestExpect.test_hypergeom  s    ..r2qb.AAO"";;[b"IIAvr2222O""#6#6[') # + +Avr2222 ?))*=*=/:.0Q2 * ? ? 	Hfb9999 eo))1b'2r1!)DDHHJJJ	o,,[[{13b - B BKB???? /((;B,-"$ ) H HGQ3333 ''++, ( 4 4FAr222222r4   c                 $   t           j                            d ddd          }dt           j                            dd          z
  }t	          ||d	           t           j                            d
 ddd          }t	          |dd	           d S )Nc                     dS r   r:   r   s    r2   rO   z)TestExpect.test_poisson.<locals>.<lambda>  s    Q r4   r  r   F)r/  r   r  r   rf   r  rV  c                     dS r   r:   r   s    r2   rO   z)TestExpect.test_poisson.<locals>.<lambda>  s     r4   T)r8   r  r   rp   r   )rr   r  prob_b_trueprob_lbs       r2   test_poissonzTestExpect.test_poisson  s    m**;;Ta7< + > >))!Q///KbAAAA-&&{{!37 ' 9 9GQ333333r4   c                     t           j        }|                    d          }|                    d           |                    d          }t          ||d           d S )N)r  r  )r{   r  rV  )r8   genhalflogisticr   r   )rr   halflogres1r  s       r2   test_genhalflogisticzTestExpect.test_genhalflogistic
  sa     '~~6~**F###~~6~**D$333333r4   c                 
   t          t          j        t          j                            dd                               t          t          j        t          j                            d d                               t          t          j        t          j                            d d                               t          t          j        t          j                            d d                               d S )Nr	  Gz?c                     dS r   r:   r   s    r2   rO   z/TestExpect.test_rice_overflow.<locals>.<lambda>       r4   )r  r  c                     dS r  r:   r   s    r2   rO   z/TestExpect.test_rice_overflow.<locals>.<lambda>  r  r4   c                     dS Nr   r:   r   s    r2   rO   z/TestExpect.test_rice_overflow.<locals>.<lambda>  r  r4   )r	   ri   r  r8   ricerh   r   rw   s    r2   test_rice_overflowzTestExpect.test_rice_overflow  s     	EJNN35566777EJ--kk-HHIIJJJEJ--kk-HHIIJJJEJ--kk-HHIIJJJJJr4   c                 (   d\  }}t           j                            d |f          }t          |||dz
  z  t	          j        d|z
            z  d           t           j                            d |f|          }t          |||z   d           d S )	N)r}  r   c                     | S ru   r:   r[   s    r2   rO   z(TestExpect.test_logser.<locals>.<lambda>   r  r4   r  rS  r   r   c                     | S ru   r:   r  s    r2   rO   z(TestExpect.test_logser.<locals>.<lambda>&  r  r4   r  )r8   r&  r   r   ri   r  )rr   ru  rd   res_0res_ls        r2   test_logserzTestExpect.test_logser  s    3##KKqd#;;QVrvb1f~~5E	C 	C 	C 	C ##KKqd#DDus{777777r4   c                     d\  }}t           j                            d ||f          }t           j                            d ||f          }t          |||z
  d           t          ||dz  z
  ||z   d           d S )N)r  r  c                     | S ru   r:   r   s    r2   rO   z)TestExpect.test_skellam.<locals>.<lambda>-      A r4   r  c                     | dz  S r  r:   r   s    r2   rO   z)TestExpect.test_skellam.<locals>.<lambda>.  r  r4   r  r   rf   )r8   r  r   r   )rr   rP  p2rr  r  s        r2   test_skellamzTestExpect.test_skellam)  s     B]!!++RH!==]!!..Bx!@@BG%0000RU
BG%888888r4   c           
          d\  }}t           j                            d ||f          }t          |t	          d t          ||          D                       ||z
  z  d           d S )N)r   q   c                     | S ru   r:   r   s    r2   rO   z)TestExpect.test_randint.<locals>.<lambda>6  r  r4   c              3      K   | ]}|V  d S ru   r:   r@   r   s     r2   r  z*TestExpect.test_randint.<locals>.<genexpr>8  s"      55!A555555r4   r   r   )r8   r@  r   r   rl  r  )rr   lohir   s       r2   test_randintzTestExpect.test_randint2  s     Bm"";;R9955uR}}55555bA	O 	O 	O 	O 	O 	Or4   c                 T    t          t          t          j        j        d d           d S )Nc                     | dz  S r  r:   r   s    r2   rO   z&TestExpect.test_zipf.<locals>.<lambda>=  s
    q!t r4   r  )r
   ry  r8   r
  r   rw   s    r2   	test_zipfzTestExpect.test_zipf:  s.    ^UZ%6#^T	+ 	+ 	+ 	+ 	+r4   c                     t           j                            d d          }t           j                            d dddd          }t          ||d	
           d S )Nc                     dS r   r:   r   s    r2   rO   z/TestExpect.test_discrete_kwds.<locals>.<lambda>A  r  r4   r  r  c                     dS r   r:   r   s    r2   rO   z/TestExpect.test_discrete_kwds.<locals>.<lambda>B  r  r4   r3      r  )r/  maxcount	chunksize	tolerancer  rV  )r8   r  r   r   )rr   n0n1s      r2   test_discrete_kwdszTestExpect.test_discrete_kwds?  sd    ]!!++D!99]!!++D+/2 " O OBB//////r4   c                     d }dD ]=}t           j                            d|          }t          | ||          d           >d S )Nc                 H    | dz  d| dz  z  z   d| dz  z  z   d| dz  z  z   | z   S )Nr   r_   r   r  r   r>  rf   r:   r6  s    r2   poiss_moment5z-TestExpect.test_moment.<locals>.poiss_moment5I  s8    q52b!e8#bQh.BE9B>>r4   )r   r#  r   r  r   )r8   r  r  r   )rr   r  r  m5s       r2   test_momentzTestExpect.test_momentF  se    	? 	? 	?  	? 	?B%%a,,BBb 1 1>>>>>	? 	?r4   c                    t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            d          d	           t          t          j                            d
          d
           d S )NrK  rS  rc   r  r_   r\   )   r  r  U   r  )r   r8   r  r   r_  r  rw   s    r2   test_challenging_cases_gh8928z(TestExpect.test_challenging_cases_gh8928P  s     	
))b)<<bAAA
))b)<<bAAA
))b)<<bAAA***77===--"-55r:::::r4   c           	      t   t           j        }|                    dd          }t          |                    dd          |           t          |                    dddd          |           t          |                    dddd          |d	z             t          |                    ddddd
          |           t          |                    dddd          d           t          |                    dddd          d           t          |                    ddddd
          d           d S )Nr_   r   rc   rp  r  r  r+  r  r  Tr  r)  g433333@g433333rU  )r8   ry  r   r   r   )rr   rA   r  s      r2   test_lb_ub_gh15855zTestExpect.test_lb_ub_gh15855Y  sH   }iiBai((!44c:::!bAA3GGG!rBBCGLLL!r04 $ 6 67:	< 	< 	< 	!rBBFKKK!rBBGLLL!r04 $ 6 679	; 	; 	; 	; 	;r4   N)r   r   r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r:   r4   r2   r  r    s        
5 5 5 5 5 5& 3  3  3D	4 	4 	44 4 4K K K
8 
8 
89 9 9O O O+ + +
0 0 0? ? ?; ; ;; ; ; ; ;r4   r  c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestNctc                     t          j        dd          }t          |                    d          d           t          j        dd          }t	          |                    d          dd           d S )Nr   r   r{   r   g K?r_   rV  )r8   nctr   rp   r   r}  s     r2   test_nc_parameterzTestNct.test_nc_parameterp  sc     Yq!__RVVAYY$$$Yq"BFF1II~rBBBBBBr4   c           	          t           j                            dt          j        dd          d d d f         t          j        ddd                    }t          g dg dg dg          }t          ||d	
           d S )Nr   r   r#  r\   r   )gMp^j?g6].ftv?gȳ'ς?gu?)g!Y<a?g]d1p?go|?g?)gHdY?g2Ԥg?g}o/u?g .mr?r  r   )r8   r 	  rh   ri   r  rX  r   r   )rr   r   rW   s      r2   test_broadcastingzTestNct.test_broadcastingx  s    immAryAqqq$w7KQ224 4JJJJJJJJJL M M 	XD111111r4   c                 t    t          j        dd          }t          |                                d           d S )Nr   r   r   )r8   r 	  r   r  r}  s     r2   test_variance_gh_issue_2401z#TestNct.test_variance_gh_issue_2401  s1    
 Yq!__RVVXXs#####r4   c                    t           j                             ddd          \  }}}}t          ||||gt          j        t          j        t          j        t          j        g           t           j                             ddd          \  }}}}t          t          j        |                     t          |||gt          j        t          j        t          j        g           t           j                             ddd          \  }}}}t          t          j        |||g                                                     t          |t          j                   d S )Nr   r}  r\  )r  ncr^  r  r  )r8   r 	  r   ri   r  r	   r  r   rE  s        r2   test_nct_inf_momentszTestNct.test_nct_inf_moments  s	   Y__V_DD
1aaAq\BFBFBFBF#CDDDY__V_DD
1aAaAY 8999Y__V_DD
1aQ1I&&**,,---Qr4   c                    t           j                            dd          }t           j                             dd          }ddg}t          ||d         d           t          ||d           t           j                            dd          }t           j                             dd          }d	d
g}t          ||d         d           t          ||d           d S )Nr   rf   g@ @g*dn?r   r  r   r   gqI  @gL) ?rF  )r8   r 	  r   r   )rr   nct_mean_df_1000nct_stats_df_1000expected_stats_df_1000nct_mean	nct_statsr  s          r2   test_nct_stats_large_df_valuesz&TestNct.test_nct_stats_large_df_values  s     !9>>$22!IOOD!44
 #56H!I(*@*C"	$ 	$ 	$ 	$)+A"	$ 	$ 	$ 	$ 9>>&!,,IOOFA..	,.@A."3%@@@@	>======r4   c           	      ~    t          t          j                            ddt	          d                    d           d S )Nrf   i   r   )r   r8   r 	  rp   r   rw   s    r2   test_cdf_large_nczTestNct.test_cdf_large_nc  s0    	aE%LL991=====r4   N)	r   r   r   r	  r	  r	  r	  r	  r	  r:   r4   r2   r  r  o  sq        C C C2 2 2$ $ $     > > >,> > > > >r4   r  c                   &    e Zd Zd Zd Zd Zd ZdS )TestRecipInvGaussc                 V    t           j                            dd          }|dk    sJ d S )Nr   r  r   )r8   recipinvgaussrh   r  s     r2   test_pdf_endpointz#TestRecipInvGauss.test_pdf_endpoint  s+    ##As++Cxxxxxxr4   c                 l    t           j                            dd          }|t          j         k    sJ d S )Nr   r  )r8   r	  r   ri   r  r  s     r2   test_logpdf_endpointz&TestRecipInvGauss.test_logpdf_endpoint  s/    "))!S11wr4   c                 n    t           j                            dd          }d}t          ||d           d S )Nr  r{   g9V9s;r  r   )r8   r	  rp   r   rr   ru  rW   s      r2   test_cdf_small_xz"TestRecipInvGauss.test_cdf_small_x  s<      ##D#..(8%000000r4   c                 l    t           j                            dd          }d}t          ||d           d S )NP   r{   glH<r9  )r8   r	  r   r   r	  s      r2   test_sf_large_xz!TestRecipInvGauss.test_sf_large_x  s7    ""2s++(8U+++++r4   N)r   r   r   r	  r	  r	  r	  r:   r4   r2   r	  r	    sP            1 1 1(, , , , ,r4   r	  c                        e Zd Zd Zd Zd ZdS )TestRicec                    g d}t          t          j        t          j                            |d                                                               t          t          j        t          j                            |d                                                               t          t          j        t          j                            |d                                                               t          t          j        t          j        	                    |d                                                               g d}t          t          j        t          j        
                    |d                                                               t          j                            dd          }t          t          j        |                                                     d}t          t          j                            |d          t          j                            ||          |d	           d S )
N)r  rS  rT  r   r1   )r\   r\   r{   r   r   r\  r]  r  r  )r	   ri   r  r8   r  rh   r   r   rp   r  r   r   )rr   r^   r~  r\  r1   s        r2   test_rice_zero_bzTestRice.test_rice_zero_b  s   MMEJNN1N334488::;;;EJ--a2-6677;;==>>>EJNN1N334488::;;;EJ--a2-6677;;==>>>   EJNN1N334488::;;;z622D!!%%''(((
 
q!,,ejnnQ.B.BQ	( 	( 	( 	( 	( 	(r4   c                     t           j        j        }t           |d          j        d           t           |dd          j        d           d S )Nr[  r"	  r   )r   r   )r1   r   )r8   r  r   r   r   rA  r%  s     r2   test_rice_rvszTestRice.test_rice_rvs  sO    jnSS2YYY^Q'''SS2F+++16:::::r4   c                    t           j                            t          j        ddd          t          j        ddd                    }g d}t          ||           t          j        ddd          }t           j                            |dd          }g d	}t          ||           t          j         j                            d
t          j        ddd                    }g d}t          ||           d S )Nr_      )g/Ƹ?g[jǊ\?g 	?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?r\   r   g     @_@r   r  )	g<~@gwd
@gC?@gb
0@g` A@@g'NxP@g33-a@g4pv@g$F@r{      )gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g<
uQ@giff T@g9r[V@g3bXQ Y@gqxJ[@g`*DD ^@g@`@gdAa@)r8   r  rp   ri   r  r   r   r7   )rr   rp   cdf_expprobabilitiesr   ppf_exps         r2   test_rice_gh9836zTestRice.test_rice_gh9836  s     jnnRYr333RYr35K5KLLO O O
 	W%%%	#q#..jnn]En;;L L L 	W%%%k""3	"c2(>(>??; ; ;
 	W%%%%%r4   N)r   r   r   r#	  r%	  r,	  r:   r4   r2   r 	  r 	    sA        ( ( (*; ; ;
'& '& '& '& '&r4   r 	  c                        e Zd Zd Zd Zd ZdS )
TestErlangc                 D    t           j                            d           d S r4  r5  rw   s    r2   r6  zTestErlang.setup_method  r7  r4   c           	         t          j                    5  t          j        dt                     t	          t          t
          j        j        dddd           g d}t
          j                            |d          }t
          j	                            |d          }t          ||d	
           d d d            d S # 1 swxY w Y   d S )Nrr  rZ  r   r   r   r  )r{   rS  r   r  r#  rd  r   )rv  rw  rx  ry  r  r8   erlangr   r   r_  r   )rr   r   result_erlangresult_gammas       r2   test_erlang_runtimewarningz%TestErlang.test_erlang_runtimewarning  s     $&& 	D 	D!'>::: .,*CQaaI I I I (''D!L,,Ta,88M ;??4A?66LM<dCCCC	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	D 	Ds   BB==CCc                     t          t          j                            dddg          t          j                            dddg                     d S )Nr{   r   r   r  )r   r8   r1	  rh   r_  rw   s    r2   test_gh_pr_10949_argcheckz$TestErlang.test_gh_pr_10949_argcheck1  sR    U\%%caW%55[__SQG_44	6 	6 	6 	6 	6r4   N)r   r   r   r6  r4	  r6	  r:   r4   r2   r.	  r.	    sD          D D D&6 6 6 6 6r4   r.	  c                       e Zd Zd Zd Zd Zej                            dddg          d             Z	ej                            ddd	gd
dgg          d             Z
d Zd ZdS )TestRayleighc                 D    t           j                            d           d S )Nr  r5  rw   s    r2   r6  zTestRayleigh.setup_method7  s    
	y!!!!!r4   c                 d    t           j                            d          }t          |d           d S )Nr<  g)Zx)r8   r*  r   r   rr   r  s     r2   r{  zTestRayleigh.test_logpdf;  s.    N!!"%%./////r4   c                 d    t           j                            d          }t          |d           d S )Nr<  i)r8   r*  r|  r   r;	  s     r2   r  zTestRayleigh.test_logsf?  s-    N  $$5!!!!!r4   rC  )gB)Q?got|?)gS2P?g3?c                    t           j                            d||          }d } |||          }t           j                            ||          \  }}t	          ||           t	          ||           t           j                            |d          \  }}t	          |d           t           j                            |          \  }}t	          | |||                     d S )Nr  r  c                 b    t          j        | |z
  dz            dt          |           z  z  dz  S )Nrf   r{   )ri   rl  r  )r   r   s     r2   r&  z(TestRayleigh.test_fit.<locals>.scale_mleH  s/    FD4KA-..!c$ii-@RGGr4   r   r  r  )r8   r*  r   r   r   )rr   r   r  r   r&  scale_expectrd   re   s           r2   r  zTestRayleigh.test_fitC  s     ~!!sy!II	H 	H 	H !yw//^''7';;
US'"""UL))) ^''R'88
UUB
 ^''--
UUIIdC0011111r4   r  r}   g̡=E?g@1d?c                 ~    t           j                            d||          }t          t           j        |           d S )Nr  r  )r8   r*  r   r   )rr   r   r  r   s       r2    test_fit_comparison_super_methodz-TestRayleigh.test_fit_comparison_super_method\  s8    
 ~!!sy!II%end;;;;;r4   c                 8    t          t          j                   d S ru   )r  r8   r*  rw   s    r2   re  zTestRayleigh.test_fit_warningsd  s    EN+++++r4   c                    t           j                            d          }d\  }}}t          j                            ||||          }t          j                            |          \  }}|t          j        |          k     sJ t          j                            ||          \  }}|t          j        |          k     sJ ||k    sJ d S )Ni  )r<  r  r~  r   r  )ri   r   r   r8   r*  r   r   r-  )	rr   r   rd   re   r   r   r   r   r   s	            r2   test_fit_gh17088zTestRayleigh.test_fit_gh17088g  s     i##C(('UDn  e$S II^'',,
$$$$"^//E/BB$$$$E!!!!!!r4   N)r   r   r   r6  r{  r  r   r   r   r  rA	  re  rD	  r:   r4   r2   r8	  r8	  6  s        " " "0 0 0" " " [03K3K3M N N2 2N N2. [0D$<4>
3K3M N N< <N N<, , ,
" 
" 
" 
" 
"r4   r8	  c                       e Zd Zd Zd Zd Zej                            dg d          d             Z	ej                            dg d          d	             Z
d
S )TestExponWeibc                     d}d}d}t           j                            |||          }t           j                            |||          }t	          ||gddg           d S )Nr\   rS  r  g:23W+g~`9k)r8   	exponweibrh   r   r   )rr   r^   r0   r  ru  rz  s         r2   test_pdf_logpdfzTestExponWeib.test_pdf_logpdfv  ss    O1a((%%aA..D	/1DE	G 	G 	G 	G 	Gr4   c                 ~   t          j        ddd          }d}d}t          j                            |||          }t          j                            ||          }t          ||           t          j                            |||          }t          j                            ||          }t          ||           d S )Nr  r   r   r   r`   )ri   r  r8   rH	  rh   weibull_minr   r   rr   r^   r0   r  ru  rW   rz  s          r2   test_a_is_1zTestExponWeib.test_a_is_1  s     KB""O1a(($((A..8$$$%%aA..$++Aq11h'''''r4   c                 z   t          j        ddd          }d}d}t          j                            |||          }t          j                            |          }t          ||           t          j                            |||          }t          j                            |          }t          ||           d S )Nrn  r   r_   )ri   r  r8   rH	  rh   r  r   r   rL	  s          r2   test_a_is_1_c_is_1z TestExponWeib.test_a_is_1_c_is_1  s    KAr""O1a((;??1%%8$$$%%aA..;%%a((h'''''r4   zx, a, c, ref))r   r  r   g=J ?)r<  r  r   g$+PR>)r  r  r   g><)r  r  r   ggX.X:)r        ?r   gRy9)r   rP	  r[  g'vR0=)g_QPr  r  gQ:<c                 l    t           j                            |||          }t          ||d           d S r  )r8   rH	  r   r   )rr   r^   r0   r  r  r   s         r2   r  zTestExponWeib.test_sf  s8     _1a((Ce,,,,,,r4   zp, a, c, ref))rk  r  r   g;y$(@)gMg<r  r   gdbq^@)r  r   rf   gE@)gvIh%L=rP	  r   g/7@)r  r  r  gTWTOc                 l    t           j                            |||          }t          ||d           d S r  )r8   rH	  r  r   )rr   ru  r0   r  r  r  s         r2   r  zTestExponWeib.test_isf  s8     o!!!Q**Su------r4   N)r   r   r   rI	  rM	  rO	  r   r   r   r  r  r:   r4   r2   rF	  rF	  t  s        	G 	G 	G( ( ( ( ( (> [	5 	5 	5	 	- -	 	-* [	4 	4 	4 . . . . .r4   rF	  c                       e Zd Zd Zd ZdS )TestFatigueLifec                 j    t           j                            dd          }t          |dd           d S )Nr  r  X9r   r   )r8   r   r   r   r  s     r2   test_sf_tailzTestFatigueLife.test_sf_tail  s8       ,,0u======r4   c                 n    d}t           j                            |d          }t          |dd           d S )NrV	  r  r  r   r   )r8   r   r  r   )rr   ru  r~  s      r2   test_isf_tailzTestFatigueLife.test_isf_tail  s:    !!!!S))5u------r4   N)r   r   r   rW	  rY	  r:   r4   r2   rT	  rT	    s2        > > >. . . . .r4   rT	  c                       e Zd Zd Zd Zej                            dddg          d             Zd Z	ej                            dd	d
g          d             Z
dS )TestWeibullc                 f    t           j                            dd          }t          |d           d S r  )r8   rK	  r   r   r;	  s     r2   r{  zTestWeibull.test_logpdf  s0    $$Q**Qr4   c                    d}d}d}t           j                            |||          }t          |t	          j        d          dz             t           j                            |||          }t          |dt	          j        d          z
             t           j                            |||          }t          |t          j
        d                      t           j                            |||          }t          |t	          j        t          j
        d                                t           j                            |||          }t          |t	          j        d                     t           j                            |||          }	t          |	d           t           j                            ddd          }t          |t	          j        d	                     t           j                            ddd          }	t          |	d	           d
}t           j                            |||          }t          |t	          j        d          dz             t           j                            |||          }t          |dt	          j        d          z
             t           j                            |||          }t          |t	          j        d                     t           j                            |||          }t          |d           t           j                            |||          }t          |t          j
        d                      t           j                            |||          }	t          |	t	          j        t          j
        d                                t           j                            ddd          }t          |t          j
        d                      t           j                            ddd          }	t          |	t	          j        t          j
        d                                d S )Nr  r   r[  r  r  r   r9  rf   r2  r  g&.gCe )r8   rK	  rh   r   ri   r   r   r  rp   r   rn  r  r   r|  weibull_max)
rr   r^   r0   r1   ru  r  r  lcrN   r  s
             r2   test_with_maxima_distribz$TestWeibull.test_with_maxima_distrib  s   .  !!!Qa!0026%==?+++%%a!%44EBF1II-...!!!Qa!00GM%000111%%a!%44BFGM%$8$8#899:::  AQ //26%==)))$$Q$33E"""   Qa 0026$<<((($$R!$44D!!! !!!Qa!0026%==?+++%%a!%44EBF1II-...!!!Qa!0026%==)))%%a!%44E"""  AQ //GM%000111$$Q$33BFGM%$8$8#899:::    33GM*@AAABBB$$UAQ$77BFGM2H$I$I#IJJKKKKKr4   re   rS  r\   c                 x    t           j                            |dz  |dz  d|          }t          |d           d S )Nro  rD  r   r  g>)r8   rK	  r  r   rH  s      r2   r  zTestWeibull.test_delta_cdfN  sI    " !,,U3Ya38 - : :566666r4   c                    t           j                            d          }d\  }}}t          j        |||          }|                    d|          }t          j                            |dd          \  }}}	t          j                            |dd          \  }
}}||cxk    rdk    sn J ||
k    sJ t          j                            |ddd	
          \  }}}|dk    sJ t          j        |||          }|                    d          }t          j        |          t          j        |          f}t          ||           d S )Nl   > )rf   rA  r{   r`   r   r  r   r   r8  rJ  rK  rM  r]  )
ri   r   r   r8   rK	  r   r   r   r  r   )rr   r   r  rd   re   rA   r   c2rR  rS  c3rU  rV  c4rX  rY  rZ  r   r  s                      r2   test_fit_minzTestWeibull.test_fit_minc  sT   i##$788#3 C//hhCch22 !,00c0BBD& ,00c0BBD&t    q      Rxxxx !,00a$0OOD&{{{{!"dF33kk$k''gcllEJsOO+S!!!!!r4   r  )r<  r   rw  )r   r   gq뮕qH)c                     t          t          j                            ||          |d           t          t          j                            ||          |d           d S r  )r   r8   rK	  r   r  r  s       r2   r  zTestWeibull.test_sf_isf  sZ     	),,Q22CeDDDD)--c155quEEEEEEr4   N)r   r   r   r{  r`	  r   r   r   r  rf	  r  r:   r4   r2   r[	  r[	    s          
RL RL RLh [WsCj117 7 217(" " "< [[+J,D+E F FF FF FF F Fr4   r[	  c                       e Zd Zd Zd ZdS )TestDweibullc                 B   t           j                            d          }d|                    dd          z  }t          j                            |          }t          j                            |          t          j        d          z
  }t          ||d           d S )N   q>~). r_   r`   r  r{   r   r   )
ri   r   r   rU  r8   dweibullrG   rK	  r  r   )rr   r   r  r   r  s        r2   rp  zTestDweibull.test_entropy  s     i##$788

2
...n$$Q''''**RVC[[8Su------r4   c                 P   t           j                            d          }d|                    dd          z  }d|                                z  }t
          j                            ||          }dt
          j                            ||          z  }t          ||d           d S )Nrk	  r_   r   r  r{   r   r   )
ri   r   r   rU  ry  r8   rl	  r   rK	  r   )rr   r   r  r^   r   r  s         r2   r  zTestDweibull.test_sf  s     i##$788


,,,n1%%E%((A...Su------r4   N)r   r   r   rp  r  r:   r4   r2   ri	  ri	    s2        . . .. . . . .r4   ri	  c                   D    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
S )TestTruncWeibullc                 r    t           j                            ddgddd          }t          |ddg           d S )Nr\   r   g)\(?gףp=
?r   )r8   truncweibull_minrh   r   r;	  s     r2   test_pdf_boundsz TestTruncWeibull.test_pdf_bounds  s<    "&&Sz3dCCQc
#####r4   c                     t           j                            dddt          j                  }t          |d           t           j                            dddd          }t          |d           d S )Nr   rS  r   r  g~?)r8   rq	  r   ri   r  r   r   r;	  s     r2   r{  zTestTruncWeibull.test_logpdf  se    "))#sC@@Q "))#sC==./////r4   c                 r    t           j                            ddgddd          }t          |ddg           d S )Nr   rS  r   r\   )r8   rq	  r   r   r;	  s     r2   test_ppf_boundsz TestTruncWeibull.test_ppf_bounds  s<    "&&Sz3SAAQc
#####r4   c                     g d}t           j                            |ddd          }t           j                            |ddd          }t	          ||           d S N)r   r\   rk  r{   r   r   rS  r   r   r[  )r8   rq	  r   rp   r   rr   r~  r^   q_outs       r2   test_cdf_to_ppfz TestTruncWeibull.test_cdf_to_ppf  s[    000"&&q"b"55&**1b"b995!!!!!r4   c                     g d}t           j                            |ddd          }t           j                            |ddd          }t	          ||           d S rw	  )r8   rq	  r  r   r   rx	  s       r2   test_sf_to_isfzTestTruncWeibull.test_sf_to_isf  s[    000"&&q"b"55&))!RR885!!!!!r4   c                    dddfdt           j                            d          }t          |d           t           j                            d          }t	          fd          \  }}t          ||           t           j                            d          }t	          fd	          \  }}t          ||           t           j                            d
          }t	          fd          \  }}t          ||           t           j                            d          }	t	          fd          \  }
}t          |	|
           d S )Nr   rS  r[  c                 T    | |z  t           j                            |           z  S ru   )r8   rq	  rh   )r^   rt  r0   r1   r  s     r2   xnpdfz)TestTruncWeibull.test_munp.<locals>.xnpdf  s)    a4.221aA>>>>r4   r   r   c                      | d          S r   r:   r^   r	  s    r2   rO   z,TestTruncWeibull.test_munp.<locals>.<lambda>      a r4   rf   c                      | d          S r  r:   r	  s    r2   rO   z,TestTruncWeibull.test_munp.<locals>.<lambda>  r	  r4   r   c                      | d          S r  r:   r	  s    r2   rO   z,TestTruncWeibull.test_munp.<locals>.<lambda>  r	  r4   r   c                      | d          S )Nr   r:   r	  s    r2   rO   z,TestTruncWeibull.test_munp.<locals>.<lambda>  r	  r4   )r8   rq	  r  r   r   r   )rr   r[  rr  m1_expectedr   r  m2_expectedm3m3_expectedr  m4_expectedr0   r1   r  r	  s              @@@@r2   	test_munpzTestTruncWeibull.test_munp  s   	? 	? 	? 	? 	? 	? 	? #**1aA66R#**1aA663333Q::QK(((#**1aA663333Q::QK(((#**1aA663333Q::QK(((#**1aA663333Q::QK(((((r4   c                 ^   d}d}d}t          j        dt          j        dt          j        dt          j        d          z              z             z
            }t          j                            ||||          }t          |d           t          j                            ||||          }t          |t          j        d                      t          j        	                    d|||          }t          ||           t          j        
                    ||||          }t          |d           t          j                            ||||          }	t          |	t          j        d                      t          j                            d|||          }
t          |
|           d S )NrS  r[  r   r   r{   r  )ri   r%  r  r   r8   rq	  rp   r   r  r   r   r|  r  )rr   r0   r1   r  x_medrp   r_	  r   r   r  r  s              r2   test_reference_valuesz&TestTruncWeibull.test_reference_values  so   BF3"rvbzz/0B)C)C#CDDDEE$((1a88S!!!#**5!Q::RVBZZK((($((aA66U####&&uaA66C   #))%Aq99RVBZZK((($((aA66U#####r4   c                 *   d}d}d}t           j        }d}t          j                            |||          }t          j                            |||||          }t          ||           t          j                            |||          }t          j                            |||||          }	t          ||	           t          j                            |||          }
t          j                            |||||          }t          |
|           t          j        	                    |||          }t          j        	                    |||||          }t          ||           t          j        
                    |||          }t          j        
                    |||||          }t          ||           t          j                            |||          }t          j                            |||||          }t          ||           t          j        
                    dd||d          }t          |t          j        d	                     t          j                            dd||d          }t          |d	           d S )
Nr  r   r   r[  r  r9  rf   r   r2  )ri   r  r8   rK	  rh   rq	  r   r   rp   r  r   r|  r   )rr   r^   r  r0   r1   re   ru  p_truncr  lp_truncrp   	cdf_truncr_	  lc_truncrN   s_truncr  ls_truncs                     r2   test_compare_weibull_minz)TestTruncWeibull.test_compare_weibull_min  se    F!!!Qe!44(,,Q1au,EE7###%%a%%88)00Aq!50IIH%%%##Aq#66*..q!Q.GG	Y'''%%a%%88)00Aq!50IIH%%%  AU 33(++Aq!Qe+DD7###$$Q$77)//1a%/HHH%%% "%%b!Q%;;26$<<(((#))"aAQ)??D!!!!!r4   c                    d\  }}}t          j        ||d          }t          j                            ||||          }t          j                            ||||          }t          j                            ||          t          j                            ||          z
  }t          j                            ||          |z  }t          j                            ||          t          j                            ||          z
  |z  }	t           j                            ||           t           j                            ||	           d S )N)r  rk  r)  r`   )	ri   rX  r8   rq	  rh   rp   rK	  rp  r   )
rr   r  r0   r1   r^   r  r  r  r  r  s
             r2   test_compare_weibull_min2z*TestTruncWeibull.test_compare_weibull_min2  s    "1aK1c""%))!Q155%))!Q155 $$Q**U->-B-B1a-H-HH $$Q**T1!%%a++e.?.C.CAq.I.II4O

""4...

""4.....r4   N)r   r   r   rr	  r{  ru	  rz	  r|	  r	  r	  r	  r	  r:   r4   r2   ro	  ro	    s        $ $ $
0 0 0$ $ $
" " "" " ") ) )6$ $ $0'" '" '"R/ / / / /r4   ro	  c                   f    e Zd Zd Zd Zej                            dg d          d             ZdS )	TestRdistc                     t           j        }g d}t          |                    |                    |d          d          |d           d S )Nrc  g     @r   rV  )r8   rdistr   rp   r   )rr   r  r  s      r2   test_rdist_cdf_gh1285zTestRdist.test_rdist_cdf_gh12850  sX    $$$FJJvzz&%'@'@%HH"A	/ 	/ 	/ 	/ 	/ 	/r4   c                 
   t          j        ddd          }d}t          dt          j        |dz  |dz                                |dz   dz            z  t          j        |                              |                     d S )NgGzr!  r_   g@r{   rf   r   )ri   rX  r   r8   r  rh   r	  )rr   r^   r  s      r2   test_rdist_betazTestRdist.test_rdist_beta7  s    KtR((C
1Q3! 4 4 8 8!a% C CC!KNN..q11	3 	3 	3 	3 	3r4   r  ))r  i  g?)r\      g;|bZ?)r{   i  g79)r   iU  g޻S/c                 f    t          t          j                            ||          |d           d S r  )r   r8   r	  r   r  s       r2   test_rdist_sfzTestRdist.test_rdist_sfE  s/     	q!,,c>>>>>>r4   N)	r   r   r   r	  r	  r   r   r   r	  r:   r4   r2   r	  r	  /  st        / / /3 3 3 [	
 	
 	
 ? ? ? ? ?r4   r	  c                   ~    e Zd Zd Zd Zd Zd Zd Zd Ze	j
                            dg d          d	             Zd
S )TestTrapezoidc                 V   g d}|D ]}d|dg}t          t          j                            |||          t          j                            ||                     t          t          j                            |||          t          j                            ||                     d S )N)r   r}  r{   r   r   r   )r   r8   r   rh   triangrp   )rr   modesmoder^   s       r2   test_reduces_to_triangz$TestTrapezoid.test_reduces_to_triangS  s        	; 	;DD!A 3 3AtT B B % 0 0D 9 9; ; ; 3 3AtT B B % 0 0D 9 9; ; ; ;		; 	;r4   c                 b   t          j        ddd          }t          t          j                            |dd          t          j                            |                     t          t          j                            |dd          t          j                            |                     d S )Nr   r   r_   )ri   rX  r   r8   r   rh   ry  rp   r  s     r2   test_reduces_to_uniformz%TestTrapezoid.test_reduces_to_uniform\  s    K1b!!EO//1a88%-:K:KA:N:NOOOEO//1a88%-:K:KA:N:NOOOOOr4   c                 n   t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            d	dd          d
           t          t          j                            ddd          d           t          t          j                            ddd          d
           t          t          j                            d	dd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           t          t          j                            ddd          d           d S )Nr   rf   r   r{   r   r  r  rS  r\   g      ?r)  r   rP	  r  g      ?)r   r8   r   rh   rp   rw   s    r2   
test_caseszTestTrapezoid.test_casesa  s   EO//1a88!<<<EO//1a88!<<<EO//Q<</	1 	1 	1EO//S#>>/	1 	1 	1 	EO//S#>>FFFEO//S#>>EEEEO//S#>>FFFEO//S#>>HHHEO//S#>>FFFEO//S#>>DDDEO//S#>>HHHEO//S#>>DDDDDr4   c                   	
 d\  	

	z
  	z
  z  	z
  	z
  z  		z
  f\  }}}}dz   
z
  	z
  z  	
fd} |d          } |d          |dz  z
  }dz
  
z   	z
  z  z   
z
  	z
  z  t          j        dz   
z
  	z
  z            z   }t          t          j                            ||||          |d           t          t          j                            ||||          |d           t          t          j                            ||||          |d           t          t          j                            ddd	d
          dd           t          t          j                            ddd	d
          dd           t          t          j                            ddd	d
          dd           d S )N)r8  r   rf   r   rf   c                     | dz   z  | dz   z  z
  z
  z  | dz   z  | dz   z  z
  z
  z  z
  z  | dz   z  | dz   z  S )Nrf   r   r:   )rt  r0   r1   r  dro  s    r2   r  z6TestTrapezoid.test_moments_and_entropy.<locals>.moment|  sn    !ac(Q1X-!A#6!Hq1Q3x/AaC89 :qSqS" #r4   r   r{   r)  rV  r   r8  r  r   r   )ri   r  r   r8   r   r   r  rG   )rr   rP  r  rd   re   r  r   r  rG   r0   r1   r  r	  ro  s            @@@@@r2   test_moments_and_entropyz&TestTrapezoid.test_moments_and_entropyu  s    "
1acac]QqSQqSM1acABU1QqM	# 	# 	# 	# 	# 	# 	# 	# 	#
 vayyfQii$'!1Qq/QqSU1W-sac!eAg0G0GGEO00ReDD "	. 	. 	. 	.EO//BUCC	- 	- 	- 	-EO33BCGG#R	1 	1 	1 	1 	EO00Ar1==r2NNNNEO00Ar1==q"MMMMEO//1b!<<aLLLLLLr4   c                    t          j        g d          }t          j        ddg          d d d f         }t          j        g d          }t          j                            |||          }t          j        |||          \  }}}t          j        |j        |j                  }t          j	        |j                  }	t          |	|                                |                                |                                          D ]+\  }
}}}t          j                            |||          ||
<   ,t          ||                    |j                  d           t          j        t          j                            ||d	                    }t          j        ||          \  }}t          j        |j        d
f          }t          j	        |j                  }	t          |	|                                |                                          D ]+\  }
}}t          j                            ||d	          ||
<   ,t          ||j                            |j                  d           d S )Nr  r{   r  )r  rk  r   r  r   r   r\  r]  r   )ri   r   r8   r   rh   broadcast_arraysemptyr   r   r  r  ravelr   r  rA  r   r  )rr   r  r	  r^   r`  ccddr  r   indr  r  c1d1s                 r2   test_trapezoid_vectz!TestTrapezoid.test_trapezoid_vect  s
   H___%%Hc3Z  D)H&&&''O1a(((Aq11
Bhrwbh///i   bhhjj"((**bhhjjII 	5 	5MAr2r_((R44CFF3;;qw//e<<<< Ju,,Q6,BBCC$Q**Bh|$$i  S"((**bhhjj99 	C 	CIAr2_**2r6*BBCFF35==11>>>>>>r4   c                 (   t          j        ddd          }t          j        d          5  t          j                            |dd          }d d d            n# 1 swxY w Y   t          |t          j                            |                     d S )Nr   r   r_   z`trapz.pdf` is deprecatedr  )	ri   rX  r   deprecated_callr8   rH   rh   r   ry  )rr   r^   r  s      r2   
test_trapzzTestTrapezoid.test_trapz  s    K1b!!#*EFFF 	. 	.[__Q1--F	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	.FEM$5$5a$8$899999s   "AA!ArL  )rh   r   rp   r  r   r|  r   r  c                    d\  }} t          t          j        |          d||          }t          j        d| d          5   t          t          j        |          d||          }d d d            n# 1 swxY w Y   ||k    sJ d S )N)r  r   r   z`trapz.z` is deprecatedr  )r-  r8   r   r   r	  rH   )rr   rL  r  r	  rW   r  s         r2   test_trapz_deprecationz$TestTrapezoid.test_trapz_deprecation  s     1375?F33Aq!<<#3F333
 
 
 	; 	; 2WU[&11!Q::F	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; !!!!!!s   &A66A:=A:N)r   r   r   r	  r	  r	  r	  r	  r	  r   r   r   r	  r:   r4   r2   r	  r	  R  s        ; ; ;P P P
E E E(M M M6? ? ?4: : : [X (E (E (E F F" "F F" " "r4   r	  c                       e Zd Zd ZdS )
TestTriangc                    t          j        d          5  t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d	           t          t          j                            dd          d           t          t          j                            dd          d
           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           t          t          j                            dd          d           d d d            d S # 1 swxY w Y   d S )Nraiser  r   r   r{   rS  r   r   rf   r   rk  )ri   ri  r   r8   r	  rh   rp   rw   s    r2   test_edge_caseszTestTriang.test_edge_cases  s   [W%%% 	6 	6))!Q//444))#q112666))!Q//444))!Q//333))#q112666))!Q//333))"b112666))#r22D999))#r22C888))"b112666))#r22D999))"b111555	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6 	6s   H)IIIN)r   r   r   r	  r:   r4   r2   r	  r	    s#        6 6 6 6 6r4   r	  c                       e Zd Zej                            dddg          d             Zej                            dg d          d             ZdS )	TestMaxwellr  )r
  gCR5&.)r}   g7q?c                 d    t          t          j                            |          |d           d S r  )r   r8   maxwellr   r  s      r2   r  zTestMaxwell.test_sf  s/     	((++Su======r4   r  ))rd  g1!@)g    ?g?)g      <gCuJ!@c                 d    t          t          j                            |          |d           d S r   )r   r8   r	  r  r  s      r2   r  zTestMaxwell.test_isf  s/    
 	))!,,c>>>>>>r4   Nr=  r:   r4   r2   r	  r	    s        
 [X::<= => >= => [X: : :; ;? ?	; ;? ? ?r4   r	  c                       e Zd Zd Zd ZdS )
TestMielkec                    d\  }}t          t          j        ||                              d          t          j                   t          t          j        |d                              d          t          j                   t          t	          j        t          j        |d                              d                               d S )N)g rh@gv?r   rS  r  )r   r8   mielker  ri   r  r	   r  )rr   r[   rN   s      r2   ra  zTestMielke.test_moments  s    1U\!Q''..q1126:::U\!S))0033RV<<<ELD1188;;<<=====r4   c                     t          j        ddd          }d\  }}t          t          j                            ||||z            t          j                            |||                     d S )Nr}   r`   r<  )g@gHzG@)ri   rX  r   r8   burrrh   r	  )rr   r^   r[   rN   s       r2   test_burr_equivalencez TestMielke.test_burr_equivalence  s^    Kc2&&1
q!QqS115<3C3CAq!3L3LMMMMMr4   N)r   r   r   ra  r	  r:   r4   r2   r	  r	    s7        > > >N N N N Nr4   r	  c                   &    e Zd Zd Zd Zd Zd ZdS )TestBurrc           	      n   t           j        ddgt           j        ddgt           j        ddgt           j        ddgt           j        ddgt           j        ddgt           j        d	d
gg}d |D             }d |D             }t	          ||           d |D             }d |D             }t	          ||           d S )Nr   r   )r{   rf   )r   r   )rf   r{   rZ  r{   rS  )r   rf   r   c                 <    g | ]\  }}} |j         |j        g|R  S r:   r  r  s       r2   rB   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  r  r4   c                     g | ]\  }}}|	S r:   r:   r  s       r2   rB   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  r  r4   c                 <    g | ]\  }}} |j         |j        g|R  S r:   )r   r0   r  s       r2   rB   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  s4    @@@<2uayry&&&&@@@r4   c                 >    g | ]\  }}}t          j        |          S r:   )ri   r  r  s       r2   rB   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>  s)    FFF)=UI26)$$FFFr4   )r8   fiskr	  burr12r   )rr   r   r  r  s       r2   test_endpoints_7491zTestBurr.test_endpoints_7491  s     Zq!Z1%Z#Z1%\8S)\63'\63') >====>>>>>!#w///@@4@@@FFFFF!#w/////r4   c                     d\  }}t          j        ||                                           \  }}d\  }}t          ||           t          ||           d S )N)rT  r   )g4U?g&MI?)r8   r	  r   )rr   r  r	  r   variancemean_hcvariance_hcs          r2   test_burr_stats_9544zTestBurr.test_burr_stats_9544
  s_    1Aq))//11h  Gg&&&+.....r4   c                    d\  }}t          j        ||                                           \  }}t          t          j        |                     t          t          j        |                     d\  }}t          j        ||                                           \  }}t          t          j        |                     t          t          j        |                     d\  }}t           j                            t          j        g d          ||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d\  }}t           j                            g d||          \  }}}}t          t          j        |                     t          t          j        |                     t          t          j        |                     t          t          j        |                     d S )N)r{   r   )r  r   rZ  )r  r   )rA  r   )rC  r   )r8   r	  r	   ri   r  r  _munpr   )	rr   r  r	  r   r	  e1e2e3e4s	            r2   test_burr_nan_mean_var_9544z$TestBurr.test_burr_nan_mean_var_9544  sb   1Aq))//11h""###1Aq))//11hD!!"""""###1))"(<<<*@*@!QGGBB1)),,,1==BBB   1)),,,1==BBB   B   1)),,,1==BBB   B   B   1)),,,1==BBB   B   B   B     r4   c                     d\  }}g d}g d}t          t          j                            |||          |d           d S )N)rT  r[  )r\   r  r  r  )g+&?gI$_@gKT@gؗVAr  r   )r   r8   r	  r  )rr   r  r	  r~  r  s        r2   test_burr_isfzTestBurr.test_burr_isf?  sV     1&&&# # #
q!Q//5AAAAAAr4   N)r   r   r   r	  r	  r	  r	  r:   r4   r2   r	  r	    sV        0 0 0(	/ 	/ 	/(! (! (!TB B B B Br4   r	  c                       e Zd Zej                            dddg          d             Zd Zej                            dg d          d             Zd	S )

TestBurr12zscale, expected)rS  gd~)rA  gR톇T c                 r    t           j                            dddd|          }t          ||d           d S )Ng     jAg     jAr   rD  r  r   r   )r8   r	  r  r   )rr   re   rW   r  s       r2   r  zTestBurr12.test_delta_cdfL  s?    ( ''S!Qe'DDxe444444r4   c                     d\  }}t           j        dz  }dt           j        dz  dz  z
  }t           j        dz  d|dz  z  z  }t           j        }||||g}t          j        ||                              d	          }t          ||d
           d S )Nr  r   r   rf   r  r   r  r  r\  r  r   )ri   rj   r  r8   r	  r   )	rr   r  r	  r   r  r  r6  r  r   s	            r2   test_moments_edgezTestBurr12.test_moments_edgec  s    
 1uQw"%(2+ouaxCH%6S$)l1a  &&v..Su------r4   zp, c, d, ref))r  r
  r{   ggx4/@)gҶOɃ;r
  r{   gI8aS@)r  rk  #   gj\/ @)g#aMR/rk  r	  g!GAc                 l    t           j                            |||          }t          ||d           d S r  )r8   r	  r  r   )rr   ru  r  r	  r  r^   s         r2   test_isf_near_zerozTestBurr12.test_isf_near_zeros  s8     LQ1%%3U++++++r4   N)	r   r   r   r   r   r   r  r	  r	  r:   r4   r2   r	  r	  J  s        [.<;=> >5 5> >5(. . .  [	0 	0 	0 , , , , ,r4   r	  c            	          e Zd Zg dZg dZg dZ ej        eeef          Zg dZ	ddddd	ej
        gZg d
Z e e ee	ee          e                    Zddddej
        dfddej
        dfddej
        dfgZej        j        d             Zej        j        d             Zej                            e          ZdZ eej                            ee                    5 Z  e!j"        e           Z#ddd           n# 1 swxY w Y   ej        $                    de#d                   d             Z%ej        $                    de#d                   d             Z&ej        j        ej        '                    d          ej        $                    de#d                   d                                     Z(ej        j        d             Z)ej        j        d             Z*ej        $                    de          d              Z+ej        j        ej        '                    d          d!                         Z,ej        j        d"             Z-d# Z.d$ Z/d% Z0dS )&TestStudentizedRange)gQ1@g33333F@g
ףp=*K@gHzM@g/$@g~j!@g33333$@g{Gz&@gh|?5	@gQ8@g&1@g|?5@g@gOn@g!rhm@gB`"@r  gʡEs@g|?5^@g/$@gV-@g/$@gF@g?5^I@)gRV@gffffffl@gp@g     r@gʡ @gHzG/@gQ82@gQ3@g!rh@g     @g+@gʡEs @gjt@gB`"[@g@gnJ@gV-@gFx@gsh|?@g+N@g/$@g @g@gGz@)gfffff"@i  i
  i  gHzG2@g(\A@gQC@gfffffE@g @gNbX9"@gHz$@g(\&@g-@gn@@gw/@g=
ףp @gJ+@g-'@gn@gHz@gV-@gnJ@g$@g/ݤ@)r  r!  r  r   r   r_   r
  x   )rf   rD  r  r
  )r\   r   i)#  gupm1f?)r   r_   r   g?<-=A?gv"?r   gd暕?ga-A?c                     | j         D ]>\  }}|\  }}}t          j                            |||          }t	          ||d           ?d S )Nr  r   )r   r8   studentized_rangerp   r   )rr   pvkr~  
p_expectedr`  r[   res_ps          r2   test_cdf_against_tablesz,TestStudentizedRange.test_cdf_against_tables  s_    i 	: 	:FC"J1+//1a88EE:D99999	: 	:r4   c                     | j         D ]>\  }}|\  }}}t          j                            |||          }t	          ||d           ?d S )NMb@?r   )r   r8   r	  r   r   )rr   r	  
q_expectedru  r`  r[   res_qs          r2   test_ppf_against_tablesz,TestStudentizedRange.test_ppf_against_tables  s^    #y 	: 	:OCGAq!+//1a88EE:D99999	: 	:r4   z&data/studentized_range_mpmath_ref.jsonNcase_resultcdf_datac                     |d         }|d         }|d         |d         |d         f}t          j        j        | }t          |||d         |d                    d S 	Nsrc_case	mp_resultr~  r[   r`  expected_atolexpected_rtolr  )r8   r	  rp   r   rr   r
  r
  r
  qkvr   s         r2   test_cdf_against_mpz(TestStudentizedRange.test_cdf_against_mp  s    z*,	smXc]HSM9%)3/Y%o6%o6	8 	8 	8 	8 	8 	8r4   pdf_datac                     |d         }|d         }|d         |d         |d         f}t          j        j        | }t          |||d         |d                    d S r
  )r8   r	  rh   r   r	
  s         r2   test_pdf_against_mpz(TestStudentizedRange.test_pdf_against_mp  r
  r4   z+intermittent RuntimeWarning: invalid value.moment_datac                    |d         }|d         }|d         |d         |d         f}t          j        d          5  t          j        j        | }d d d            n# 1 swxY w Y   t          |||d         |d	         
           d S )Nr
  r
  r_  r[   r`  r\  r]  r
  r
  r  )ri   ri  r8   r	  r  r   )rr   r
  r
  r
  mkvr   s         r2   test_moment_against_mpz+TestStudentizedRange.test_moment_against_mp  s     z*,	smXc]HSM9 [*** 	7 	7)0#6C	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	Y%o6%o6	8 	8 	8 	8 	8 	8s   AA!$A!c                     d\  }}t          t          j        j        dt          j        ||f          }t          |d         d           d S )Nr   r_   r   r  r   )r   r8   r	  rh   ri   r  r   )rr   r[   r`  r   s       r2   test_pdf_integrationz)TestStudentizedRange.test_pdf_integration  sG    15*.26AGGGA"""""r4   c                    d\  }}t          j        ddd          }t          j                            |||          dd          }t          j                            |||          }t          ||          }t          ||d           d S )	Nr
  r   r_   r}   )stepr   r  r   )ri   r  r8   r	  rp   rh   r   r   )rr   r[   r`  r^   y_cdf	y_pdf_rawy_pdf_cumulatives          r2   test_pdf_against_cdfz)TestStudentizedRange.test_pdf_against_cdf  s    1
 Ia$''''++Aq!44QRR8+//1a88	/	1== 	(%d;;;;;;r4   r_case_resultc                     |\  }}}}t          j        d          5  t          j                            |||          }d d d            n# 1 swxY w Y   t          ||           d S )Nr\  r]  )ri   ri  r8   r	  rp   r   )rr   r
  r~  r[   r`  r_resr   s          r2   test_cdf_against_rz'TestStudentizedRange.test_cdf_against_r  s     '1a[*** 	7 	7)--aA66C	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7 	7U#####s   "AAAc                    t          j        d          5  t          j                            ddgddgddg          }d d d            n# 1 swxY w Y   t          |j        d	           t          j        t          d
          5  t          j                            dddgg d           d d d            d S # 1 swxY w Y   d S )Nr\  r]  r   rf   r   r   r_   r+  r  z...could not be broadcast...r  )r_   r+  rU  )
ri   ri  r8   r	  r	  r   rA  r   r   r  r(  s     r2   test_moment_vectorizationz.TestStudentizedRange.test_moment_vectorization  sh    [*** 	H 	H'--q!fq!fr2hGGA	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	&&&]:-KLLL 	C 	C#))!aV\\\BBB	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	C 	Cs#   (A

AA&B88B<?B<c                    t                      5 }t          j        d          5  |                    t                     t
          j                            g d          \  }}}}d d d            n# 1 swxY w Y   d d d            n# 1 swxY w Y   t          t
          j        	                    ||                     d S )Nr\  r]  r
  )
r   ri   ri  rR   r   r8   r	  r  r	   	_argcheck)rr   r  r[   r  r   s        r2   test_fitstart_validz(TestStudentizedRange.test_fitstart_valid  sF      	GCX)F)F)F 	G 	GJJ)***1;;IIIFFKAr1a	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	'11!R8899999s5   B	AA2&B	2A6	6B	9A6	:B		BBc                    t           j                            ddt          j                  }t           j                            ddd          }t          ||dd           t           j                            ddt          j                  }t           j                            ddd          }t          ||dd           d S )Nr   r_   韆 r  r  )r8   r	  rh   ri   r  r   rp   )rr   r   
res_finites      r2   test_infinite_dfz%TestStudentizedRange.test_infinite_df  s     %))!R88,00B>>
Zd>>>>%))!R88,00B>>
Zd>>>>>>r4   c                 Z   t           j                            ddd          }t           j                            ddd          }t           j                            ddd          }t          t          t
          ||dd           t          ||dd           t           j                            ddd          }t           j                            ddd          }t           j                            ddd          }t          t          t
          ||dd           t          ||dd           d S )Nr   r_   r   r'
  i r  r  )r8   r	  rh   r  AssertionErrorr   rp   )rr   r   r(
  
res_sanitys       r2   test_df_cutoffz#TestStudentizedRange.test_df_cutoff&  s    %))!R88,00B>>
,00B>>
nosJd	, 	, 	, 	,
JTEEEE%))!R88,00B>>
,00B>>
nosJd	, 	, 	, 	,
JTEEEEEEr4   c                     d\  }}}t           j                            |||          }t          |dd           |dk    sJ d S )N)gaRA@r   iS  r   r  r   )r8   r	  r   r   )rr   r~  r[   r`  ru  s        r2   test_clippingz"TestStudentizedRange.test_clipping;  sO     .1a#&&q!Q//15))))Avvvvvvr4   )1r   r   r   q05q01q001ri   r  qspsr  vskslistr  r'   r   r_datar   r   r   r	  r   r 
  ospathdirnamer$  path_prefixrelative_pathopenr  filejsonr#  pregenerated_datar   r
  r
  xfail_on_32bitr
  r
  r
  r 
  r"
  r%
  r)
  r-
  r/
  r:   r4   r2   r	  r	    s       ' ' 'C' ' 'C( ( (D 
c4(	)	)B			B
QBRV	$B	B4GGBB'',,--D
 	*(	
Arv()	
Arv()	
B)*F [: : : [: : : '//(++K<M	bgll;66	7	7 ,4%DIdOO, , , , , , , , , , , , , , , [],=j,IJJ8 8 KJ8 [],=j,IJJ8 8 KJ8 [[ MNN[],=m,LMM8 8 NM ON 8 [# # # [< < < [_f55$ $ 65$ [[ MNNC C ON C [: : :	? 	? 	?F F F*    s   %DD	Dr	  c                  ,   t          t          j                            d          ddd           t          t          j                            d          ddd           t          t          j                            dd	d
          ddd           d S )Ng2g?r_   test_540_567)rW  r  g2gk?g;B.?gͣh?gHŎ*?rc   g.y?)r   r8   r  rp   r:   r4   r2   rD
  rD
  E  s    
}557J "N< < < <
}557K "N< < < <
}.-; ' = =+ "N< < < < < <r4   c                  d    t          t          j                            dd          dd           d S )Nr   rf   r{   r  rd  r:   r4   r2   test_regression_ticket_1326rF
  Q  s*    
sA..R88888r4   c            	         t          j        ddd          } t          j        d          5  dddt          j        dgdgdgg          fD ]{}t          j                            | |          }t          |dk                                               t          t          j	        |                                                      |t          j        dgdgd	gg          }t          j                            | |          }d d d            n# 1 swxY w Y   t          t          j	        |                                                      t          |d
         dk                                               t          |d         dk                                               t          |d         dk    
                                           t          |d         dk    
                                           d S )N      rT  r]   r\  r  r   r"  rn  r   r   r   rf   )ri   rX  ri  r   r8   r*   rh   r	   r   r  r   )r^   r  ru  s      r2   test_regression_tukey_lambdarJ
  V  s    	D#s##A	H	%	%	% * *tRXvutf.E%F%FG 	( 	(C!%%a--AQ#XNN$$%%%RXa[[__&&&''''hu-..!!!S))* * * * * * * * * * * * * * * RXa[[__QqTS[   QqTS[   QqTS[   QqTS[     s   CDDDzdocstrings strippedr  c                      t          dt          j        j        v           t          dt          j        j        v            d S )Nzpdf(x, mu, loc=0, scale=1)zpmf(x,)r	   r8   r  r  r:   r4   r2   test_regression_ticket_1421rL
  k  s9    (0EEFFFH--.....r4   c            	      	   t          j        d          5  t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j        	                    dt           j                                       t          t          j        t          j        
                    dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            dt           j                                       t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j        	                    t           j        d                               t          t          j        t          j        
                    t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               t          t          j        t          j                            t           j        d                               d d d            d S # 1 swxY w Y   d S )Nr\  r]  r   r{   )ri   ri  r	   r  r8   r'  r  r  rp   r|  r   rh   r   r   r  r  rO  r  r:   r4   r2    test_nan_arguments_gh_issue_1362rN
  q  s)   	X	&	&	& < <262233444Q//00111q"&1122333Arv..//000Q//00111262233444Q//00111Q//00111//<<==>>>,,RVS99::;;;..rvs;;<<===++BFC8899:::,,RVS99::;;;//<<==>>>,,RVS99::;;;,,RVS99::;;;#< < < < < < < < < < < < < < < < < <s   RR44R8;R8c                     t           j                            d           t          j        g d          } t          j                            | d         | d         | d         d          }t          j        d	          5  t          j        t          j                            |d
                    }d d d            n# 1 swxY w Y   t          || d           t          j        t          j                            |dd                    }t          || d           t          j        t          j                            |dd                    }t          || d           t          j        t          j                            |dd                    }t          || d           t           j                            d           d}d}t          j
                            |dd          }t          j        t          j
                            ||                    }t          j        |t          j        ||z
  dz                                            g          }t          ||d           d S )Ni.  )rk  r   r{   r   r   rf   r`   r:  r\  rI
  r   r   rV  r{   )r   rd   rk  )r   rd   rB  r   r   r   )ri   r   r   r   r8   r'  r   ri  r   r   r  r%  r   )truer^   rq  rd   r   rW   s         r2   test_frozen_fit_ticket_1536rQ
    sL   INN48OOO$$D$q'47DG#>>A	H	%	%	% 9 9%-++AB+77889 9 9 9 9 9 9 9 9 9 9 9 9 9 9 a0000Xem''#1'==>>Fa0000Xem''d'::;;Fa0000Xem''d';;<<Fa0000INN4
CD
sBS))AXejnnQTn2233Fxrw4!'9'9';';<<=>>H!444444s    4C  CCc                      t           j                            d           t          j                            d          } t          j                            |           }d}t          ||d           d S )Ni	 r`   r:  )g
ףp=
?gʡE?r   rV  )ri   r   r   r8   r*  r   r   r   )r   rq  rW   s      r2   test_regression_ticket_1530rS
    sc    INN6
,



$
$C\c""FH!444444r4   c                     t           j                            d           t           j                            d          } dD ]K}t          j                            | |z             \  }}t          ||d           t          |dd           Ld S )Nr   rz  )r  g   6ArS  r   r  )ri   r   r   r  r8   r*  r   r   )r^   offsetrd   re   s       r2   test_gh_pr_4806rV
    s    INN4
	A' . .\%%a&j11
UV#....s-----. .r4   c                  t   t           j                             dd          } dt          j        dz  dz  ddg}t	          | |d           t           j                             d	d          } g d
}t	          | |d           t           j                             dd          } g d}t	          | |d           d S )Nr   r\  r]  rf   r   r  r_   rV  g
ףp=
	@)r   gz5v?r   gRTgQ?)r   gNg @r   gJFٻ)r8   r*   ri   rj   r   )rc  rW   s     r2   "test_tukeylambda_stats_ticket_1545rX
    s     
		 	 F	 	3	3B25!8A:q#&HHb1111			 	 v	 	6	6BCCCHHb1111			 	 v	 	6	6BCCCHHb111111r4   c                      t          t          j        t          j                            dd                               d S )Nr  r  )r	   ri   r  r8   r  r  r:   r4   r2   test_poisson_logpmf_ticket_1436rZ
    s2    BK,,T3778899999r4   c                      ddg} | D ]6\  }}t           j                             |d          }t          ||           7dS )a  Test the powerlaw stats function.

    This unit test is also a regression test for ticket 1548.

    The exact values are:
    mean:
        mu = a / (a + 1)
    variance:
        sigma**2 = a / ((a + 2) * (a + 1) ** 2)
    skewness:
        One formula (see https://en.wikipedia.org/wiki/Skewness) is
            gamma_1 = (E[X**3] - 3*mu*E[X**2] + 2*mu**3) / sigma**3
        A short calculation shows that E[X**k] is a / (a + k), so gamma_1
        can be implemented as
            n = a/(a+3) - 3*(a/(a+1))*a/(a+2) + 2*(a/(a+1))**3
            d = sqrt(a/((a+2)*(a+1)**2)) ** 3
            gamma_1 = n/d
        Either by simplifying, or by a direct calculation of mu_3 / sigma**3,
        one gets the more concise formula:
            gamma_1 = -2.0 * ((a - 1) / (a + 3)) * sqrt((a + 2) / a)
    kurtosis: (See https://en.wikipedia.org/wiki/Kurtosis)
        The excess kurtosis is
            gamma_2 = mu_4 / sigma**4 - 3
        A bit of calculus and algebra (sympy helps) shows that
            mu_4 = 3*a*(3*a**2 - a + 2) / ((a+1)**4 * (a+2) * (a+3) * (a+4))
        so
            gamma_2 = 3*(3*a**2 - a + 2) * (a+2) / (a*(a+3)*(a+4)) - 3
        which can be rearranged to
            gamma_2 = 6 * (a**3 - a**2 - 6*a + 2) / (a*(a+3)*(a+4))
    )rS  )r{   r  r   r  )r   )gUUUUUU?r  g^cQg333333r\  r]  N)r8   rf  r   )r  r0   
exact_mvskr\  s       r2   test_powerlaw_statsr]
    s[    > ,=?E 4 4:~##Av#66!$
33334 4r4   c                  f    t           j                            dd          } t          | d           d S )Nr   r   r   )r8   rf  r   r   ru  s    r2   test_powerlaw_edger`
    s/    a##ACr4   c                  x   t           j                            dd          } t          | d           t           j                            dg d          } t          | t
          j        ddg           t           j                            dg d          } t          | t
          j        dt
          j         g           d S )Nr   r   r   )rk  rS  r  rS  )r8   r  r   r   rh   ri   r  r_
  s    r2   test_exponpow_edgerb
    s    a##AC 	1...//ARVS#&'''a!1!1!122ARVS26'*+++++r4   c                  h    t           j                            ddd          } t          | d           d S )Nr   r   rS  )r8   gengammarh   r   r_
  s    r2   test_gengamma_edgere
    s1    1a##ACr4   za, c, ref, tol))g    `6Ar   g2j!@r   )r5  r   ggA@r   )r  r   rI  r   )r  r   g #@r   )g    `FAr  gI~mr   )gl$W}Lr  g.I#Ur   c                 f    t          t          j                            | |          ||           d S rQ  )r   r8   rd
  rG   )r0   r  r  r  s       r2   test_gengamma_extreme_entropyrg
    s1    " EN**1a00#C@@@@@@r4   c                      t           j                            ddd          } | dk    sJ t           j                            ddd          }|t          j         k    sJ d S )Nr   r   r   r   )r8   rd
  rh   r   ri   r  )ru  rz  s     r2   !test_gengamma_endpoint_with_neg_cri
    sV    1a$$A8888>  Ar**DBF7??????r4   c                      t           j                            ddd          } t          | d           t           j                            ddd          } t          | d           d S )Nr   r  rS  g>r_   gqq?)r8   rd
  r	  r   r_
  s    r2   test_gengamma_munprk
  &  sZ    Rb))A:&&&RR((A6"""""r4   c                     t          j        g d          } t          j        d          5  t                      5 }|                    t
          d           |                    t          d           t          j        	                    |            d d d            n# 1 swxY w Y   d d d            d S # 1 swxY w Y   d S )N)0g>X*ȿgPix#?g=?g&^?goϿg뵏˿gO_ZQ?g\?g~?g)/?gRܶ?g핚οgH߃[g?gS"gm_ пg7k?g#BF?gKU=?gT?gZg[Qs?g2?g6Hwƭ8?g*-
?ga]?g'?g޻?g?J_ ?g~sw?g0FfͿgg"@ӿg?%:˿g&zM?g?Gg	F?g~,g HgW2ҿgTzy?gwmǿg @gW=ֿg	't?g".v1glg.Hꮿg,?g*˿r\  r]  z:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integer)
ri   r   ri  r   rR   r   ry  r8   r  r   )r	  r  s     r2   test_ksone_fit_freezerm
  /  sK   
		/ 		/ 		/
	0 
	0A 
X	&	&	&     	CJJ)#$ $ $ JJ~FH H HKOOA	 	 	 	 	 	 	 	 	 	 	 	 	 	 	                 s5   B5ABB5B!	!B5$B!	%B55B9<B9c            	      r   t          j        t          t          ddd                               } g d}t	          t          j                                        |           |d           t	          t          j                                        | dz             j        |d           t
          j                            | dz             d	z  j	        }t          j
        t
          j                            |           t
          j                            |           z
            }t	          ||d	           d S )
Nr   r	  r   )gDB.g8_$g%`OAgjhwHRgWMB@v`g7VY}igۦx\Arg	xg#g/dg3$gegd)gNq{3gيGǓgr4g37'
gfFg?dJgضg2,
gm%gӅJgz;pgɿ{gk2gij<%giVSͶgBR4g
Q/Mr  r   y        +=y        |=r  )ri   r   r7
  r  r   r8   r  r  realimagr   r   )r^   rW   derivderiv_expecteds       r2   test_norm_logcdfrs
  G  s
    
Dq#q))**	+	++A0 0 0H EJLL''**H4@@@@ EJLL''F
338(NNNN Zq6z**506EVEJ--a005:3D3DQ3G3GGHHNE>666666r4   c                  "   t          j        g d          } t          j        g d          }t          j                            |           }t          ||d           t          j                            |          }t          || d           d S )N)r   rS  r{   r\   r}   rd  )g~V1?r  gba"?g܄4ťY?r  g$%+Ir  r   r   )ri   r   r8   r%  rp   r   r   )r^   rW   r  r  s       r2   test_levy_cdf_ppfru
  `  s    
33344A x 1 1 1 2 2H 	
qAAxe,,,, 
	!	!BB&&&&&&r4   c                      t          j        g d          } t          j        g d          }t          j                            |           }t          ||d           d S )N)rW  rz  gMraB3Gr  )gep[>g}XEQ=gѭEG<g?_%~:r  r   )ri   r   r8   r%  r   r   r^   rW   r  s      r2   test_levy_sfrx
  x  sh    
)))**Ax 0 0 0 1 1H 	
aAAxe,,,,,,r4   zp, expected_isf))r  gj1e2H)r  g6C)r+  gnE@)rw  g!^x1?)r  gZ?)g   ?g:}!Nu?c                 h    t           j                            |           }t          ||d           d S )Nr9  r   )r8   r%  r  r   )ru  expected_isfr^   s      r2   test_levy_isfr{
    s2     	
qAA|%000000r4   c                      t          j        g d          } t          j        g d          }t          j                            |           }t          ||d           d S )N)gMb{Gzg{Gztg~jtX)g#]<gOul2;gޢا6g̅7=!r   r   )ri   r   r8   r&  r   r   rw
  s      r2   test_levy_l_sfr~
    sh    
11122Ax 1 1 1 2 2H 	AAxe,,,,,,r4   c                      t          j        g d          } t          j                            |           }t          j                            |          }t          || d           d S )N)g [n<rk  r!  r  r   )ri   r   r8   r&  r  r   r   )ru  r^   r~  s      r2   test_levy_l_isfr
    s[    
&&&''AAAAqu%%%%%%r4   c                     t          t          j                            dddd          d           t          t          j                            dddd          d           t          t          j                            dddd          d           t          t          j                            d	d
d
d          d           t          t          j                            dd
d
d          d           d S )Nr  i i  i  )g      c@g     h@g=
ףp=?Gz?)g      c@g     h@r  r`   rD  r   )r   r8   r  r  r   r:   r4   r2   test_hypergeom_interval_1802r
    s    ))#vucBB! ! !))$sCC! ! ! ))#vucBB! ! ! $$T3Q77;;;$$QS!44a88888r4   c                     t           j                            d           t          j        ddd          } t	          t
          t          j        j        | ddd	           t	          t
          t          j        j        | ddd
d	           t	          t
          t          j        j        | ddd
d           t	          t
          t          j        j        | dddd           t	          t
          t          j        j	        dddd           t	          t
          t          j        j
        | dddd           t	          t
          t          j        j        | dddd           t	          t
          t          j        j        dddd           t	          t
          t          j        j        dddd           t	          t
          t          j        j        | dddd           t          j                            | dd           t          j                            | ddd
           t          j                            dd           t          j                            ddd
           t          j                            ddd
d           t          j        	                    ddd
d           t          j                            t          j        	                    dd          d           t          j                            | dd	           t	          t
          t          j        j        | ddd
           t	          t
          t          j        j        | ddd
	           t	          t
          t          j        j        | dd	           t	          t
          t          j        j        | dd
dd	           t	          t
          t          j        j        | dd
ddd           t	          t
          t          j        j        | dd
ddd	           t	          t
          t          j        j        | dd
dddd	  	         t          j                            | dd
ddd           d S )Nr   r\   r  r   numrf   r   rS  r  r   r{   rc   r   rc  r#  r:  r  r  )ri   r   r   rX  r  r  r8   r_  rh   r   rp   r   rG   r   rj  rO  r  rH	  r3  r   s    r2   test_distribution_too_many_argsr
    sX   INN4 	C!$$$A)U[_aA3????)U[_aAqcBBBB)U[_aAq!<<<)U[_aA3cJJJJ)U[_b!CHHHH)U[_aQCsKKKK)U[_aQCsKKKK)U[.A3cJJJJ)U[0"aSLLLL)U[_aQCsKKKK 
KOOAq!	KOOAq!Q	Kb!	Kb!Q	Kb!Q%%%	KOOB1a   	KOOEKOOBQO//444 
JNN1aQN)UZ^Q1a888)UZ^Q1!<<<< )U[_a<<<<)U_0!Q1#FFFF)U_0!Q1c3GGG)UY]Aq!QsCCCC)UY]Aq!Q3cJJJJ	IMM!Q1a%%%%%r4   c                      t           j                            t          j        ddd          dd          } t           j                            t          j        ddd          dd          }t          | |dd           d S )	Nr
  r  r  rf   gYZ@rd  r   re  )r8   ncx2rp   ri   r  _cdfvecr   rE  s     r2   test_ncx2_tails_ticket_955r
    sm     	
ryR--q.AAA
29RS111nEEAAqt!,,,,,,r4   c            
      *   t          j                    5  t          j        dt                     t	          t
          j                            dt          j	        dd          d          d           t
          j        
                    dt          j	        dd          d          } d d d            n# 1 swxY w Y   t          t          j        |                                                      t          j                    5  t          j        dt                     t	          t
          j                            ddd	          d           t          t
          j        
                    ddd	          d
           d d d            d S # 1 swxY w Y   d S )Nrr  r   iT  i^  rf   r   r4  r   rU  gsq6)rv  rw  rx  ry  r   r8   r
  rh   ri   r  r   r	   r|  r   r   )logvals    r2   test_ncx2_tails_pdfr
    s    
	 	"	" > >g~666UZ^^Aryc':':A>>BBB""1biS&9&91==> > > > > > > > > > > > > > >
 BK##%%&&& 
	 	"	" M Mg~666UZ^^E1b111555
))%B779KLLLM M M M M M M M M M M M M M M M M Ms%   BB11B58B5A9FFFzmethod, expectedrp   gu%>g	;Q=rh   g<x>gRz\R>r   gʎK$/gԆX1r   gfHu@ge:@c                 z     t          t          j        |           dddgd          }t          ||d           d S )Nr\   r   r   r_   )r	  r  r   r   )r-  r8   r
  r   )rL  rW   r  s      r2   test_ncx2_zero_ncr
    sE      )WUZ((!QB???FFH5111111r4   c                      t           j                            ddd          } t           j                            dd          }t	          | |d           d S )Nr_   r   r   )r  r	  r   )r  r   r   r   )r8   r
  r   re  r   )r  rW   s     r2   test_ncx2_zero_nc_rvsr
     sO     Z^^raa^88Fz~~!~44HFH5111111r4   c                      dt          j        dd          z  } t          t          j                            dd|           d           d S )Nr_   r   r  r   r  r	  r   )ri   r  r   r8   r
  rp   )r	  s    r2   test_ncx2_gh12731r
     sB    	RYq"	Bb11155555r4   c                      t          j        g d          } d\  }}t          j                            | ||          }g d}t          ||d           d S )N)gю]	@gj%@gb	y/7@g H@gIZ@gXl@g'/2?8@gݰmА@gU@gy]`'@g@g*\@g48c@)r
  gh ?8@r
  )rS  rS  rS  rS  rS  g?gy[qD?r   r   r   r   r   r   r  r   )ri   r   r8   r
  r   r   )r^   nur  r   sf_expecteds        r2   test_ncx2_gh8665r
  !   st    
 " " " 	# 	#A
 %GB	qRC	(	(B' ' 'K
 B%000000r4   c            	         d} d}t          j        t          j                            d| |          t          j                            d| |          d          }t          j                            || |          }t          j                            || |z   t          j        d| z  d|z  z                       }t          ||d	
           d S )Ni,  i  rd  r  r4  r
  rf   r   r  r   )	ri   rX  r8   r
  r   rh   r  r%  r   )r  r	  r^   ncx2_pdfgauss_approxs        r2   test_ncx2_gh11777r
  <   s    
 
B	B
EJNN5"b11JNN5"b11u	> 	> 	>Az~~aR((H:>>!R"Wbga"fq2vo.F.FGGLHl666666r4   zx, c, expected))rf   r   g|1q?)rf   rf   g~?)r	  r   V<3T1=) 7yQCr   u	lY<)r	  g   vHGBg^b!*1=)r  r  gS?c                 h    t           j                            | |          }t          ||d           d S Nr  )r8   
foldcauchyr   r   r^   r  rW   r   s       r2   test_foldcauchy_sfr
  Y   s4     
			Q	"	"BB%(((((r4   rw  ))rf   g?)r	  r
  )r
  r
  )g6ްPg8R#/c                 f    t           j                            |           }t          ||d           d S r
  )r8   r  r   r   )r^   rW   r   s      r2   test_halfcauchy_sfr
  g   s2     
			Q		BB%(((((r4   zp, expected))g?g*wӄZ>)333333?gN9?)r{   rS  )r}   g8<,O@)r  g:B)gl ׶w/gMb}[Pc                 d    t           j                            |           }t          ||           d S ru   )r8   r  r  r   )ru  rW   r^   s      r2   test_halfcauchy_isfr
  s   s0     	QAAx     r4   c                  x    t          j        dd          } t          |                     d          d           d S )Nr   r   r  )r8   r  r   rp   )rv  s    r2   test_foldnorm_zeror
     s6    		#	#	#BAr4   ))rf   r   gwo{?)r
  r   gGd-P/)r_   r>  gof?)r  r>  gOul";c                 h    t           j                            | |          }t          ||d           d S )Nr  )r8   r  r   r   r
  s       r2   test_foldnorm_sfr
     s3     
		1a	 	 BB%(((((r4   c                     t           j                             g ddd          } t           j                             ddgdd          }t          d |D                       }t          ||            t           j                             g d          } t           j                             ddg          }t          d	 |D                       }t          ||            d S )
N)r   r{   rS  r   r{   rS  c              3   R   K   | ]"}t           j        t           j        |f         V  #d S ru   ri   rM  r  r  s     r2   r  z-test_stats_shapes_argcheck.<locals>.<genexpr>   s/      88q"%	*888888r4   )rf   r  r   rf   r  c              3   R   K   | ]"}t           j        |t           j        f         V  #d S ru   r
  r  s     r2   r  z-test_stats_shapes_argcheck.<locals>.<genexpr>   s/      88q"%26	*888888r4   )r8   r!  tupler   r'  )mv3mv2mv2_augmenteds      r2   test_stats_shapes_argcheckr
     s     .

3
7
7C
.

Sz1c
2
2C88C88888M$$$ -

lll
+
+C
-

q#h
'
'C88C88888M$$$$$r4   c                       e Zd Zd ZdS )
_distr_genc                     dS Nrz  r:   rr   r^   r0   s      r2   _pdfz_distr_gen._pdf   s    rr4   Nr   r   r   r
  r:   r4   r2   r
  r
     s#            r4   r
  c                       e Zd Zd ZdS )_distr2_genc                     d|z  |z   S r
  r:   r
  s      r2   _cdfz_distr2_gen._cdf       Avzr4   N)r   r   r   r
  r:   r4   r2   r
  r
     s#            r4   r
  c                       e Zd Zd Zd ZdS )_distr3_genc                     ||z   S ru   r:   rr   r^   r0   r1   s       r2   r
  z_distr3_gen._pdf   s    1ur4   c                     d|z  |z   S r
  r:   r
  s      r2   r
  z_distr3_gen._cdf   s     Avzr4   Nr   r   r   r
  r
  r:   r4   r2   r
  r
     s2              r4   r
  c                       e Zd Zd Zd ZdS )_distr6_genc                     ||z  |z   S ru   r:   r
  s       r2   r
  z_distr6_gen._pdf   s    sQwr4   c                     d|z  |z   S r
  r:   r
  s       r2   r
  z_distr6_gen._cdf   r
  r4   Nr
  r:   r4   r2   r
  r
     s2              r4   r
  c                   t    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zd Zd Zd ZdS )TestSubclassingExplicitShapesc                 r    t          dd          }t          |                    dd          d           d S )Ndummyr0   r  r  r   r  rz  r
  r   rh   rr   dummy_distrs     r2   test_correct_shapesz1TestSubclassingExplicitShapes.test_correct_shapes   s:     gc:::[__Q!_,,b11111r4   c                 v    t          dd          }t          t          |j        dfi t	          d           d S )Nr
  Ar
  r   r  )r
  r  r  rh   r  r
  s     r2   test_wrong_shapes_1z1TestSubclassingExplicitShapes.test_wrong_shapes_1   s>     gc:::i!AAtayyyAAAAAr4   c                 ~    t          dd          }t          ddd          }t          t          |j        dfi | d S )Nr
  za, b, cr
  r   rf   r   r/  )r
  r  r  r  rh   )rr   r
  r.  s      r2   test_wrong_shapes_2z1TestSubclassingExplicitShapes.test_wrong_shapes_2   sJ     gi@@@Q!q!!!i!;;s;;;;;r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  rz  r
  )r  r  r  r
  rr   r.  s     r2   test_shapes_stringz0TestSubclassingExplicitShapes.test_shapes_string   s2    +++i33s33333r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  z(!)r
  r  r  SyntaxErrorr
  r
  s     r2   test_shapes_identifiers_1z7TestSubclassingExplicitShapes.test_shapes_identifiers_1   s2    ...k:5555555r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  4chanr
  r
  r
  s     r2   test_shapes_identifiers_2z7TestSubclassingExplicitShapes.test_shapes_identifiers_2   2    000k:5555555r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  zm(fti)r
  r
  r
  s     r2   test_shapes_identifiers_3z7TestSubclassingExplicitShapes.test_shapes_identifiers_3   s2    111k:5555555r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  za=2r
  r
  r
  s     r2   "test_shapes_identifiers_nodefaultsz@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaults   s2    ...k:5555555r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  z*argsr
  r
  r
  s     r2   test_shapes_argsz.TestSubclassingExplicitShapes.test_shapes_args   r
  r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  z**kwargsr
  r
  r
  s     r2   test_shapes_kwargsz0TestSubclassingExplicitShapes.test_shapes_kwargs   s2    
333k:5555555r4   c                 X    t          dd          }t          t          t          fi | d S )Nr
  za, b, c, lambdar
  r
  r
  s     r2   test_shapes_keywordsz2TestSubclassingExplicitShapes.test_shapes_keywords   s3    (9:::k:5555555r4   c                      G d dt           j                  } |d          }t          |                    dd          t           j                            d          dz             d S )Nc                       e Zd Zd ZdS )FTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_genc                 F    t           j                            |          |z  S ru   r8   r  r
  r
  s      r2   r
  zKTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_gen._pdf!      zq))A--r4   Nr
  r:   r4   r2   	_dist_genr
  !  #        . . . . .r4   r
  r0   r  r{   rf   r  r8   rE   r   rh   r  rr   r
  rA   s      r2   test_shapes_signaturez3TestSubclassingExplicitShapes.test_shapes_signature!  s|    	. 	. 	. 	. 	.+ 	. 	. 	. y$$$TXXcQX'')<)<Q)>?????r4   c                      G d dt           j                  } |d          }t          t          |j        dfi t          dd           d S )	Nc                       e Zd Zd ZdS )STestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_genc                 F    t           j                            |          |z  S ru   r
  r
  s      r2   r
  zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_gen._pdf!  r
  r4   Nr
  r:   r4   r2   r
  r
  !  r
  r4   r
  r  r
  r{   r   rf   rE  )r8   rE   r  r  rh   r  r
  s      r2   "test_shapes_signature_inconsistentz@TestSubclassingExplicitShapes.test_shapes_signature_inconsistent!  so    	. 	. 	. 	. 	.+ 	. 	. 	. y'''i3AA$a...AAAAAr4   c                     G d dt           j                  } |d          }t          |                    dd          t           j                            d          dz             t          |                    dd          t           j                            d          dz             t          t          |j        dfi t          d           d S )	Nc                       e Zd Zd ZdS )?TestSubclassingExplicitShapes.test_star_args.<locals>._dist_genc                 V    |d         }t           j                            |          |z  S Nr   r
  )rr   r^   r/  extra_kwargs       r2   r
  zDTestSubclassingExplicitShapes.test_star_args.<locals>._dist_gen._pdf!  s$    "1gzq))K77r4   Nr
  r:   r4   r2   r
  r  !  s#        8 8 8 8 8r4   r
  r  r
  r{   !   r  )xxx)r8   rE   r   rh   r  r  r  r  r
  s      r2   test_star_argsz,TestSubclassingExplicitShapes.test_star_args!  s    	8 	8 	8 	8 	8+ 	8 	8 	8
 y...TXXcrX22EJNN34G4G4JKKKTXXc2&&
s(;(;B(>???i3??$2,,,?????r4   c                 p    G d dt           j                  } |d          }t          |                    ddd          t           j                            d          dz  dz              t          |                    ddd          t           j                            d          dz  dz              d S )	Nc                       e Zd Zd ZdS )ATestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_genc                 \    |d         }t           j                            |          |z  |z   S r  r
  )rr   r^   rU
  r/  r  s        r2   r
  zFTestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_gen._pdf%!  s)    "1gzq))K7&@@r4   Nr
  r:   r4   r2   r
  r  $!  s(        A A A A Ar4   r
  zoffset, extra_kwargr
  r{   o   r  )rU
  r  r
  r
  s      r2   test_star_args_2z.TestSubclassingExplicitShapes.test_star_args_2!!  s    	A 	A 	A 	A 	A+ 	A 	A 	A
 y 5666TXXc#2X>>Z^^C((+c1	3 	3 	3TXXc3++Z^^C((+c1	3 	3 	3 	3 	3r4   c                      G d dt           j                  } |d          }t          |                    dd          t           j                            d                     d S )Nc                       e Zd Zd ZdS )BTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_genc                 r    |                     dd          }t          j                            |          |z  S )Nr  r   )popr8   r  r
  )rr   r^   r/  kwargsr  s        r2   r
  zGTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_gen._pdf3!  s0     %jj::zq))K77r4   Nr
  r:   r4   r2   r
  r  2!  s#        8 8 8 8 8r4   r
  r  r
  r   r   r	  r
  )rr   r
  rA   s      r2   test_extra_kwargz.TestSubclassingExplicitShapes.test_extra_kwarg/!  sw    	8 	8 	8 	8 	8, 	8 	8 	8 z///TXXaQX//1B1BCCCCCr4   c                      G d dt           j                  } |d          }t          |                    d          t           j                            d                     d S )Nc                       e Zd Zd ZdS )ITestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_genc                 @    t           j                            |          S ru   )r8   r  rh   r  s     r2   r
  zNTestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_gen._pdf@!  s    z~~a(((r4   Nr
  r:   r4   r2   r
  r  ?!  s#        ) ) ) ) )r4   r
   r
  r{   r
  r
  s      r2   test_shapes_empty_stringz6TestSubclassingExplicitShapes.test_shapes_empty_string=!  sq    	) 	) 	) 	) 	)+ 	) 	) 	) y###TXXc]]EJNN3$7$788888r4   N)r   r   r   r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r  r  r  r  r  r:   r4   r2   r
  r
     s"       2 2 2B B B< < <
4 4 4
6 6 6
6 6 66 6 66 6 66 6 66 6 66 6 6
@ @ @B B B@ @ @3 3 3D D D9 9 9 9 9r4   r
  c                       e Zd Zd Zd Zej                            ed          d             Z	ej                            ed          d             Z
d Zd Zd	 Zd
 ZdS )TestSubclassingNoShapesc                 p    t          d          }t          |                    dd          d           d S )Nr
  r  r   r  rz  r
  r
  s     r2   test_only__pdfz&TestSubclassingNoShapes.test_only__pdfJ!  s8     g...[__Q!_,,b11111r4   c                 p    t          d          }t          |                    dd          d           d S )Nr
  r"  r   r  )r
  r   rh   r
  s     r2   test_only__cdfz&TestSubclassingNoShapes.test_only__cdfN!  s8    !w///KOOAO33Q77777r4   docstring strippedr  c                     t          d          }t          |j        d           t          |j        d           t	          j        d|j                  }t          t          |          dk               d S )Nr
  r"  r   r0   zlogpdf\(x, a, loc=0, scale=1\))	r
  r   numargsr  refindallr  r	   r  rr   r
  r   s      r2   test_signature_inspectionz1TestSubclassingNoShapes.test_signature_inspectionS!  sr     !g...[(!,,,['---j:$,. .CAr4   c                     t          d          }t          |j        d           t          |j        d           t	          j        d|j                  }t          t          |          dk               d S )Nr
  r"  rf   r  z!logpdf\(x, a, b, loc=0, scale=1\)r   )	r
  r   r(  r  r)  r*  r  r	   r  r+  s      r2   test_signature_inspection_2argsz7TestSubclassingNoShapes.test_signature_inspection_2args^!  sr     "w///[(!,,,['000j=$,. .CAr4   c                 >    t          t          t          d           d S )Nr
  r"  )r  r  r
  rw   s    r2   0test_signature_inspection_2args_incorrect_shapeszHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapesh!  s    i7;;;;;;r4   c                 x     G d dt           j                  }t          t          |fi t	          d           d S )Nc                       e Zd ZddZdS )>TestSubclassingNoShapes.test_defaults_raise.<locals>._dist_genrz  c                     dS r
  r:   r
  s      r2   r
  zCTestSubclassingNoShapes.test_defaults_raise.<locals>._dist_gen._pdfo!      rr4   N)rz  r
  r:   r4   r2   r
  r3  n!  s(             r4   r
  r
  r"  r8   rE   r  r  r  rr   r
  s     r2   test_defaults_raisez+TestSubclassingNoShapes.test_defaults_raisel!  Z    	 	 	 	 	+ 	 	 	 	iAAd.@.@.@AAAAAr4   c                 x     G d dt           j                  }t          t          |fi t	          d           d S )Nc                       e Zd Zd ZdS )>TestSubclassingNoShapes.test_starargs_raise.<locals>._dist_genc                     dS r
  r:   )rr   r^   r0   r/  s       r2   r
  zCTestSubclassingNoShapes.test_starargs_raise.<locals>._dist_gen._pdfv!  r5  r4   Nr
  r:   r4   r2   r
  r<  u!  #            r4   r
  r
  r"  r6  r7  s     r2   test_starargs_raisez+TestSubclassingNoShapes.test_starargs_raises!  r9  r4   c                 x     G d dt           j                  }t          t          |fi t	          d           d S )Nc                       e Zd Zd ZdS )<TestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_genc                     dS r
  r:   )rr   r^   r0   r  s       r2   r
  zATestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_gen._pdf}!  r5  r4   Nr
  r:   r4   r2   r
  rB  |!  r>  r4   r
  r
  r"  r6  r7  s     r2   test_kwargs_raisez)TestSubclassingNoShapes.test_kwargs_raisez!  r9  r4   N)r   r   r   r#  r%  r   r   r  DOCSTRINGS_STRIPPEDr,  r.  r0  r8  r?  rD  r:   r4   r2   r   r   G!  s        2 2 28 8 8
 [+4HII  JI [+4HII  JI< < <B B BB B BB B B B Br4   r   r&  c                      g d} t           j        D ]k}t          t           |          }t          |t           j        t           j        f          r.| D ]+}t          t          j        ||j	                  d u            ,ld S )N)z,\s*,z\(\s*,z^\s*:)
r8   rQ   r-  rC  rD   rE   r	   r)  searchr  )badonesdistnamerA   regexs       r2   r+  r+  !  s    ---GM @ @uh''dU.0CDEE 	@  @ @	%66$>????	@ @r4   c                      t          t          j                            t          j        dd          d           t          t          j                            t          j        dd          d           d S )Nr_   r+  r   rD  r\   r   )r   r8   r  r   ri   r  r
  r
  r:   r4   r2   test_infinite_inputrL  !  sR    ((R88!<<<
377;;;;;r4   c                      t           j                            t           j                            dd          d          } t	          | d           d S r  )r8   lomaxr   rp   r   r_
  s    r2   test_lomax_accuracyrO  !  s=    22A66AAvr4   c                      t           j                            t           j                            dd          d          } t	          | d           d S r  )r8   r  r   rp   r   r_
  s    r2   test_truncexpon_accuracyrQ  !  sC    U-11&!<<a@@AAvr4   c                      t           j                            t           j                            dd          d          } t	          | dd           d S )Nrp  r   rX  r>  rV  )r8   r*  r  r   r   r_
  s    r2   test_rayleigh_accuracyrS  !  sF    5>,,Q22A66A3++++++r4   c                     t          j        d          5 } t          j        d           t          j                            dd           t          j                            dd           t          j                            dd           t          j                            t          j
         d           t          |           }t          |d           ddd           dS # 1 swxY w Y   dS )zregression test for gh-6219T)r  alwaysr{   r   r   N)rv  rw  rx  r8   r  rp   rh   r   r   ri   r  r  r   )r
  number_of_warnings_throwns     r2    test_genextreme_give_no_warningsrW  !  s    
	 	-	-	- 3h'''R###R###R###---$'FF!.2223 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3s   B?C""C&)C&c                     d} t           j                            d          }t          |d| z  dz   d           t           j                            d          }t          || dz   d           t           j                            d          }t	          |d           t           j                            d	d
          }t          || dz  t          j        d
          z   dz   d           t           j                            d
          }t          |d| z  dz   d           t           j                            d          }t          |d| z  dz   d           d S )Ngox?r"  rf   r   r  r   r   rS  rn  r_   r  r   rW  r  r+  )r8   r  rG   r   r   ri   r  )euler_gammaro  s     r2   test_genextreme_entropyrZ  !  sD   $K  &&AAq}q(u5555  ##AA{QU3333  %%AA  R 00AA{1}rvbzz1A5EBBBB  $$AAr+~)6666  %%AAr+~)666666r4   c                  R   d} t           j                            | d          }t          |d           t           j                            |d          }t          ||            d} t           j                            | d          }t          |d           t           j                            |d          }t          ||            d} t           j                            | d          }t          |d           t           j                            |d          }t          ||            d S )	Nr   r  g'b%4gQ@r  gؗҜ;r   g.l6?)r8   r  r   r   r  )r^   rN   r  s      r2   test_genextreme_sf_isfr\  !  s   2 	AAv&&AA-...				a	(	(BBAAu%%AA()))				a	'	'BBAAq!!AA-...				a	#	#BBr4   c                  l    d} t           j                            | dd          }t          |d           d S )Nr  rf   r   gH&8>)r8   r	  r   r   )probr  s     r2   test_burr12_ppf_small_argr_  !  s9    D|a++H H455555r4   c                     t          j        ddd          dd         } t          j                            | dd          }t          j        g d	          }t          ||d
           t          j                            | dd          }t          j        g d          }t          ||d
           t          j                            | dddd          }t          j        g d          }t          ||d
           t          j                            | dd          }t          j        g d          }t          ||d
           t          j                            | dd          }t          j        g d          }t          ||d
           t          j                            | dddd          }t          j        g d          }t          ||d
           dS )z
    All values are calculated using the independent implementation of the
    ROOT framework (see https://root.cern.ch/).
    Corresponding ROOT code is given in the comments.
    rH
  rT  r  Nr   rS  r   )r  r_  )gC,d	Ɣ?gH㸘?g5?gM"M#w?gɫs^?g @?gƴ?g@w?ɫs^?|?q ?g C?rb  ra  gJó?g,BV\ۤ?g;?g#ek?g%ǓE?g(Ȍx?g>J>rd  r   r[  )g#{`?gdf?g Jq?gSS){?g'	w?uL? T)?cAJ?GTn?R1#?gA]P?rg  rf  re  rd  gvӢ?gKq?gL?g
	N<!?gAw>r{   )r  r_  rd   re   )g=aO}?gI8?g#T?aW)?ǓI?
J?E?d۳?GTn?8?R1#?kP?g(*T?ro  rn  rm  rl  rk  rj  ri  rh  )gD
)?g:3P?g9?g?S[?ra  gOqx?gD
)?g9?gɫs^?gK?gX?g3<֌?gM+?gyS
c?gI`s?g辜?g{i ?g^0?g?#c?)g%r?gc@v?ghtj}?g(˔^?gHK4U?rc  ğ@ _?y}D?焂Rr/?N?YjhG?a0L?4f?<@?@CH?g	ސF?g5+-#?g?g?q ?rp  )g}'v?rc  g*V?rq  gr/0+?rr  g[8	?rs  gΥ?rt  gY?ru  g#)a?rv  g?̔?rw  g]ؚ?rx  g|c ?ry  )ri   rX  r8   crystalballrh   r   r   rp   )r7  
calculatedrW   s      r2   test_crystalball_functionr|  "  s<    	D#r""3B3'A "&&qsc&::Jx & & & ' 'H
 Hju5555 "&&qsc&::Jx 3 3 3 4 4H
 Hju5555 "&&qscs#&NNJx $ $ $ % %H
 Hju5555 "&&qsc&::Jx K K K L LH Hju5555 "&&qsc&::Jx # # # $ $H
 Hju5555 "&&qscs#&NNJx K K K L LH Hju555555r4   c                     t          j        g d          } t          j        g d          }t          j        g d          }t          j                            d| |          }t          ||d           t          j        g d          }t          j        dd	t           j        d
dg          }||z  }t          j                            d| |          }t          ||d           t          j        t           j        t           j        t           j        ddg          }||z  }t          j                            d| |          }	t          ||	d           t          j        t           j        t           j        t           j        t           j        dg          }||z  }
t          j                            d| |          }t          |
|d           t          j        t           j        t           j        t           j        t           j        dg          }||z  }t          j                            d| |          }t          ||d           t          j        t           j        t           j        t           j        t           j        dg          }||z  }t          j                            d| |          }t          ||d           dS )zg
    All values are calculated using the pdf formula and the integrate function
    of Mathematica
    )r   rS  r[  r   r[  )r[  r[  r   r  rX  )rS  rS  rS  rS  rS  r   rd  r   )gԚh@g[&@gͪ@g2dQ@gn6-@g?ޫV&̿g BgQCRgQF\ jr   g
@gn(@rf   g?Җ)r   gMg'#@r   g('UHr   N)ri   r   r8   rz  r	  r   r  )r  r_  expected_0th_momentcalculated_0th_momentr  r0   expected_1th_momentcalculated_1th_momentexpected_2th_momentcalculated_2th_momentexpected_3th_momentcalculated_3th_momentexpected_4th_momentcalculated_4th_momentexpected_5th_momentcalculated_5th_moments                   r2   !test_crystalball_function_momentsr  I"  sg    8---..D
***++A (#<#<#<==!-33AtQ??')>UKKKK 8DDDEED
(HbfiCDDAd(!-33AtQ??')>UKKKK
"&"&"&&(;<<Ad(!-33AtQ??')>UKKKK
"&"&"&"&*=>>Ad(!-33AtQ??')>UKKKK
"&"&"&"&':;;Ad(!-33AtQ??')>UKKKK
"&"&"&"&(;<<Ad(!-33AtQ??')>UKKKKKKr4   c                     t          j        dd          } |                                 }d\  }}}t          j        |||          }t          t          |                     |                    |          }t          ||d           d S )Nrf   r   )ir9  r-  r  r   )	r8   rz  rG   ri   rX  r   r   rh   r   )cbr  r  r  r  r^   r  s          r2   test_crystalball_entropyr  w"  sy    		1a	 	 B::<<D"IBA
BAAT"&&))__a((DD$T******r4   c                      dd} t          j        g d          }t          j                            |d|           \  }}}t          |dd           |dk    sJ t          |d	d           d
S )a?  
    Test fitting invweibull to data.

    Here is a the same calculation in R:

    > library(evd)
    > library(fitdistrplus)
    > x = c(1, 1.25, 2, 2.5, 2.8,  3, 3.8, 4, 5, 8, 10, 12, 64, 99)
    > result = fitdist(x, 'frechet', control=list(reltol=1e-13),
    +                  fix.arg=list(loc=0), start=list(shape=2, scale=3))
    > result
    Fitting of the distribution ' frechet ' by maximum likelihood
    Parameters:
          estimate Std. Error
    shape 1.048482  0.2261815
    scale 3.099456  0.8292887
    Fixed parameters:
        value
    loc     0

    r:   r   c                 ,    t          | |||dd          S )Nr  )r/  dispxtolftol)r%   )r   x0r/  r  s       r2   ro  z&test_invweibull_fit.<locals>.optimizer"  s    D"4dUKKKKr4   )r   r)  rf   r  r  r   r  r   r   rD  r_   rU  @   c   )r   ro  g`?r  r   g [@N)r:   r   )ri   r   r8   r#  r   r   )ro  r^   r  rd   re   s        r2   test_invweibull_fitr  "  s    .L L L L 	HHHIIA$((i(HHMAsEAxd++++!8888E8$//////r4   ))r   r  g7Ըh?)r   r  gz]r>)r   g     "@goBڱ9)rW  r  g$=cC;c                 j    t           j                            | |          }t          ||d           d S r   )r8   r#  r   r   )r^   r  rW   r  s       r2   test_invweibull_sfr  "  s7     ""1a((HHhU333333r4   zp, c, expected)r{   r  g9?)geK<r   g@c                 j    t           j                            | |          }t          ||d           d S r   )r8   r#  r  r   )ru  r  rW   r  s       r2   test_invweibull_isfr  "  s7     ##Aq))HHhU333333r4   z	df1,df2,x)r   r  rS  r  r   r+  r#  r  r  c                 ^   d}t           j                            || |          }t           j                            || ||          }t	          ||d           t           j                            || |          }t           j                            || ||          }t	          ||d           d S )Nr   r  r   r  )r8   r  rp   r3  r   rh   )df1df2r^   r	  expected_cdfcalculated_cdfr   calculated_pdfs           r2   test_ncf_edge_caser  "  s     
B7;;q#s++LY]]1c333NL.u==== 7;;q#s++LY]]1c333NL.t<<<<<<r4   c                  l    t           j                            ddd          } t          | dd           d S )Nrf   r  r   g     `E@r  r   )r8   r3  r  r   )r`  s    r2   test_ncf_variancer  "  s6     		aAAAu5))))))r4   c                      t           j                            dddd          } d}t          |t	          j        | d                     d S )Nr
  r  r  gffffff>@g&4I,)?)decimals)r8   r3  rp   r   ri   round)	scipy_val	check_vals     r2   test_ncf_cdf_spotcheckr  "  sG    
 	b!R..IIIrx	A>>>?????r4   r  z(On some 32-bit the warning is not raisedc                     t          j        ddd          } d| d<   dt          j        t                    5  t          j        j        | gR  }fd| D             }d d d            n# 1 swxY w Y   t          ||           d S )Nr   r   r  r  )r\   rf   r   r   r   c                 >    g | ]}t          j        j        |gR  S r:   )r8   r3  r   )r@   xipars     r2   rB   z,test_ncf_ppf_issue_17026.<locals>.<listcomp>"  s-    222"eimB%%%%222r4   )	ri   rX  r   r
  ry  r8   r3  r   r   )r^   r~  q0r  s      @r2   test_ncf_ppf_issue_17026r  "  s     	Aq#AAaD
C	n	%	% 3 3IM!"c"""22222223 3 3 3 3 3 3 3 3 3 3 3 3 3 3 Ars   &A**A.1A.c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestHistogramc                 J   t           j                            d           t          j        g dd          }t	          j        |          | _        t          j                            dddd	          }t          j        |d
          }t	          j        |          | _	        d S )Nr   )r   rf   rf   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r#  r#  r#  rD  rD  rp  rD  binsrS  r  r4  {   r  r<  )
ri   r   r   	histogramr8   rF   templater  r   norm_template)rr   r  r   norm_histograms       r2   r6  zTestHistogram.setup_method"  s    
	t L "@ "@ "@FGI I I	*955z~~#Su3~OOd444"/??r4   c                    t          j        g d          }t          j        g d          }t          | j                            |          |           t          | j                            d          d           t          | j                            d          d           t          | j                            d          d           t          | j                            d          d           t          j        d	d
d          }t          | j                            |          t          j
                            |dd          d           d S )Nr   r{   rS  r  r   r  r[  rA  r  rC  rT        @r  r  r*  ro  r        !@rX  r  )r   r   rL  rL  {Gz?r  Q?r  {Gz?r  r  r  r  r  r  r  r  r  r   r   r  r  r  rX  r   r  r   rf   r_   rS  r  rc   r\   r   )ri   r   r   r   r  rh   r   rX  r  r8   r  )rr   r  
pdf_valuesr^   s       r2   rQ  zTestHistogram.test_pdf #  sX    M M M N NZ !I !I !I J J

 	))&11:>>> 	DM--c22H===DM--c22H=== 	DM--c22H===DM--d33X>>>KAr""*..q11
qc==C	I 	I 	I 	I 	I 	Ir4   c                 6   t          j        g d          }t          j        g d          }t          | j                            |          |           t          | j                            |dd                   |dd                    t          j        ddd          }t          | j                            | j                            |                    |           t          j        ddd          }t          | j                            | j                            |                    |           t          j        d	dd
          }t          | j                            |          t          j
                            |dd          d           d S )Nr  )r   r   r   r  rL  r  r  
ףp=
?Q?{Gz?r5  r{   r  (\?RQ?=
ףp=?)\(?r
  rS  rS  rf   r   rS  rX  r`   r   r   r_   r  rc   r\   r   )ri   r   r   r   r  rp   r   rX  r  r8   r  )rr   r  
cdf_valuesr^   s       r2   r  zTestHistogram.test_cdf_ppf#  s    M M M N NZ !M !M !M N N

 	))&11:>>>))*QrT*:;;VAbD\JJJ KS#&&))$-*;*;A*>*>??CCCKS#&&))$-*;*;A*>*>??CCCKAr""*..q11
qc==C	I 	I 	I 	I 	I 	Ir4   c                 :   d}| j                             |d          }t          t          j        |dk               d           t          t          j        |dk              d|z  d	           t          t          j        |d
k              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |dk              d|z  d	           t          t          j        |d k              d!|z  d	           t          t          j        |d"k              d#|z  d	           t          t          j        |d$k              d%|z  d	           t          t          j        |d&k              d|z  d	           t          t          j        |d&k              d|z  d	           t          t          j        |d&k              d           d S )'Nr4  r  r   rS  r   r   rL  r  r   r  r  r[  r  r\   rA  r  r  r  rC  r  rT  r5  r  r  r{   r  r  r  r  r*  r  ro  r  r  r  r  r
  rX  )r  r   r   ri   rl  r   )rr   r  r  s      r2   rI  zTestHistogram.test_rvs0#  s   """<<RVFSL))3///v}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHRVFSL))3/////r4   c                     t          d          D ]R}t          | j                            |          t	          j        dd                              |          d           Sd S )Nr   rS  r  r  r   )r  r   r  r	  r8   r  r  r  s     r2   r	  zTestHistogram.test_munpF#  sx    q 	G 	GAD.44Q77!JsC0077::G G G G G	G 	Gr4   c                     t          | j                                        t          j                            dd          d           d S )NrS  r  rc   r  r   )r   r  rG   r8   r  rw   s    r2   rp  zTestHistogram.test_entropyK#  sT    *2244
**s#*>>T	K 	K 	K 	K 	K 	Kr4   N)	r   r   r   r6  rQ  r  rI  r	  rp  r:   r4   r2   r  r  "  s        @ @ @ I I I4I I I,0 0 0,G G G
K K K K Kr4   r  c                     ddgg d}} t          j        | |fd          }t          j                            |                    ddg          ddg           |                                dk    sJ t          j        | |fd          }t          j                            |                    ddg          d	           |                                d
k    sJ d}t          j        t          |          5  t          j        | |f          }|                                d
k    sJ 	 d d d            n# 1 swxY w Y   t          j        | g df          }|                                dk    sJ d S )Nr   )r   r   r3  F)r  r{   r  r	  Tg'^P?g     H@z(Bin widths are not constant. Assuming...r  r  )
r8   rF   ri   rp  r   rh   r  r   r
  ry  )countsr  rA   r  s       r2   test_histogram_non_uniformr  P#  s   FLLLDFvtne<<<DJtxxc
33c6]CCC;;==Avtnd;;;DJtxxc
33V<<<;;==F"""" 9G	nG	4	4	4 ' '!64.11{{}}&&&&&' ' ' ' ' ' ' ' ' ' ' ' ' ' '
 vyyy122D;;==As   61D44D8;D8c                   f    e Zd Zd Zej                            dddg          d             Zd ZdS )TestLogUniformc                 ~   t           j                            d          }t          j        dd          }|                    d|          }t           j                            d          }t          j        dd          }|                    d|          }t          ||           t          j        t          j	        |          d          \  }}d|
                                cxk    r|                                cxk    rd	k    sn J t          j        t          j        |          d
z
            dk    sJ d S )N   0o[ rd  r   r4  r   r_   r  r  iL  r   )ri   r   r   r8   
loguniformr   
reciprocalr   r  log10r-  ro  r   r  )rr   r   rv  r   rv2r   rG  r   s           r2   
test_aliaszTestLogUniform.test_aliash#  s    i##K00h00ff%cf22i##K00x11wwEw44c""",rx}}2666adhhjj6666DHHJJ6666$666666vbioo,--333333r4   rL  rO  rJ  c                 D   t           j                            d          }t          j                            ddd|          }t          j                            ||          \  }}}}|dk    sJ t          j                            |d|          \  }}}}|dk    sJ d S )	Nr  r\   r   r   r   rN  rf   rK  )ri   r   r   r8   r  r   r   )rr   rL  r   r   r0   r1   rd   re   s           r2   test_fit_overridez TestLogUniform.test_fit_overridey#  s     i##K00""33"GG +//F/CC1c5zzzz +//Af/MM1c5zzzzzzr4   c                    t           j                            d          }d\  }}t          j        ||          }|                    ddd          }t          |                    |                    |                    |           |	                    d          }t          |                    |                    |                    |           dt          j
        dd	          z  }|                    |          }t          |d d
         |dd          z  d           ||z
  t          j        |          t          j        |          z
  z  }	t          |                                |	           d S )Nl   eVi
P )gN~hgZbtir   r   r   r:  r  i8r  r   r_   )ri   r   r   r8   r  ry  r   rp   r   r   r  rh   r  r   )
rr   r   r0   r1   rA   rp   r   r^   rh   r   s
             r2   test_overflowzTestLogUniform.test_overflow#  s<    i##$78811%% kk!QTk**#//555hhDh!!#//555 4%%%hhqkkCRCQRR("--- Aq		BF1II-.		T*****r4   N)	r   r   r   r  r   r   r   r  r  r:   r4   r2   r  r  g#  sd        4 4 4" [Xt}55
 
 65
+ + + + +r4   r  c                      e Zd Zd Zej                            dddgddgddgg          d	             Zej                            d
ddg          d             Zej                            dg d          d             Z	ej                            dg d          d             Z
ej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zej                            dg d          d             Zd S )!	TestArgusc                     t           j                            ddd          }t          t          j        d                                          |                                d           d S )Nr<  r~  E  r   r   rV  )r8   argusr   r   r   r  s     r2   test_argus_rvs_large_chiz"TestArgus.test_argus_rvs_large_chi#  sR    KOOBSsO;;EKOO0022AFFHHaHHHHHHr4   zchi, random_stater\   r  rZ     rA     c                     t           j                            |d|          }t          j        |d|f          \  }}t	          |dk               d S )Nr~  r   r  r  r8   r  r   r  r	   )rr   r  r   r^   r   ru  s         r2   rI  zTestArgus.test_rvs#  sN     KOOCcOEE|Aw001Dr4   r  rF  r  c                     t           j                            |dd          }t          j        |d           \  }}t	          |dk               d S )Nr~  ie r   c                     dd| dz  z
  dz  z
  S )Nr   rf   r  r:   r   s    r2   rO   z.TestArgus.test_rvs_small_chi.<locals>.<lambda>#  s    a!Q$h#->)> r4   r  r  )rr   r  r  r   ru  s        r2   test_rvs_small_chizTestArgus.test_rvs_small_chi#  sN    
 KOOCcO??|A>>??1Dr4   zchi, expected_mean))r   g щi?)r_   g.憃?)r  g\paP?)r  g	?)r  g,6?c                 l    t           j                            |d          }t          ||d           d S )Nr   r  r   r   )r8   r  r   r   )rr   r  expected_meanr_  s       r2   r  zTestArgus.test_mean#  s9     KS**=u555555r4   zchi, expected_var, rtol))r   gLH'B?r   )r_   go$?r-  )r  g
=>r  )r  g2W>r  )r  gb~P>r  c                 l    t           j                            |d          }t          |||           d S )Nr   r  r   )r8   r  r  r   )rr   r  expected_varr   r`  s        r2   r  zTestArgus.test_var#  s6     KOOCqO))<d333333r4   zchi, expected, rtol))r   gwM?r  )r{   gj?r  )r\   gHEA`!?r  )r}   gcف>r   )rd  gF=r  )r  g߹Q#B=r  )r  g0ޟ<r  )rF  g*W%:r   c                 D    t          t          |          ||           d S rQ  )r   r#   )rr   r  rW   r   s       r2   test_argus_phi_small_chiz"TestArgus.test_argus_phi_small_chi#  s%     	
3======r4   zchi, expected))r{   )g-\/?g+p7c?g5Ϧ\?)r  )g
f?gi{?ٸ?gZ@7?)r\   )gB	?g]?gR{?)r}   )glͅw?g,?g[Z=?)rd  )gz,?g]?gѪ1?)r  )g8<?gE-?gI?)r  )g~7?g7B.?g9?)rF  )g;?g9B.?g}5?c                     t          j        g d          }t          t          j                            ||          |d           d S )Nr\   r{   r   r   r   )ri   r   r   r8   r  rh   rr   r  rW   r^   s       r2   test_pdf_small_chizTestArgus.test_pdf_small_chi#  B     H___%%3//FFFFFFr4   ))r{   )gQ߹?e?grJ,?g򺗄?)r  )gΎd?g?gh?)r\   )g|
o?gvb?g+@?)r}   )g̈́On?ge?gC|[3?)rd  )g!?m?g{jiH?gu53?)r  )g~m?g0-.?g3?)r  )g~m?g7;B.?gŗ3?)rF  )g~m?g9B.?gŗ3?c                     t          j        g d          }t          t          j                            ||          |d           d S )Nr  r  r   )ri   r   r   r8   r  r   r  s       r2   test_sf_small_chizTestArgus.test_sf_small_chi#  sB     H___%%q#..uEEEEEEr4   ))r{   )g+&?gk?gμm/?)r  )g?CL\f?g^N?g]AͭR?)r\   )ga>$?g;Lf?gaW?)r}   )gx?g 43n?gwY?)rd  )go7🤎?g
+-oGn?gIQ9Y?)r  )gT?gGn?g@̋Y?)r  )gU?g{Gn?giG͋Y?)rF  )gDU?g {Gn?gH͋Y?c                     t          j        g d          }t          t          j                            ||          |d           d S )Nr  r  r   )ri   r   r   r8   r  rp   r  s       r2   test_cdf_small_chizTestArgus.test_cdf_small_chi#  r  r4   ))r{   )gQ)?g6{?r  )gB`"۹?)g?g8%?r-  )r\   )g388?gV%?r   )r}   )g*j?gRS%?r   )rd  )g!|?gZ%?r   )r  )gy[|?gG%?r   )r  )g"3|?gW%?r   )rF  )g!3|?gW%?r   c                 l    t           j                             |d          }t          |||           d S )Nrc  r]  r   )r8   r  r   )rr   r  rW   r   rH  s        r2   test_stats_small_chizTestArgus.test_stats_small_chi$  s9     kT22XD111111r4   N)r   r   r   r  r   r   r   rI  r  r  r  r  r  r  r  r  r:   r4   r2   r  r  #  s       I I I
 [0#J#J#J3
  
  

 [UT4L11  21 [18 8 89 96 69 96
 [6B B BC C4 4C C4
 [2D D DE E> >E E> [	M 	M 	M	N 	NG G	N 	NG
 [	N 	N 	N	O 	OF F	O 	OF
 [	P 	P 	P	Q 	QG G	Q 	QG
 [	C 	C 	C	D 	D2 2	D 	D2 2 2r4   r  c                      e Zd Zd Zd Zej                            dg d          d             Zej                            dg d          d             Z	d Z
ej                            d	g d
          d             Zej                            d          ej                            dg d          ej                            dg d          ej                            dg d          d                                                 Zej                            dg d          ej                            dg d          d                         ZdS )TestNakagamic                 n    d}d}t           j                            ||          }t          |d           d S )Nr  r  gM+)r8   nakagamir   r   )rr   r
  r^   rz  s       r2   r{  zTestNakagami.test_logpdf$  s<     ~$$Q++122222r4   c                     d}d}t           j                            ||          }t          |dd           t           j                            ||          }t          ||d           d S )Nr  rT  g"S+:r   r   )r8   r  r   r   r  )rr   r
  r  r   r  s        r2   r  zTestNakagami.test_sf_isf)$  sm     ^r2&&1>>>>^B''BU++++++r4   zm, ref))r   g|Bd븿)r{   r  )r_   g/ۿc                 d    t          t          j                            |          |d           d S )Ng^~z=r   r   r8   r  rG   rr   r_  r  s      r2   rp  zTestNakagami.test_entropy<$  s/      	..q113WEEEEEEr4   ))r  g}Ô%I)r  gq_)g    ScAgB4U)g    cAgu1U)r  gb>%)r  gWҙ\c                 `    t          t          j                            |          |           d S ru   r  r  s      r2   test_extreme_nuzTestNakagami.test_extreme_nuN$  s*    
 	..q11377777r4   c                     t          j        t          j                            d                    sJ t          j        t          j                            d                    sJ d S )Nr  r  )ri   r  r8   r  _entropyrw   s    r2   test_entropy_overflowz"TestNakagami.test_entropy_overflowU$  sT    {5>22599:::::{5>226::;;;;;;;r4   znu, ref))r  g2H?)r  g:U?)r  g>c                 d    t          t          j                            |          |d           d S r  )r   r8   r  r   )rr   r
  r  s      r2   r  zTestNakagami.test_meanY$  s/     	++B//5AAAAAAr4   z+Fit of nakagami not reliable, see gh-10908.r  r
  )r8  r  r  rd   )r~   r_   r	  re   )r)  r   r
  c                   
 d
t           j                            
|||d          t           j                                      \  }}}t	          ||d           t	          ||d           t	          ||d           fd}
fd}
fd}	t	           ||||          d	d
           t	           ||||          d	d
           t	           |	|||          d	d
           d S )Nr`   9  r   r
  rd   re   r   r  r   c                     d| z  dz   t          j        d|z
  z            z  d| z  |dz  z  t          j        |z
            z  z   S )Nr   r   rf   ri   rl  )r
  rd   re   r  s      r2   	dlogl_dnuz(TestNakagami.test_fit.<locals>.dlogl_dnut$  sR    UQY"&GcM):";";;d5!8mbfWs]&;&;;< =r4   c                     dt          j        |           z   t          d|           z
  z  dt          j        t          j        |z
  |z                      z  z   t          j        |z
  |z  dz            z
  S )Nr   r   rf   )ri   r  r   rl  r
  rd   re   r  r  s      r2   
dlogl_dlocz)TestNakagami.test_fit.<locals>.dlogl_dlocx$  sv    RVBZZ)Ar*:*::;rvw}&=>>???@fw}59::; <r4   c                 h    dz  | z  |z  d| z  |dz  z  t          j        |z
  dz            z  z   S )Nr   rf   r   r  r  s      r2   dlogl_dscalez+TestNakagami.test_fit.<locals>.dlogl_dscale}$  sG    !GbL5("fuz)BFGcMa3G,H,HHI Jr4   r   rd  r   )r8   r  r   r   r   )rr   r
  rd   re   nu_estloc_est	scale_estr  r  r  r  r  s             @@r2   r  zTestNakagami.test_fite$  s[    .$$!+0t % E E%*^%7%7%@%@"----3////	5s3333	= 	= 	= 	= 	=	< 	< 	< 	< 	< 	<
	J 	J 	J 	J 	J 	J 			&'9==qtLLLL

67I>>MMMMVWi@@!$OOOOOOr4   c                    d}d}t           j                            ||||d          }t           j                            ||          \  }}}t	          j        |          }	t	          j        t	          j        ||z
  dz                      }
t          ||d           t          ||	d           t          ||
d           d S )	Nr{   r`   r  r  r#  rf   r  r   )	r8   r  r   r   ri   r-  r%  r   r   )rr   rd   re   r
  rt  r  r  r  r  loc_theo
scale_theos              r2   test_fit_nuzTestNakagami.test_fit_nu$  s    
 .$$!+0t % E E%*^%7%7B%7%G%G" 6'??WRWg&7A%=>>??
....5555	:D999999r4   N)r   r   r   r{  r  r   r   r   rp  r  r  r  r  r  r  r:   r4   r2   r  r  $  s       3 3 3", , ,& [X	$ 	$ 	$% %F F	% %F [X	D 	D 	DE E8 8	E E8< < < [Y> > >? ?B B	? ?B [KLL[T???33[UNNN33[Wkkk22P P 32 43 43 MLP8 [UNNN33[Wkkk22: : 32 43: : :r4   r  c                        e Zd Zd Zd Zd ZdS )TestWrapCauchyc                 L   t          j        ddgddgg          }t          j        dgdgg          }t          j                            ||          }|j        dk    sJ d t          j        ||f          D             }t          |                                |d	
           d S )NQ?rk  r{   r   rS  r  r  c                 T    g | ]%\  }}t           j                            ||          &S r:   )r8   
wrapcauchyrp   )r@   r  r	  s      r2   rB   z>TestWrapCauchy.test_cdf_shape_broadcasting.<locals>.<listcomp>$  s?     < < <%b" )--b"55 < < <r4   r   r   )	ri   r   r8   r!  rp   rA  nditerr   r	  )rr   r  r^   ru  scalar_valuess        r2   test_cdf_shape_broadcastingz*TestWrapCauchy.test_cdf_shape_broadcasting$  s     HtTlS$K011HsecU^$$  A&&w&    < <)+Aq6):):< < <		=u======r4   c                 ~    t           j                            t          j        d          }t          |dd           d S )Nr  r{   r  r   )r8   r!  rp   ri   rj   r   r  s     r2   test_cdf_centerzTestWrapCauchy.test_cdf_center$  s7      --3U++++++r4   c                    d}d}d}t           j                            ||g|          }d|z   d|z
  z  }t          |d         t	          j        |t	          j        |dz            z            t          j        z             t          |d         dt	          j        |t	          j        t          j        |dz  z
            z            t          j        z  z
             d S )NrS  r  r   r   r   rf   )r8   r!  rp   r   ri   arctantanrj   )rr   r  r  r  ru  crs         r2   r[  zTestWrapCauchy.test_cdf$  s      "b1--!ea!e_!bi26"Q$<<88>???!a")Brvbebdl/C/C,C"D"DRU"JJKKKKKr4   N)r   r   r   r$  r&  r[  r:   r4   r2   r  r  $  sF        
> 
> 
>, , ,L L L L Lr4   r  c                       G d dt           j                  }  | d          }t          t          d          5  |                                 d d d            d S # 1 swxY w Y   d S )Nc                       e Zd Zd ZdS )/test_rvs_no_size_error.<locals>.rvs_no_size_genc                     dS r   r:   rw   s    r2   _rvsz4test_rvs_no_size_error.<locals>.rvs_no_size_gen._rvs$  s    1r4   N)r   r   r   r/  r:   r4   r2   rvs_no_size_genr-  $  s#        	 	 	 	 	r4   r0  rvs_no_sizer"  z_rvs\(\) got (an|\d) unexpectedr  )r8   rE   r  r  r   )r0  r1  s     r2   test_rvs_no_size_errorr2  $  s        %-    "/}555K	y(J	K	K	K                   s   AA!$A!zdistname, argsc                 n   | t           v rt          j        d|  d           t          t          |           }t          |t          j                  rt          |          dk    rA |j        | \  }}t          |t          j                   t          |t          j                   d\  }} |j        g |||R  \  }}t          |t          j                   t          |t          j                   d S  |j        | \  }	}
t          |	t          j                   t          |
t          j                   d S )Nz6skipping test for the support method for distribution .r   r  )$skip_test_support_gh13294_regressionr   r   r-  r8   rC  rE   r  supportr   ri   r  )rI  r/  rA   a0b0r  r  a1b1r0   r1   s              r2   test_support_gh13294_regressionr;  $  s8   777 0$,0 0 0 	1 	1 	15(##D$+,,  t99>>!T\4(FBRV$$$RV$$$
 f2t2T26222BR   R     t|T"1QQr4   c                  \   t           j                            g dg d          \  } }t          j        t          j         t          j         t          j         t          j        g          }t          j        t          j        t          j        t          j        t          j        g          }t          | |           t          ||           | j        |j        k    sJ |j        |j        k    sJ t           j                            g g           \  }}t          j        g           t          j        g           }}t          ||           t          ||           |j        |j        k    sJ |j        |j        k    sJ t           j                            g ddg          \  }}	t          j        dt          j        gz            }
t          j        dt          j        gz            }t          ||
           t          |	|           |j        |
j        k    sJ |	j        |j        k    sJ d S )N)r   r   r   r   )r   r   r   r   r   r   )	r8   r  r6  ri   r   r  r  r   rA  )r7  r8  ex_a0ex_b0r9  r:  ex_a1ex_b1rQ  rN  ex_a2ex_b2s               r2   ,test_support_broadcasting_gh13294_regressionrC  $  s   Zmmm<<FBHrvgw899EHbfbfbfbf566EUU8u{""""8u{""""ZB''FB8B<<"5EUU8u{""""8u{""""Zrd33FBHQxZ  EHQxZ  EUU8u{""""8u{""""""r4   c                  2   ddg} dgdgdgg}t          t          j                            | |          ddgddgddgg           t	          j        d          } t	          j        d          }t          j                            | |          j        dk    sJ d S )	Nr   rS  r   r[  r  rX  r>   r  )r   r8   r  r  ri   r	  rA  rc   s     r2   *test_stats_broadcasting_gh14953_regressionrE  $  s    r(CTB4"EU++r2hR2r(-KLLL
(5//CHVE:>>#u%%+v555555r4   )gn!	g:I"<)gQ	@gE?c                     t          t          j                            |           |           t          t          j                            |            |           d S ru   )r   r8   cosinerp   r   )r^   rW   s     r2   test_cosine_cdf_sfrH  %  sJ     EL$$Q''222ELOOQB''22222r4   ))r  gkM6O)rZ  g0ӭ!	)r
  g;'u(@c                     t          t          j                            |           |           t          t          j                            |           |            d S ru   )r   r8   rG  r   r  )ru  rW   s     r2   test_cosine_ppf_isfrJ  %  sL    
 EL$$Q''222EL$$Q''(33333r4   c                      t           j                            t          j         t          j        g          } t          | d           d S )NgrB)r8   rG  r   ri   rj   r   )rz  s    r2   test_cosine_logpdf_endpointsrL  %  s:    <//D d./////r4   c                      d t           D             } d t          D             }| |k    sJ d t          D             }d t          D             }||k    sJ d S )Nc                 B    h | ]\  }}t          |t                    |S r:   )rC  rK   r@   r  r   s      r2   	<setcomp>z*test_distr_params_lists.<locals>.<setcomp>%  s:     4 4 474'c224$ 4 4 4r4   c                     h | ]\  }}|S r:   r:   rO  s      r2   rP  z*test_distr_params_lists.<locals>.<setcomp>!%  s    AAAgdATAAAr4   c                     h | ]\  }}|S r:   r:   rO  s      r2   rP  z*test_distr_params_lists.<locals>.<setcomp>$%  s    333wtQd333r4   c                     h | ]\  }}|S r:   r:   rO  s      r2   rP  z*test_distr_params_lists.<locals>.<setcomp>%%  s    999'$999r4   )r    r!   r   r   )discrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamess       r2   test_distr_params_listsrX  %  s    4 4l 4 4 4AAAAA!6666633(333N99[999.......r4   c                      t           j                            dd           t           j                            dd          dk    sJ t           j                            dd          dk    sJ d S )Nr   r[   r  r   )rG  r0   r[  )r8   r2  _statsr  r	  r:   r4   r2   test_moment_order_4r[  )%  sr     
NAs+++ >  qA ..#5555 >1%%,,,,,,r4   c                      e Zd Zej        d             Zej                            dg d          d             Zej                            dg d          d             Z	ej        j
        ej                            d ej        d	d
ej        j                   ej        ddej        j
                   ej        ddej        j
                  g          d                         ZdS )TestRelativisticBWc                     t          j        t          t                    j        dz            }t           j                            |j        d          }|S )a&  Sample data points for pdf computed with CERN's ROOT

        See - https://root.cern/

        Uses ROOT.TMath.BreitWignerRelativistic, available in ROOT
        versions 6.27+

        pdf calculated for Z0 Boson, W Boson, and Higgs Boson for
        x in `np.linspace(0, 200, 401)`.
        z-data/rel_breitwigner_pdf_sample_data_ROOT.npyzx,pdf,rho,gammar!  r  r  s     r2   ROOT_pdf_sample_dataz'TestRelativisticBW.ROOT_pdf_sample_data>%  sM     wNN!;<
 
 v  /@ AAr4   zrho,gamma,rtol))qVEB@gj+@r  )FC@Gz @r  )ND@_LU?r  c                     ||d         |k    |d         |k    z           }|d         |d         }}t          |t          j                            |||          |           d S )Nrhor_  r^   rh   r  r   )r   r8   rel_breitwignerrh   )rr   r_  rg  r_  r   r   r^   rh   s           r2   test_pdf_against_ROOTz(TestRelativisticBW.test_pdf_against_ROOTQ%  s     $!%(C/#G,57
 cDK3&**1c*??d	
 	
 	
 	
 	
 	
r4   zrho, Gamma, rtol))r`  ra  r  )rb  rc  r  )rd  re  g&.>c                    d }t          j        ddd          }t          j                            |||          }t          j                            |||          } ||||z  |          }t          |||           d S )Nc                    t          j        |dz  |dz  |dz  z   z            }dt          j        d          z  |z  |z  |z  t           j        t          j        |dz  |z             z  z  }|| dz  |dz  z
  dz  |dz  |dz  z  z   z  S r  )ri   r%  rj   )Er  Gammar_  r[   s        r2   rh   zFTestRelativisticBW.test_pdf_against_simple_implementation.<locals>.pdfj%  s    GAqDAqD5!8O455ERWQZZ!#e+e3EBGAqD5L1113AA1q(1a4q=899r4   r  r  r_   r  r   )ri   rX  r8   rh  r   rh   r   )	rr   rg  rm  r   rh   ru  r^   r   r  s	            r2   &test_pdf_against_simple_implementationz9TestRelativisticBW.test_pdf_against_simple_implementationb%  s    	: 	: 	: KdB''!%%aE%::#''3e'<<c!SY&&St,,,,,,r4   z	rho,gammar`  ra  r  rb  rc  rd  re  c                    d}t           j                            |          }t          j                            ||d|          }t          j                            |d          }t          |d         |d         f||fd           |d	         dk    sJ t          j                            |d|
          }t          |d         |d           |d	         |d         fd|fk    sJ dS )zpTests fit for cases where floc is set.

        `rel_breitwigner` has special handling for these cases.
        l   s;
rl# r   )re   r   r   r   r   rf   r  r   r   r  r}   N)ri   r   r   r8   rh  r   r   r   )rr   rg  r_  r   r   r   r   s          r2   test_fit_flocz TestRelativisticBW.test_fit_flocv%  s    & #i##D))$((u4c ) 
 
 #''1'55QQ(3,TBBBB1v{{{{#''1U'CCA$////AAAu:------r4   N)r   r   r   r   r;  r_  r   r   ri  rn  r   r  r   rp  r:   r4   r2   r]  r]  =%  se       ^  ^$ [ 
 
 
 
 
 
 [/ 2 2 2  - - - [[FL"F&+2B   FL!50A   FL &0A  

 . .  . . .r4   r]  c                   Z    e Zd Zej                            dddg          d             ZdS )TestJohnsonSUrX  )r}
  r  r  r  g={?g?5mV>gn?g\}\1@)g`fo@g$ں_@r   r   gvUgN<fj?gwCg~l
@c                 v    t          j        j         |d d         ddi}t          ||dd          d           d S )Nr   r^  r\  r  r   )r8   r  r   )rr   rX  r   s      r2   test_moment_gh18071z!TestJohnsonSU.test_moment_gh18071%  sF     o#T"1"X>v>>T!""XE222222r4   N)r   r   r   r   r   r   rt  r:   r4   r2   rr  rr  %  sZ        [VOJ&K L L
3 3L L
3 3 3r4   rr  c                   2   e Zd Zd Zej                            dddg          ej                            dddg          ej                            dddg          ej                            dddg          d                                                 Zd	S )
TestTruncParetoc                 H   d\  }}t          j        dd          }t          j        ||                              |          }t          j        |                              |          t          j        |                              |          z  }t          ||           d S )N)?333333@rx  ry  )ri   rX  r8   truncparetorh   rD  rp   r   )rr   r1   r  r^   r   r  s         r2   rQ  zTestTruncPareto.test_pdf%  s    1KS!!1%%))!,,l1oo!!!$$u|A':':1'='==S!!!!!r4   r   TFr  rK  r^  c                    t           j                            d          }d\  }}}}	t          j        ||||	          }
|
                    d|          }i }|r||d<   |r|	|d<   |r||d<   |r||d	<   |rU|rS|rQ|rOd
}t          j        t          |          5  t          j        j	        |fi | d d d            d S # 1 swxY w Y   d S t          t          j        |fi | d S )Nl   Z#Lm )rx  ry  r   r  rc   r~  r   r   r   r   r  r  r  )ri   r   r   r8   rz  r   r   r   r  r   r   )rr   r   r  rK  r^  r   r1   r  rd   re   rA   r   r   r  s                 r2   r  zTestTruncPareto.test_fit%  s}    i##$788+1c5 A3e<<<xxSsx33 	DL 	#"DN 	DJ 	DJ 	Ky 	KU 	Ku 	KKG|7;;; 4 4!%d33d3334 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 *%*;TJJTJJJJJs   B>>CCN)r   r   r   rQ  r   r   r   r  r:   r4   r2   rv  rv  %  s        " " " [Yu66[[4-88[WtUm44[WtUm44K K 54 54 98 76K K Kr4   rv  c                       e Zd Zd ZdS )
TestKappa3c                     dt           j                            dd          z
  }t           j                            dd          }t	          ||           d S )Nr   r{   g     j@)r8   kappa3rp   r   r   )rr   sf0r  s      r2   r  zTestKappa3.test_sf%  sK     %,""3,,,looc3''S!!!!!r4   N)r   r   r   r  r:   r4   r2   r}  r}  %  s#        " " " " "r4   r}  c                       e Zd Z ej        dd          Z ej        d          Z ej        d          Zd Z	d Z
d Zd Zd Zd	 Zd
 Zd Zd ZdS )TestIrwinHallr   r   r_   c                 V    t          | j                            d          d           d S )Nr\  )r   g?r   gQ)r   ih10r8   rw   s    r2   test_stats_ih10zTestIrwinHall.test_stats_ih10%  s)     	TY__V446JKKKKKr4   c                      g d} fdt          t          |                    D             }t          ||            j                            d          }d}t          ||           d S )N)	r   gUUUUU9@g     0a@i  gx@gn۶mˠ@g    :PAg8)Ag   SAc                 J    g | ]}j                             |d z              S r	  )r  r  )r@   rt  rr   s     r2   rB   z3TestIrwinHall.test_moments_ih10.<locals>.<listcomp>%  s-    CCCQ49##AaC((CCCr4   r<  g2⍚H)r  r  r   r  r  )rr   rG  r^  m50	m50_exacts   `    r2   test_moments_ih10zTestIrwinHall.test_moments_ih10%  s~    - - - DCCC%D		2B2BCCCWd+++ir""H	S),,,,,r4   c                     t          j        ddd          }| j                            |          }| j                            |          }t          ||d           d S Nr   r   r`   r_   maxulp)ri   rX  unifrh   ih1r   )rr   ptspdf_unifpdf_ih1s       r2   test_pdf_ih1_unifzTestIrwinHall.test_pdf_ih1_unif%  sX     k!Q$$9==%%(,,s##Whr::::::r4   c                    t          j        d          }d}t          j        dd|          }t          j        dd|          }d||dz   dz  d          z
  ||dz   dz  d <   |                    |          }t          ||d           d S )Nrf   r]   r   r   r_   r  )r8   r4  ri   rX  rh   r   )rr   ih2nptsr  rW   pdf_ih2s         r2   test_pdf_ih2_trianglez#TestIrwinHall.test_pdf_ih2_triangle%  s    oa  k!Q%%;q!T**%&4!8/2B2B)C%C$(q!!"''#,,Whr::::::r4   c                     t          j        ddd          }| j                            |          }| j                            |          }t          ||d           d S r  )ri   rX  r  rp   r  r   )rr   r  cdf_unifcdf_ih1s       r2   test_cdf_ih1_unifzTestIrwinHall.test_cdf_ih1_unif&  sV    k!Q$$9==%%(,,s##Whr::::::r4   c                     t          j        dd          }t          j        |          }|                    |dz            }t          j        dt          |                    }t          ||d           d S )Nr   r_   rf   r{   r  )ri   r  r8   r4  rp   r[  r  r   )rr   rt  ihih_cdfexacts        r2   r[  zTestIrwinHall.test_cdf&  sg    Ia_QA	#s1vv&&VU2666666r4   c                 2   g d}t          | j                            t          j        d                    |d           t          | j                            d          dd           d}t          | j                            d          |d           d S )	N)r   g\xO~>g-P2?g8ʝi?gg{Ȇ?r{   g&M?g׈Y?gB?gDl?r   r+  r_   r  r\   g+|<rS  g#@)r   r  rp   ri   r  r  s      r2   test_cdf_ih10_exactz!TestIrwinHall.test_cdf_ih10_exact&  s    ( ( ( 	TY]]29R==994KKKKTY]]4002EbQQQQ1TY]]5113rBBBBBBr4   c                     g d}|dg|d d d         z   z  }t          | j                            t          j        d                    |d           d S )N)r   g4V>gP3NV?g*8f?gNgX?gjS?r   r+  r_   r  )r   r  rh   ri   r  rr  s     r2   test_pdf_ih10_exactz!TestIrwinHall.test_pdf_ih10_exact'&  s\     JII$ttt*,,TY]]29R==994KKKKKKr4   c           	      ,   t          | j                            t          j        d                    d| j                            t          j        d                    z
             d}t          | j                            d          |d           d S )Nr+  r   rS  r\   r_   r  )r   r  r   ri   r  rp   r   )rr   r  s     r2   test_sf_ih10_exactz TestIrwinHall.test_sf_ih10_exact.&  st    	RYr]]33QryQS}}9U9U5UVVV 2TY\\$//R@@@@@@r4   N)r   r   r   r8   ry  r  r4  r  r  r  r  r  r  r  r[  r  r  r  r:   r4   r2   r  r  %  s        5=AD
%/!

C5?2DL L L- - -
; 
; 
;; ; ;; ; ;7 7 7C C C L L LA A A A Ar4   r  rX  ))r  NNNN)rX  NNNN)r'  NNNN)rN  NNNN)rD  NNNNc                    | \  }}}}}t          j        d          }|pd}|pd}|pd}|pd}t          t          |          }t	          t
                    |         } || }	t          j        ||          }
|	                    |	                    |
                    }t          ||
||           dt          j        ||d          z
  }
|	                    |	                    |
                    }t          ||
||           d S )	Nr{   iir   r  r  r   r
  )
ri   r  r-  r8   r  r   r  r   r  r   )rX  rI  lp1lp2r   r   lpmrA   rq  dist_frozenr  r   s               r2   test_sf_isf_overridesr  :&  s
    &*"Hc3d
(3--C
+C
*C91D=5D5(##D(^^H%F$-K +c3

C
..--
.
.CC4d3333 bk#sB''
'C
..--
.
.CC4d333333r4   ru   )NF(  r  rv  r)  r  r  pathlibr   r9
  r@
  r  numpy.testingr   r   r   r   r   r	   r
   r   r   r   r   r   r   r  numpyri   r   r   numpy.lib.recfunctionsr   r7   r   scipy._lib._utilr   r  r   r   r   r   scipy.statsr8   !scipy.stats._distn_infrastructurer   scipy.stats.distributionsscipy.specialr   r   r   scipy.stats._distr_paramsr   r   test_discrete_basicr    r!   scipy.stats._continuous_distnsr"   r#   scipy.optimizer$   r%   r&   	itertoolsr'   flagsoptimizerE  r  r  r5  r3   r;   rX   rZ   r   r  r   r   r0  r2  r]  r  r  r  r  r  r  r  r6  r?  rg  r  r  r  r  r  r  r  r  r  r  r  rv  r  r  r  r  r  r#  r-  r?  rk  r  r  r  r  r  r  r  r@  rU  rd  ru  r  r  r  r  r  r  r  r%  rj   rv  r/  rx  r  r  r  r  r  r  r  r  r  r  r>  rQ  rS  rb  rj  ru  rz  r"  r(  r0  r2  rj  r  r  r	  r 	  r.	  r8	  rF	  rT	  r[	  ri	  ro	  r	  r	  r	  r	  r	  r	  r	  r	  rD
  rF
  rJ
  r  rL
  rN
  rQ
  rS
  rV
  rX
  rZ
  r]
  r`
  rb
  re
  rg
  ri
  rk
  rm
  rs
  ru
  rx
  r{
  r~
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  r
  rE   r
  r
  r
  r
  r
  r   r+  rL  rO  rQ  rS  rW  rZ  r\  r_  r|  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r2  r;  rC  rE  rH  rJ  rL  rX  r[  r]  rr  rv  r}  r  r  r:   r4   r2   <module>r     s!     				 



        				  : : : : : : : : : : : : : : : : : : : : : : : : : :
  * * * * * *     " " " " " " " " 4 4 4 4 4 4       / / / / / /3 3 3 3 3 3 3 3 3 3 3 3       8 8 8 8 8 8         0 0 0 0 0 0 0 0 0 0 ; ; ; ; ; ; ; ; > > > > > > > > C C C C C C C C = = = = = = = = = =       i(1,  |x'M.>h.>.@.@H.L )6z'B $$ $ $ $8 8 8
  G@ G@ G@ G@ G@ G@ G@ G@T4 4 4 4D. . .. > > >? ?

6 
6? ?

69 9 9 9 9 9 9 9>G, G, G, G, G, G, G, G,T* * * * * * * *       >       /B /B /B /B /B /B /B /Bd# # # # # # # #<E; E; E; E; E; E; E; E;PG G G G G G G GT2 2 2 2 2 2 2 2.CD CD CD CD CD CD CD CDLA: A: A: A: A: A: A: A:H2 2 2 2 2 2 2 2"'K 'K 'K 'K 'K 'K 'K 'KT> > > > > > > >*'D 'D 'D 'D 'D 'D 'D 'DT
C 
C 
C 
C 
C 
C 
C 
CA2 A2 A2 A2 A2 A2 A2 A2H4 4 4 4 4 4 4 4D;6 ;6 ;6 ;6 ;6 ;6 ;6 ;6|* * * * * * * *. G  G  G  G  G  G  G  GFK" K" K" K" K" K" K" K"\=I =I =I =I =I =I =I =I@`& `& `& `& `& `& `& `&FXD XD XD XD XD XD XD XDvD D D D D D D D,D D D D D D D D,U< U< U< U< U< U< U< U<p%( %( %( %( %( %( %( %(P"B "B "B "B "B "B "B "BJT# T# T# T# T# T# T# T#nt: t: t: t: t: t: t: t:nUO UO UO UO UO UO UO UOp< < < < < < < <~'* '* '* '* '* '* '* '*TO@ O@ O@ O@ O@ O@ O@ O@d/ / / / / / / /2!, !, !, !, !, !, !, !,HME ME ME ME ME ME ME ME`m5 m5 m5 m5 m5 m5 m5 m5`7F 7F 7F 7F 7F 7F 7F 7FtT6 T6 T6 T6 T6 T6 T6 T6n9J 9J 9J 9J 9J 9J 9J 9Jx0D 0D 0D 0D 0D 0D 0D 0Df4D 4D 4D 4D 4D 4D 4D 4Dn( ( ( ( ( ( ( (VcA cA cA cA cA cA cA cALaJ aJ aJ aJ aJ aJ aJ aJH*9 *9 *9 *9 *9 *9 *9 *9Z+G +G +G +G +G +G +G +Gl 7271ag;		
	gbga25k""	"	
	1RU7$$	$		AbeG%%	%		GBGAqwK((	(	* + 	7271c"%i=!!7271c"%i=)))7271c"%i=)))50gbgaRUm,,,g53ru9...	9; < "WRWQruW


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#

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-
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0
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 '!  H^V ^V ^V ^V ^V ^V ^V ^VB6 6 6 6 6 6 6 6&5 5 5 5 5 5 5 5:
8 
8 
8 
8 
8 
8 
8 
8s5 s5 s5 s5 s5 s5 s5 s5l/, /, /, /, /, /, /, /,d	E 	E 	E 	E 	E 	E 	E 	E       /G /G /G /G /G /G /G /Gd7B 7B 7B 7B 7B 7B 7B 7BtoC oC oC oC oC oC oC oCdN" N" N" N" N" N" N" N"bi> i> i> i> i> i> i> i>X	3 	3 	3P6 P6 P6 P6 P6 P6 P6 P6f'C 'C 'C 'C 'C 'C 'C 'CT& & & & & & & &>$ $ $ $ $ $ $ $*n
 n
 n
 n
 n
 n
 n
 n
b) ) ) ) ) ) ) )       , , , mG mG mG mG mG mG mG mG`e, e, e, e, e, e, e, e,Pw; w; w; w; w; w; w; w;t>> >> >> >> >> >> >> >>B", ", ", ", ", ", ", ",JB& B& B& B& B& B& B& B&J6 6 6 6 6 6 6 68;" ;" ;" ;" ;" ;" ;" ;"|e. e. e. e. e. e. e. e.P. . . . . . . ..SF SF SF SF SF SF SF SFl. . . . . . . .2J/ J/ J/ J/ J/ J/ J/ J/Z ?  ?  ?  ?  ?  ?  ?  ?Fh" h" h" h" h" h" h" h"V6 6 6 6 6 6 6 6(? ? ? ? ? ? ? ?,N N N N N N N NRB RB RB RB RB RB RB RBj2, 2, 2, 2, 2, 2, 2, 2,jC C C C C C C CL	< 	< 	<9 9 9
! ! !* '0EFF/ / GF/
< < <*5 5 585 5 5. . .2 2 2(: : :#4 #4 #4L  	, 	, 	,   )J J JK K
A 
AK K
A  # # #  07 7 72' ' '0	- 	- 	-. *F F FG G1 1G G1
	- 	- 	-& & &9 9 9%& %& %&P- - -M M M" +
HBHo7889
HBHo7889xrx|4556
HBHk;/001	.  2 2 22 2 26 6 61 1 167 7 7: ); ; ;< <) )< <) : : :; ;
) ); ;
) ; ; ;< <! !< <!
  ( ); ; ;< <
) )< <
)
% % %*    $   
    %%   
    %%       %%   u9 u9 u9 u9 u9 u9 u9 u9p8B 8B 8B 8B 8B 8B 8B 8Bv '0DEE@ @ FE@< < <
    , , ,3 3 37 7 7.) ) )X6 6 6D6 D6 D6N+L +L +L\+ + +0 0 0D )F F FG G
4 4G G
4 )<<>? ?4 4? ?4
 !!!""""#___ = = = * * *@ @ @ CK5(E  G G G G^K ^K ^K ^K ^K ^K ^K ^KB  .3+ 3+ 3+ 3+ 3+ 3+ 3+ 3+lv2 v2 v2 v2 v2 v2 v2 v2r@: @: @: @: @: @: @: @:FL L L L L L L L8	 	 	 )?[+HII    JI 4# # #26 6 6 ;467 73 37 73
 7 7 78 84 4	8 84
0 0 0/ / /- - -(W. W. W. W. W. W. W. W.t3 3 3 3 3 3 3 3 #K #K #K #K #K #K #K #KL" " " " " " " "]A ]A ]A ]A ]A ]A ]A ]AF  "G "G "G H H
4 4H H
4 4 4r4   