o
    g                    @   s  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 ddlZddlmZ ddl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.m/Z/ ddl0m1Z1m2Z2 ddl3m4Z4m5Z5 ddl6m7Z7m8Z8 ddl9m:Z:m;Z; ddl<m=Z= ej>j?dkZ@ej	dkoe	A dkZBddgZCdddZDdd ZEdd ZFdd ZGdd  ZHd!d" ZId#d$ ZJd%d& ZKejLMd'g d(d)d* ZNejLMd+g d,d-d. ZOd/d0 ZPejLMd1g d2d3d4 ZQd5d6 ZRd7d8 ZSd9d: ZTejLMd;g d<d=d> ZUG d?d@ d@ZVG dAdB dBZWG dCdD dDZXG dEdF dFZYG dGdH dHZZG dIdJ dJZ[G dKdL dLZ\G dMdN dNZ]G dOdP dPZ^G dQdR dRZ_G dSdT dTZ`G dUdV dVZaG dWdX dXZbG dYdZ dZZcG d[d\ d\ZdG d]d^ d^ZeG d_d` d`ZfG dadb dbZgG dcdd ddZhG dedf dfZiG dgdh dhZjG didj djZkG dkdl dlZlG dmdn dnZmG dodp dpZnG dqdr drZoG dsdt dtZpG dudv dvZqG dwdx dxZrG dydz dzZsG d{d| d|ZtG d}d~ d~ZuG dd devZwG dd dZxG dd dZydd Zzdd Z{dd Z|ejLMdg dejLMdddgddgddgg dg dgddgddggdgdgggdd Z}ejLMdddgddgddgg dg dgddgddggdgdgggdd Z~G dd dZG dd dZddeddej   ddeddej   ddeddej   ddeddej   ddeddej   g	fdeddej  ddeddej   ddeddej   d ddeddej   d ddeddej   d g	fddedej  dddedej   dddedej   dddedej   dddedej   dddedej   dddedej   dgfgZG dd dZG dd dZG dd dZG dd dZG ddÄ dÃZG ddń dŃZG ddǄ dǃZG ddɄ dɃZG dd˄ d˃ZG dd̈́ d̓ZG ddτ dσZG ddф dуZG ddӄ dӃZG ddՄ dՃZG ddׄ d׃ZG ddل dكZG ddۄ dۃZG dd݄ d݃Zdd߄ ZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd devZG dd dZG dd dZG dd dZG dd dZG d d dZG dd dZdd Zdd Zdd	 Zd
d ZejLje@dddd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ ZejLMd0g d1d2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; ZejLĐd<d=d> ZŐd?d@ ZejLMdAdBedCdDgfdEedFdGgfdHedIdJgfdKedLdMgfgdNdO ZǐdPdQ ZejLĐd<dRdS ZejLĐd<dTdU ZʐdVdW ZːdXdY Z̐dZd[ ZG d\d] d]e(j΃ZG d^d_ d_e(j΃ZG d`da dae(j΃ZG dbdc dce(j΃ZG ddde deZG dfdg dgZejLje@dhddidj ZՐdkdl Z֐dmdn Zאdodp Zؐdqdr Zِdsdt Zڐdudv Zېdwdx Zܐdydz Zݐd{d| Zސd}d~ Zߐdd Zdd Zdd ZejLMdg ddd ZejLMdddgdd ZejLMdddg dfddg dfddg dfgdd Zdd Zdd ZejLjejdkdddd ZG dd dZdd ZG dd dZG dd dZG dd dZG dd dZdd ZejLMde5e2 dd Zdd Zdd ZejLMdddgdd ZejLMdg ddd Zdd Zdd Zdd Zd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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)productdarwinx86_64tukeylambdapearson3c                 C   s*   |d u r
d| |f }t t| ||d d S )Nz%s does not have attribute %smsg)r   hasattr)abr*    r.   b/home/ubuntu/cloudmapper/venv/lib/python3.10/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattr4   s   r0   c                   C   s   t tjjd d S )Nf_gen)r0   scipystatsdistributionsr.   r.   r.   r/   test_api_regression:      r5   c                 C   s8   t j| ||d}t||||dtj |   d S )Nlocscale   )r3   vonmisesr   pdfnumpypikLsxvmr.   r.   r/   check_vonmises_pdf_periodic?   s   (rE   c                 C   s@   t j| ||d}t||d ||dtj |  d  d S )Nr7   r   r:   )r3   r;   r   cdfr=   r>   r?   r.   r.   r/   check_vonmises_cdf_periodicD   s   0rG   c                  C   sj   t tjjj} dd tD }dd tD }g d}|| | }t tdd |}| d | |ks3J d S )Nc                 S      g | ]}|d  qS r   r.   .0distr.   r.   r/   
<listcomp>K       z0test_distributions_submodule.<locals>.<listcomp>c                 S   rH   rI   r.   rJ   r.   r.   r/   rM   L   rN   )rv_discreterv_continuousrv_histogramentropytrapzc                 S   s   t | d S )N<)str
startswithrB   r.   r.   r/   <lambda>S       z.test_distributions_submodule.<locals>.<lambda>gilbrat)	setr2   r3   r4   __all__r   r   filterremove)actual
continuousdiscreteotherexpectedr.   r.   r/   test_distributions_submoduleI   s   
rd   c                  C   sx   dD ]7} ddt jddfD ],}t| dd| t| dd| t| dd| t| dd| t| dd| t| dd| qqd S )N)皙?r   e   r   r   
   d   )r=   r>   rE   rG   )r@   rC   r.   r.   r/   test_vonmises_pdf_periodic[   s   ri   c                   C   s&   t tjjtj  t tjjtj d S N)r   r3   vonmises_liner,   npr>   r-   r.   r.   r.   r/   test_vonmises_line_supportg   s   rm   c                  C   s   t d} t| dd d S )N   r         ?)r3   r;   r   rF   )rD   r.   r.   r/   test_vonmises_numericall   s   
rp   zx, kappa, expected_pdf))re   {Gz?g|65?)re         9@g?U?)re   rn   g"?)       @rq   gDfI?)rs   rr   g1<)rs   rn           c                 C       t j| |}t||dd d S NV瞯<rtol)r3   r;   r<   r   )rC   kappaexpected_pdfr<   r.   r.   r/   test_vonmises_pdf{      r|   zkappa, expected_entropy))r   gA	?)   g,eޞ?)rh   gBb9d22)  g
G )  gc                 C      t j| }t||dd d S )NvIh%<=rx   )r3   r;   rR   r   )rz   expected_entropyrR   r.   r.   r/   test_vonmises_entropy   s   r   c                  C   s   t td} tj| }tj| }tj| }tjddddj|d}tjddtj ddj|d}tjdddtj t | d dj|d}t	||dd t	||dd d S )	Nvon_mises_rvsr   r   r7   )random_stater:   rw   atol)
abshashrl   randomdefault_rngr3   r;   rvsr>   r   )seedrng1rng2rng3rvs1rvs2rvs3r.   r.   r/   test_vonmises_rvs_gh4598   s   r   zx, kappa, expected_logpdf))re   rq   gEJ?)re   rr   goι?)re   rn   g0,)rs   rq   gdty)rs   rr   gʹw[A)rs   rn   gc                 C   ru   rv   )r3   r;   logpdfr   )rC   rz   expected_logpdfr   r.   r.   r/   test_vonmises_logpdf   r}   r   c                  C   s  t jd} | dd \}}}tj||ddd }t|d t |jt j	s+J ||dt j
  f}tj||djd	d g|R  }t|d t |jt j	sSJ ||dt j
  f}tj||djd
d g|R ddi}tt ||dt j
   t |jt jsJ 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.
    l   kD +xNn    rg   )r8   rz   c                 S      dS Nr   r.   rC   r.   r.   r/   rX          z&test_vonmises_expect.<locals>.<lambda>r   r:   c                 S   r   r   r.   r   r.   r.   r/   rX      r   c                 S   s   t d|  S )Ny              ?)rl   expr   r.   r.   r/   rX      s    complex_funcN)rl   r   r   r3   r;   expectr   
issubdtypedtypefloatingr>   anglecomplexfloating)rngr8   rz   lbresboundsr.   r.   r/   test_vonmises_expect   s"   
 
r   c                 K   sf   | j |fi |}tt| | j |fi |}|||}|||}||ks/tj||dds1J dS dS )aS  
    This utility function checks that the log-likelihood (computed by
    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.
    rw   rx   N)fitsupertyperl   allclose)rL   datafunckwdsmle_analyticalnumerical_optll_mle_analyticalll_numerical_optr.   r.   r/   _assert_less_or_close_loglike   s   

r   c                 C   s  ddg}| j rt| j d}|g dd | 7 }tt|tt|}g d}tjt	dd | j
|fi | W d    n1 sDw   Y  tjtdd | 
tjg W d    n1 sbw   Y  tjtdd | 
tjg W d    n1 sw   Y  tjtd	d | j
|d
d W d    n1 sw   Y  tjtdd | j
|gdgt|d  R   W d    d S 1 sw   Y  d S )Nflocfscale,)f0f1f2r   r:   r   z3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:r:   )extra_keywordzToo many positional arguments.r   )shapeslensplitdictziprl   arangepytestr   RuntimeErrorr   
ValueErrornaninf	TypeError)rL   paramnshapes	all_fixedr   r.   r.   r/   assert_fit_warnings   s6   ""r   rL   )alpha	betaprimefatiguelifeinvgammainvgauss
invweibull	johnsonsblevylevy_llognormgibratpowerlognormrayleighwaldc                 C   s   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   getattrr3   r   r<   r,   r   r   rl   r   r-   )rL   dctargsr.   r.   r/   test_support   s   
"r   c                   @   ,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestRandIntc                 C      t jd d S N  rl   r   r   selfr.   r.   r/   setup_method     zTestRandInt.setup_methodc                 C   s   t jjdddd}tt|dk t|dk@  tt|dk t jjdddd}tt|dk t|jj	t
d v  t jdd}t|dk|dk @  tt|tjtt|d	 t ddd
}t|jj	t
d v  d S )Nr~      rh   sizer:   2   
AllInteger   .   r)   r   )r3   randintr   r   r=   allr   shaper   charr   
isinstance
ScalarTypereprr   r   valsvalr.   r.   r/   test_rvs  s    zTestRandInt.test_rvsc                 C   sF   t jdd }t |dk|dk @ dd}tj|dd}t|| d S )Nr   $   r~   r   {Gz?)r=   r_wherer3   r   pmfr   )r   r@   outr   r.   r.   r/   test_pdf  s   zTestRandInt.test_pdfc                 C   sd   t ddd}t|}t|dk|dkgd|d d d	 gd}tj|dd}t||d
d d S )Nr   r   rh   r   r~         ?      @r   rr      decimal)	rl   linspacer=   floorselectr3   r   rF   r   )r   rC   r@   r  r   r.   r.   r/   test_cdf$  s
   
*zTestRandInt.test_cdfN)__name__
__module____qualname__r   r   r  r  r.   r.   r.   r/   r     s
    r   c                   @   4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )	TestBinomc                 C   r   r   r   r   r.   r.   r/   r   -  r   zTestBinom.setup_methodc                 C   s   t jjdddd}tt|dkt|dk@  tt|dk t|jjt	d v  t jdd}tt
|t t ddd}tt
|tj t|jjt	d v  d S Nrg         ?r   r   r   r   r   )r3   binomr   r   r=   r   r   r   r   r   r   intndarrayr   r.   r.   r/   r   0  s    zTestBinom.test_rvsc                 C   sD   t jddd}t jddd}t|dddd t|dddd d S )Nrh   r   r   r  rw   ry   r   )r3   r  r  r   )r   vals1vals2r.   r.   r/   test_pmf;  s   zTestBinom.test_pmfc                 C   s|   t dd}tg d}tt|| }| }t|| t dd}| }t|d t dd}| }t|d d S )Nr:   ro   )      ?ro   r  rt   r  )	r3   r  rl   r   sumr   rR   r   r   )r   r-   
expected_p
expected_hhr.   r.   r/   test_entropyB  s   

zTestBinom.test_entropyc                 C   sj   t  ' t dt ttjddd d ttjddd d W d    d S 1 s.w   Y  d S )Nerrorr:   r   np)	warningscatch_warningssimplefilterRuntimeWarningr   r3   r  meanstdr   r.   r.   r/   test_warns_p0R  s
   
"zTestBinom.test_warns_p0N)r  r  r  r   r   r  r#  r.  r.   r.   r.   r/   r  ,  s    r  c                   @      e Zd Zdd ZdS )TestArcsinec                 C   s&   t jddg}t|tjtjg d S Nr   r   )r3   arcsiner<   r   rl   r   r   r'  r.   r.   r/   test_endpoints\  s   zTestArcsine.test_endpointsN)r  r  r  r4  r.   r.   r.   r/   r0  Z      r0  c                   @   $   e Zd Zdd Zdd Zdd ZdS )TestBernoullic                 C   r   r   r   r   r.   r.   r/   r   d  r   zTestBernoulli.setup_methodc                 C   s   t jjddd}tt|dkt|dk@  tt|dk t|jjt	d v  t jd}tt
|t t dd}tt
|tj t|jjt	d v  d S )Nr  r   r   r   r   r   r   )r3   	bernoullir   r   r=   r   r   r   r   r   r   r  r  r   r.   r.   r/   r   g  s    zTestBernoulli.test_rvsc                 C   st   t d}dtd dtd  }| }t|| t d}| }t|d t d}| }t|d d S )Nr        пr  rt   r  )r3   r8  rl   logrR   r   r   )r   r-   r!  r"  r.   r.   r/   r#  r  s   




zTestBernoulli.test_entropyN)r  r  r  r   r   r#  r.   r.   r.   r/   r7  c      r7  c                   @   r/  )TestBradfordc                 C   s:   d}t dd}tj||}tj||}t|| d S )Nre   )rl   logspacer3   bradfordrF   ppfr   )r   crC   qxxr.   r.   r/   test_cdf_ppf  s
   zTestBradford.test_cdf_ppfN)r  r  r  rE  r.   r.   r.   r/   r<    r5  r<  c                   @   s,   e Zd ZdZdZdd Zdd Zdd Zd	S )
TestChignT9;g2 >h?@c                 C   s"   t jdd}t|| jdd d S )Nrg      rw   rx   )r3   chisfr   CHI_SF_10_4r   rB   r.   r.   r/   test_sf     zTestChi.test_sfc                 C   s"   t j| jd}t|ddd d S )NrG  rg   rw   rx   )r3   rH  isfrJ  r   r   rC   r.   r.   r/   test_isf     zTestChi.test_isfc                 C   s"   t jjdd}t|| jdd d S )Nr   )df-q=rx   )r3   rH  r,  r   CHI_MEAN_1000rO  r.   r.   r/   	test_mean  rM  zTestChi.test_meanN)r  r  r  rJ  rT  rL  rP  rU  r.   r.   r.   r/   rF    s    rF  c                   @   r   )

TestNBinomc                 C   r   r   r   r   r.   r.   r/   r     r   zTestNBinom.setup_methodc                 C   s   t jjdddd}tt|dk tt|dk t|jjt	d v  t jdd}tt
|t t ddd}tt
|tj t|jjt	d v  d S r  )r3   nbinomr   r   r=   r   r   r   r   r   r   r  r  r   r.   r.   r/   r     s   zTestNBinom.test_rvsc                 C   sH   t t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   rl   r   r3   rW  logpmfr  r2   r   )r   r   r.   r.   r/   r    s
   zTestNBinom.test_pmfc                 C   s@   t jjg dddd}tt jjg dddd}t|| d S )N)r   r~   r   r~   333333@?r%  )r3   rW  logcdfrl   r:  rF   r   )r   r   refr.   r.   r/   test_logcdf_gh16159  s   zTestNBinom.test_logcdf_gh16159N)r  r  r  r   r   r  r]  r.   r.   r.   r/   rV    s
    rV  c                   @   st   e Zd Zdd Zejjdd Zejjdd Zejjdd Z	ejjd	d
 Z
dd Zdd Zdd Zdd ZdS )TestGenInvGaussc                 C   r   r   r   r   r.   r.   r/   r     r   zTestGenInvGauss.setup_methodc                 C   :   t dd}t |jddd|j\}}t|dkd d S )Nffffff@      ?  r   r   r   皙?Tr3   geninvgausskstestr   rF   r   r   gig_r'  r.   r.   r/   test_rvs_with_mode_shift     z(TestGenInvGauss.test_rvs_with_mode_shiftc                 C   r_  )N?r  rb  r   rc  rd  Tre  rh  r.   r.   r/   test_rvs_without_mode_shift  rl  z+TestGenInvGauss.test_rvs_without_mode_shiftc                 C   r_  )Nre   皙?rb  r   rc  rd  Tre  rh  r.   r.   r/   test_rvs_new_method  rl  z#TestGenInvGauss.test_rvs_new_methodc                 C   s<   dd }t |ddd t |ddd t |ddd d S )Nc                 S   s0   t | |}|jddd}t ||jd dkS )Nrb  r   rc  r   rd  )r3   rf  r   rg  rF   )r'  r-   ri  r   r.   r.   r/   my_ks_check  s   z4TestGenInvGauss.test_rvs_p_zero.<locals>.my_ks_checkr   ro  Trm  ra  )r   )r   rq  r.   r.   r/   test_rvs_p_zero  s   zTestGenInvGauss.test_rvs_p_zeroc                 C   s6   t tddjddddtddjddd  d S )N      r:   rg   r   rc  r   ra  )r   r3   rf  r   r   r.   r.   r/   test_rvs_negative_p  s   z#TestGenInvGauss.test_rvs_negative_pc                 C   s   t jjddddd}tt j|ddgdd dkd	 d
tddd}}t jj|dd| |d}t|t 	|| t jj
|dd| |d}t|t 	|
| d S )Nrb        r   r   )r   r'  r-   r   r   r   333333?Trh   rq   rg   )r'  r-   r9   )r3   rf  r   r   rg  rl   r  r<   r   r   rF   )r   igmurC   pdf_igcdf_igr.   r.   r/   test_invgauss  s    zTestGenInvGauss.test_invgaussc                 C   s6   t g d}t 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?rq   r~   rg   ro   r   )rl   r   r  r   r3   rf  r<   )r   vals_RrC   r.   r.   r/   
test_pdf_R  s   zTestGenInvGauss.test_pdf_Rc                 C   s0   t tjdddd t tjdddd d S )Nr   ro   g    >Ar   r:   )r   r3   rf  r<   r   r.   r.   r/   test_pdf_zero   s   zTestGenInvGauss.test_pdf_zeroN)r  r  r  r   r   markslowrk  rn  rp  rr  rt  r|  r~  r  r.   r.   r.   r/   r^    s    




r^  c                   @   T   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd ZdS )TestGenHyperbolicc                 C   r   r   r   r   r.   r.   r/   r   	  r   zTestGenHyperbolic.setup_methodc           
      C   l   t g d}d\}}}d\}}||| || f}tj|||d}t ddd}	t||	|ddd	 d S )
N)
gF^T=g{X'=gNunƢsy>g7!t?gɫzI?g̸?g?gq6.?gmPZz?g:PgN?r:   r:   r   ro   ra  r7   rg   r   r   r   ry   )rl   r   r3   genhyperbolicr  r   r<   
r   r}  lmbdar   betary  deltar   ghrC   r.   r.   r/   
test_pdf_r     
zTestGenHyperbolic.test_pdf_rc           
      C   r  )
N)
g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?r  r  r7   r  rg   r   ư>r  )rl   r   r3   r  r  r   rF   r  r.   r.   r/   
test_cdf_r"  r  zTestGenHyperbolic.test_cdf_rc                    s\   g d}d\}}}d\|| | f  fddt ddD }t||dd	d
 d S )N)g@쐧@g@쐧 @g܊B@gvGăi@r  r  c                    s$   g | ]}t j d |qS )r7   )r3   r  moment)rK   ir   r  ry  r.   r/   rM   H  s    z4TestGenHyperbolic.test_moments_r.<locals>.<listcomp>r   r~   r   r   r  )ranger   )r   r}  r  r   r  vals_usr.   r  r/   test_moments_r8  s   	
z TestGenHyperbolic.test_moments_rc           
      C   sd   d\}}}d\}}||| || f}t j|||d}t |jddd|j\}}	t|	dkd d S )	Nr  r  r7   rb  r   rc  rd  T)r3   r  rg  r   rF   r   )
r   r  r   r  ry  r  r   r  rj  r'  r.   r.   r/   r   O  s   
zTestGenHyperbolic.test_rvsc           	      C   s   t ddd}t |dt t jj d}}dt |}}| d ||f}tj|||d}t |	d|	dd	d d t j
f }t||tj||dd
d d S )Nr   r   rg   r:   r   r7   rq   Gz?r   r  r  )rl   r  float_powerfinfofloat32epssqrtr3   r  rA  newaxisr   r<   t)	r   rR  r   r  ry  r  r   r  rC   r.   r.   r/   
test_pdf_t\  s    (
zTestGenHyperbolic.test_pdf_tc           	      C   s   dt t jjd}}}d\}}|||f}tj|||d}t |d|ddd d t jf }t	|
|tj
|ddd	 d S )
Nru  r   )r   r   r7   rq   r  r   r  r  )rl   r  r  r  r3   r  r  rA  r  r   r<   cauchy)	r   r  r   r  ry  r  r   r  rC   r.   r.   r/   test_pdf_cauchyn  s   
(
z!TestGenHyperbolic.test_pdf_cauchyc           	      C   s   t ddd}t t jj}d\}}}||| || f}tj|||d}t dddd d t jf }t|	|tj
j	||ddd	d
d d S )Nr  rg   )r   r   r   r7   r=     r   r   r   dy=r  )rl   r  r  r  r  r3   r  r  r   r<   laplace)	r   r8   r  r  r   r  r   r  rC   r.   r.   r/   test_pdf_laplace  s   

z"TestGenHyperbolic.test_pdf_laplacec           	   	   C   s   t dddt dddt dtd t dddt dddf\}}}}d	}||| || f}tj|||d
}t |d|ddd d t jf }t|	|tj
j	|||||dddd d S )Nr   r  rg   r      rh   ru  r7   rq   r  r   )r,   r-   r8   r9   r   r  )rl   r  r  r  r3   r  rA  r  r   r<   norminvgauss)	r   r   r  r  ry  r  r   r  rC   r.   r.   r/   test_pdf_norminvgauss  s   (

z'TestGenHyperbolic.test_pdf_norminvgaussN)r  r  r  r   r  r  r  r   r  r  r  r  r.   r.   r.   r/   r    s    r  c                   @   s^   e Zd Zdd Zdd Zdd Zejdg dd	d
 Z	dd Z
dd Zdd Zdd ZdS )TestNormInvGaussc                 C   r   r   r   r   r.   r.   r/   r     r   zTestNormInvGauss.setup_methodc                 C   @   t g d}t g d}tjj|ddd}t||dd d S )N)gp~٧>g @X>g}e?g{)߳?gwH?ir      r   r   ro   r,   r-   &.>r   )rl   r   r3   r  rF   r   )r   r_cdfx_testvals_cdfr.   r.   r/   
test_cdf_R  s   zTestNormInvGauss.test_cdf_Rc                 C   r  )N)gp϶>g\H55$?geСt&?go NiH?g]u>r  r   ro   r  r  r   )rl   r   r3   r  r<   r   )r   r_pdfr  vals_pdfr.   r.   r/   r~    s   zTestNormInvGauss.test_pdf_Rzx, a, b, sf, rtol))r  r   r   !7?r   )   r   r   ?=-C6?)r   r~   rs  gy5`?rS  )rg   r~   rs  gMLC9r  c                 C   s@   t j|||}t|||d t j|||}t|||d d S Nrx   r3   r  rI  r   rN  )r   rC   r,   r-   rI  ry   rB   r  r.   r.   r/   test_sf_isf_mpmath  s   &z#TestNormInvGauss.test_sf_isf_mpmathc                 C   s^   ddg}ddg}d}ddg}t j|||}t||ddd	 t j|||}t||d
d d S )Nr  r  r   r   r  r  r   缉ؗҜ<r  r  rx   r  )r   rC   r,   r-   rI  rB   r  r.   r.   r/   test_sf_isf_mpmath_vectorized  s   z.TestNormInvGauss.test_sf_isf_mpmath_vectorizedc                 C   s<   t dd}tddd}||}||}t|| d S )Nr   r   r  r:   )r3   r  rl   r   rI  rN  r   )r   dstrC   rI  rN  r.   r.   r/   test_gh8718  s
   

zTestNormInvGauss.test_gh8718c                 C   s   d\}}t |d |d  }|| |d |d  d| |t |  ddd|d  |d    | f}t|tjj||dd d S )	Nr   ro   r:   r         @r   rG  mvskmoments)rl   r  r   r3   r  )r   r,   r-   gammav_statsr.   r.   r/   
test_stats  s   (zTestNormInvGauss.test_statsc                 C   s@   d\}}t g d}tj|||}t|tj||| d S )Nr  MbP?ro   +?)rl   r   r3   r  rA  r   rF   )r   r,   r-   r  r   r.   r.   r/   test_ppf  s   zTestNormInvGauss.test_ppfN)r  r  r  r   r  r~  r   r  parametrizer  r  r  r  r  r.   r.   r.   r/   r    s    
&r  c                   @   r  )TestGeomc                 C   r   r   r   r   r.   r.   r/   r     r   zTestGeom.setup_methodc                 C      t jjddd}tt|dk tt|dk t|jjt	d v  t jd}tt
|t t dd}tt
|tj t|jjt	d v  d S )Nr  r   r   r   r   r   )r3   geomr   r   r=   r   r   r   r   r   r   r  r  r   r.   r.   r/   r        zTestGeom.test_rvsc                 C   sT   t jd}tjjt dd|d}|jt jksJ t 	|t 
t jjks(J d S )Nl   A: ir~   rc  )rl   r   r   r3   r  r   r   r   int64r   iinfoint32max)r   r   r   r.   r.   r/   test_rvs_9313  s    zTestGeom.test_rvs_9313c                 C   s$   t jg dd}t|g d d S )Nr   ro   )ro   r        ?)r3   r  r  r   r   r   r.   r.   r/   r  '  s   zTestGeom.test_pmfc                 C   sV   t tjg dd}tjg dd}t||ddd tjdd}t|d d S )Nr   ro   rw   r   r  r   rt   )rl   r:  r3   r  r  rX  r   r   )r   r  r  r   r.   r.   r/   test_logpmf+  s
   zTestGeom.test_logpmfc                 C   sL   t jg dd}t jg dd}tg d}t|| t|d|  d S )Nr   ro   ro   r        ?r   )r3   r  rF   rI  r   r   r   r   vals_sfrc   r.   r.   r/   test_cdf_sf5  s
   
zTestGeom.test_cdf_sfc                 C   sV   t jg dd}t jg dd}tg d}t|t| t|t|  d S )Nr   ro   r  )	r3   r  r[  logsfr   r   rl   r:  log1pr  r.   r.   r/   test_logcdf_logsf<  s
   zTestGeom.test_logcdf_logsfc                 C   ,   t jg dd}tg d}t|| d S )Nr  ro   )r  rs   r  )r3   r  rA  r   r   r   r   rc   r.   r.   r/   r  C     zTestGeom.test_ppfc                 C   s   t tjddddd d S )N#B;r  +=r   )r   r3   r  rA  r   r.   r.   r/   test_ppf_underflowH  s   zTestGeom.test_ppf_underflowN)r  r  r  r   r   r  r  r  r  r  r  r  r.   r.   r.   r/   r    s    	
r  c                   @   r6  )
TestPlanckc                 C   r   r   r   r   r.   r.   r/   r   N  r   zTestPlanck.setup_methodc                 C   r  )Nr   r  )g|dy?g8'\>ggrU!>)r3   planckrI  r   r   r  r.   r.   r/   rL  Q  s   zTestPlanck.test_sfc                 C   r  )N)     @@     @@     p@r  )g    P.g    h>g    TF)r3   r  r  r   r   r  r.   r.   r/   
test_logsfX  r  zTestPlanck.test_logsfN)r  r  r  r   rL  r  r.   r.   r.   r/   r  M  s    r  c                   @   r   )
TestGennormc                 C   0   g d}t j|d}t j|}t|| d S Nr   r   )r3   gennormr<   r  r   r   pointspdf1pdf2r.   r.   r/   test_laplace_     zTestGennorm.test_laplacec                 C   4   g d}t j|d}t jj|dd}t|| d S Nr   r:   g;f?r9   )r3   r  r<   normr   r  r.   r.   r/   	test_normf     zTestGennorm.test_normc                 C   s   t jd td}|jdd}t||jjdksJ td}|jdd}tj	jdd}t
||jdks:J td}|jdd}tjjddd	}t
||jdksXJ d S )
Nr   ro   r   r   re   r   r:   g;f?)r9   r   )rl   r   r   r3   r  r   rg  rF   pvaluer  ks_2sampr  )r   rL   r   rvs_laplacervs_normr.   r.   r/   r   m  s   


zTestGennorm.test_rvsc                 C   s   t jd tddgddgg}|jg dd}t|d d ddf tdjd d	ks0J t|d d ddf tdjd d	ksGJ t|d d ddf tdjd d	ks^J t|d d ddf tdjd d	ksuJ d S )
Nr   ro   r  rs   r  )r   r:   r:   r   r   re   )rl   r   r   r3   r  r   rg  rF   )r   rL   r   r.   r.   r/   test_rvs_broadcasting~  s   ...2z!TestGennorm.test_rvs_broadcastingN)r  r  r  r  r   r   r  r.   r.   r.   r/   r  ^  s
    r  c                   @   r6  )TestHalfgennormc                 C   r  r  )r3   halfgennormr<   exponr   r  r.   r.   r/   
test_expon  r  zTestHalfgennorm.test_exponc                 C   r  r  )r3   r  r<   halfnormr   r  r.   r.   r/   test_halfnorm  r  zTestHalfgennorm.test_halfnormc                 C   s6   g d}t j|d}t j|d}t|d|  d S )Nr   g
(?r:   )r3   r  r<   r  r   r  r.   r.   r/   test_gennorm  s   zTestHalfgennorm.test_gennormN)r  r  r  r
  r  r  r.   r.   r.   r/   r    s    r  c                   @   r6  )TestLaplaceasymmetricc                 C   s6   t g d}tj|d}tj|}t|| d S r  )rl   r   r3   laplace_asymmetricr<   r  r   r  r.   r.   r/   r    s   z"TestLaplaceasymmetric.test_laplacec                 C   sL   t g d}d}d| }tj||}tj||d  |}t|| d S )Nr   r:   r   )rl   r   r3   r  r<   r   )r   r  rz   kapinvr  r  r.   r.   r/   test_asymmetric_laplace_pdf  s   z1TestLaplaceasymmetric.test_asymmetric_laplace_pdfc              	   C   s   t t d t dg}d}tj||}tj||}tj||}t ddg}t ddg}t dd	g}tj||}	|}
tj	||}|}t
t ||||	|ft ||||
|f d S )
N   rg   r:   re   gMbp?ro  gV-?皙?gMb`?)rl   r   r:  r3   r  r<   rF   rI  rA  rN  r   concatenate)r   r  rz   r  cdf1sf1r  cdf2sf2ppf1ppf2isf1isf2r.   r.   r/   !test_asymmetric_laplace_log_10_16  s   z7TestLaplaceasymmetric.test_asymmetric_laplace_log_10_16N)r  r  r  r  r  r  r.   r.   r.   r/   r    s    	r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
d0d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eZejd"ed#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/S )1TestTruncnormc                 C   r   r   r   r   r.   r.   r/   r     r   zTestTruncnorm.setup_methodc              	   C   J   t jjg ddddgd dd}ttjdd	dd
dtjg}t|| d S )Nru  r   r  ro   gH.?r   r:         r  r      r:   r7   r   fO?l@r~   )r3   	truncnormrA  rl   r   r   r   r  r.   r.   r/   test_ppf_ticket1131  
   
z!TestTruncnorm.test_ppf_ticket1131c              	   C   r  )Nr   r!  r  r   r"  r:   r7   r~   r$  r#  r   )r3   r%  rN  rl   r   r   r   r  r.   r.   r/   test_isf_ticket1131  r'  z!TestTruncnorm.test_isf_ticket1131c                 C   s   d\}}t jj||dddd}t||   k o"|   k o"|k n   d\}}t jj||dddd}t||   k oK|   k oK|k  d S    d S )N)ir  r   r   rg   r   )rg      r3   r%  r   r   minr  r   lowhighrC   r.   r.   r/   test_gh_2477_small_values  s   .8z'TestTruncnorm.test_gh_2477_small_valuesc                 C   sH  d\}}t jj||dddd}t||   ko"|   ko"|kn  t|||gf d\}}t jj||dddd}t||   k oO|   k oO|k n   d\}}t jj||dddd}t||   k ou|   k ou|k n   d\}}t jj||dddd}t||   k o|   k o|k  d S    d S )	N)rh   rf   r   r   rg   r   )r     )'  i'  )i)r3   r%  r   r   r+  r  rU   r,  r.   r.   r/   test_gh_2477_large_values  s   <..8z'TestTruncnorm.test_gh_2477_large_valuesc                 C   s  ddgddgfD ]\}}t t j ||t jg}|| d }tj|||}tj|||}tj|||}t g d}t g d}	t g d}
|d	k rVt g d
}
t|| t||	 t||
 tt 	|
d |
d  |d  t g d}tj
|||}t |t |d |g}t|| |d	k rttj|||d ttj|||d nttj|||d ttj|||d tj|||}tt 	||
d  |d d  qd S )Nr   rG  r>  rs   r   r   r   r   r  r  rt   rt   )r   d._MT
@BKg?r   r   )r   r8  r7  r   r   r:   ro   r   ro   r  gĖy	@gdv*?g,mj%V?r  )rl   r   r   r3   r%  rF   rI  r<   r   r:  rA  sign)r   r-  r.  xvalsxmidcdfssfspdfsexpected_cdfsexpected_sfsexpected_pdfspvalsppfsexpected_ppfsr<   r.   r.   r/   test_gh_9403_nontail_values  sJ   



"z)TestTruncnorm.test_gh_9403_nontail_valuesc                 C   s  ddgddgfD ];\}}t t j ||t jg}|| d }tj|||}tj|||}tj|||}t g d}t g d}	t g d}
|d	k rWt g d
}
t|| t||	 t||
 tt 	|
d |
d  |d  t g d}tj
|||}t |t |d |g}t|| tj|||}t|| |d	k rttj|||d ttj|||d nttj|||d ttj|||d tj|||}tt 	||
d  |d d  t ||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  qd S )N'   (   irs   r5  r6  )r   pGC@Ff<r   r   )r   rK  rJ  r   r   r:   ro   r9  gEC@g i?gspXio)>r  r)  r  )rl   r   r   r3   r%  rF   rI  r<   r   r:  rA  r:  r  )r   r-  r.  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  r<   xvals2r.   r.   r/   test_gh_9403_medium_tail_values  sd   




 z-TestTruncnorm.test_gh_9403_medium_tail_valuesc                 C   s6   t tdddd t tdtjdd d S )Ng      *@g      .@      ,@g T?r  g @gR?)r   r3   r%  rF   rl   r   r   r.   r.   r/   test_cdf_tail_15110_14753A  s   z'TestTruncnorm.test_cdf_tail_15110_14753Hz>c                 C   sb   |d d \}}}}t jj ||dd\}	}
}}t|	| t|
| t|||d t|||d d S )NrG  r  r  rx   r3   r%  r   )r   r,   r-   rc   ry   m0v0s0k0mvrB   r@   r.   r.   r/   _test_moments_one_rangeK  s   

z%TestTruncnorm._test_moments_one_range)r   rt   r  rt   rt   )r  rg   rt   r  rt   gLFu)r4  r   rt   gMFmz%?rt   gſ)r:   rt   ghI}?rt   gHNMr   gQ63E?gnl$A?gr1"D?gK8L?gQ63Egr1"D)r  r   gU*? bn?gnA??c3TXʿ)r4  r   gU*ҿr[  gnAr\  )r  g"$7"gOxr?gp7`g'>K@casec                 C   sL   |\}}}}}}t jj ||dd\}}	}
}t||	|
|g||||gdd d S )Nr  r  FFg<r   rQ  )r   r^  r,   r-   rR  rS  rT  rU  rV  rW  rB   r@   r.   r.   r/   test_moments|  s   "zTestTruncnorm.test_momentsc                 C   s0   t jj dtjdd\}}t|d t|d d S )Nr   mvr  g e3E?g:&A?)r3   r%  rl   r   r   )r   rV  rW  r.   r.   r/   test_9902_moments  s   
zTestTruncnorm.test_9902_momentsc                 C   sV   d\}}t jj||dddd}t||   k o%|   k o%|k  d S    d S )N)rg   r   r   r   rg   r   r*  r,  r.   r.   r/   test_gh_1489_trac_962_rvs  s   8z'TestTruncnorm.test_gh_1489_trac_962_rvsc                 C   s   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j||dt|fd
}t |dt|fks=J tt ||j	ddk tt |j
dd|k d S )Nr  rg   r  irH  r)  r~   rI  -   r   r   )axis)rl   r   r3   r%  r   r   r   r   r   r+  r  r,  r.   r.   r/   test_gh_11299_rvs  s   & zTestTruncnorm.test_gh_11299_rvsc                 C   s.   t tjdrtjjdddtj d d S d S )Nr   r  r  r~   rc  )r+   rl   r   r3   r%  r   r   r   r.   r.   r/   test_rvs_Generator  s
   
z TestTruncnorm.test_rvs_Generatorc                 C   s   t t j t j dt j dg}t t jt jddt jg}t g d}g d}tt|||| tt| | | | d S )Nrg   r  )rg         @ri  	   r  )gOul"gځ=!gL!g>EG	f g^K[X)rl   r   r   r   r3   r%  r[  r  )r   r,   r-   rC   rc   r.   r.   r/   test_logcdf_gh17064  s    "z!TestTruncnorm.test_logcdf_gh17064N)rP  )r  r  r  r   r&  r(  r/  r3  rF  rM  rO  rX  rl   r   _truncnorm_stats_datar   r   r  r  r`  rb  rc  rf  rg  rk  r.   r.   r.   r/   r    sL    
#/


#

r  c                   @   s&   e Zd Zejdg ddd ZdS )TestGenLogisticx, expected))ig4`n)ig4	ncg)r   gX
=)rh   gh@X)r   gh<c                 C   s$   d}t j||}t||dd d S )Nra  r   rx   )r3   genlogisticr   r   )r   rC   rc   rB  logpr.   r.   r/   test_logpdf  s   zTestGenLogistic.test_logpdfN)r  r  r  r   r  r  rq  r.   r.   r.   r/   rm    s    rm  c                   @   r  )TestHypergeomc                 C   r   r   r   r   r.   r.   r/   r     r   zTestHypergeom.setup_methodc                 C   s   t jjddddd}tt|dkt|dk@  tt|dk t|jjt	d v  t jddd}tt
|t t dddd}tt
|tj t|jjt	d v  d S )Nr  rg   r   r   r   r   r   )r3   	hypergeomr   r   r=   r   r   r   r   r   r   r  r  r   r.   r.   r/   r     s   zTestHypergeom.test_rvsc                 C   s6   d}d}d}|}|}t jd|||}t|dd d S )Ni	  r     r:   gkㅒP?r)  )r3   rs  r  r   )r   Mr&  Ntotgoodhgpmfr.   r.   r/   test_precision  s   zTestHypergeom.test_precisionc                 C   sl   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   r:   r   r  r)  rt   )r   r3   rs  r  r   r.   r.   r/   	test_args  s   zTestHypergeom.test_argsc                 C   s4   t dtjdddd  kodk d S    d S )Nr   r   io i  if0  r  )r   r3   rs  rF   r   r.   r.   r/   test_cdf_above_one  s   4z TestHypergeom.test_cdf_above_onec                    s   d dt g dd }d fdd|D }t g d}t||d	d
d g d}tj|   d}g d}t||d	d
d d S )Ng    +@g     @)r   ffffff@333333@rG  gffffff@g@r~        @     @c                    s"   g | ]}t j   |qS r.   )r3   rs  rI  )rK   eatenorangespearsquantiler.   r/   rM     s    z1TestHypergeom.test_precision2.<locals>.<listcomp>)r   gpR(g㘍R2gJޱ p9g?Mf=
G?r   r   gƠ>r  )g     @r  g     @g     @g     @)r   r  g)9g"1)rl   r   r   r3   rs  rI  )r   fruits_eatenr   rc   	quantilesres2	expected2r.   r  r/   test_precision2  s   zTestHypergeom.test_precision2c                 C   sd   t ddd}| }tddg}tt|| }t|| t ddd}| }t|d d S )NrG  r   r  r  rt   )	r3   rs  rR   rl   r   r  r   r   r   )r   hgr"  r   r!  r.   r.   r/   r#    s   
zTestHypergeom.test_entropyc                 C   sl   d}d}d}d}t j||||}d}t||dd d}d	}d
}d}t j||||}d}t||dd d S )Nr      cA    .A     j@gor   r
  r   @  X  ,  g_7	j$r   )r3   rs  r  r   r   r@   ru  r&  rv  resultrc   r.   r.   r/   r    s   zTestHypergeom.test_logsfc                 C   s   d}d}d}d}t j||||}d}t||dd d}d	}d
}d}t j||||}d}t||dd d}d	}d}d}t j||||}d}t||dd tg d}d	}d
}d}t j||||}tdd}t||dd d S )Nr   r  r  r  g)\Ur   r
  rH  r  r   r  g*@Vr   }      rt  gר)rH  rH  rH  )r3   rs  r[  r   rl   r   fullr  r.   r.   r/   test_logcdf  s8   zTestHypergeom.test_logcdfN)r  r  r  r   r   rz  r{  r|  r  r#  r  r  r.   r.   r.   r/   rr    s    
	rr  c                   @   sP   e Zd Zejdddgdd Zdd Zdd	 Zejd
ddgdd Z	dS )TestLoggammazx, c, sf)rG  ra  gQOu3;)   rh   g\Z{0c                 C   s<   t j||}t||dd t j||}t||dd d S )NrS  rx   )r3   loggammarI  r   rN  )r   rC   rB  rI  rB   yr.   r.   r/   test_sf_isfK  s   zTestLoggamma.test_sf_isfc                 C       t jdd}t|ddd d S )Nir:   g     @r  rx   )r3   r  r   r   )r   lpr.   r.   r/   rq  S  s   zTestLoggamma.test_logpdfc                 C   sT   t g ddd}|D ]\}}}}}tjj|dd}t|||||gdd qd S )N)ro   g"~jg46<@g oŏ      @r  g	h"lxgQ?gZd;333333@g      (@g{/L@g??gгYҿgh|?5?r  r~   msvkr  rG  r
  )rl   r   reshaper3   r  r   )r   tablerB  r,  varskewkurtcomputedr.   r.   r/   r  [  s   zTestLoggamma.test_statsrB  re   r  c                 C   sx   t jj|dd}t| sJ t j|}t t||k t	|}|j
dd}|jd  k r7|jk s:J  J d S )N順 r   r  )confidence_levelro   )r3   r  r   rl   isfiniter   median	binomtestcount_nonzeror   proportion_cir-  r.  )r   rB  rC   medbtestcir.   r.   r/   r   j  s   $zTestLoggamma.test_rvsN)
r  r  r  r   r  r  r  rq  r  r   r.   r.   r.   r/   r  D  s    

r  c                   @   sp   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zej	
dddgdd Zdd Zej	
dddgdd ZdS )TestLogisticc                 C   2   t dd}tj|}tj|}t|| d S Nr=  r  )rl   r  r3   logisticrF   rA  r   r   rC   r  rD  r.   r.   r/   rE  {     zTestLogistic.test_cdf_ppfc                 C   r  r  )rl   r  r3   r  rI  rN  r   r  r.   r.   r/   r    r  zTestLogistic.test_sf_isfc                 C   s4   d}d}t tjd| | t tj|| d S )Ng      <gg|EA@r   )r   r3   r  rA  rN  )r   r'  desiredr.   r.   r/   test_extreme_values  s   z TestLogistic.test_extreme_valuesc                 C   s*   t jg d}g d}t||dd d S )N)ir   rg   )gm\  .g9B.gO& $r   rx   )r3   r  r   r   )r   rp  rc   r.   r.   r/   test_logpdf_basic  s   zTestLogistic.test_logpdf_basicc                 C   s"   t jddg}t|ddg d S )Nrn   )r3   r  r   r   r   rp  r.   r.   r/   test_logpdf_extreme_values  s   z'TestLogistic.test_logpdf_extreme_valueszloc_rvs,scale_rvs)g9x&?gi '?)gB"?gs^&?c                 C   sR   t jjd||d}dd }t|t j||fdj}t j|}t||dd d S )Nrh   r   r8   r9   c                 S   s   | \}}t |}tt|| | dt|| |   |d  }t|| | t|| | d t|| | d   | }||fS Nr   r:   )r   rl   r  r   )inputr   r,   r-   r&  x1x2r.   r.   r/   r     s   z#TestLogistic.test_fit.<locals>.funcrv  gKH9r   )r3   r  r   r"   	_fitstartrC   r   r   )r   loc_rvs	scale_rvsr   r   expected_solution
fit_methodr.   r.   r/   test_fit  s   
zTestLogistic.test_fitc                 C   sl   t jjdddd}|t j|fg}t j|i d }tt j|| tt j||dd tt j||dd d S )Nrh   ro   r:   r  r   r   r   )r3   r  r   r  _reduce_funcr   )r   r   r   r   r.   r.   r/   test_fit_comp_optimizer  s   z$TestLogistic.test_fit_comp_optimizer
testlogcdfTFc                 C   sH   t g d}|rtj|}ntj| }g d}t||dd d S )N)r2  r     r   rt  )     g      g%h9fg?~T}%mgCx^&ْgV瞯<rx   )rl   r   r3   r  r[  r  r   )r   r  rC   r  rc   r.   r.   r/   test_logcdfsf_tails  s   z TestLogistic.test_logcdfsf_tailsN)r  r  r  rE  r  r  r  r  r   r  r  r  r  r  r.   r.   r.   r/   r  y  s    

r  c                   @   r   )

TestLogserc                 C   r   r   r   r   r.   r.   r/   r     r   zTestLogser.setup_methodc                 C   r  )Nr  r   r   r   r   r   )r3   logserr   r   r=   r   r   r   r   r   r   r  r  r   r.   r.   r/   r     r  zTestLogser.test_rvsc                 C   s   t jdd}t|d d S )NrG  r  g&Y3)r3   r  r  r   r   rV  r.   r.   r/   test_pmf_small_p  s   zTestLogser.test_pmf_small_pc                 C      t jd}t|d d S )N:0yE>gW  ?)r3   r  r,  r   r  r.   r.   r/   test_mean_small_p  s   zTestLogser.test_mean_small_pN)r  r  r  r   r   r  r  r.   r.   r.   r/   r    s
    r  c                	   @   s   e Zd Zejdd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d Zejdej	dfej
dfgdd ZdS )TestGumbel_r_lfunctionscopec                 C      t jdS r   rl   r   r   r   r.   r.   r/   r        zTestGumbel_r_l.rngrL   r  r  r   r   r  re   r   r~   zfix_loc, fix_scaleTFc                 C   sp   |j d|||d}|||fg}||i d }	t }
|r$|d |
d< |r,|d |
d< t|||	fi |
 d S )Nrh   )r   r8   r9   r   r   r:   r   r   )r   r  r  r   r   )r   rL   r  r  fix_loc	fix_scaler   r   r   r   r   r.   r.   r/   r    s   
z&TestGumbel_r_l.test_fit_comp_optimizerz	dist, sgnr   r  c                 C   s@   |t g d }||\}}t||d  t|ddd d S )N)r   r   r   r   r   r   r   gW  @g   @g3qtw>r  rx   )rl   r   r   r   )r   rL   sgnzr8   r9   r.   r.   r/   r    s   zTestGumbel_r_l.test_fitN)r  r  r  r   fixturer   r  r  r3   gumbel_rgumbel_lr  r  r.   r.   r.   r/   r    s    

r  c                   @   s  e Zd Zdd Zdd Zejdddd Zej	d	ej
d
ddgej
dddgej
dddgdd Zej
d
ddgej
dddgej
dddgej
ddd eddgddD ejdddd Zejdddd  Zd!d" Zd#d$ Zd%S )&
TestParetoc                 C   s  t  R t dt tjjddd\}}}}t|tj t|tj t|tj	 t|tj	 tjjddd\}}}}t|tj t|tj t|tj	 t|tj	 tjjddd\}}}}t|d t|tj t|tj	 t|tj	 tjjddd\}}}}t|d t|tj t|tj	 t|tj	 tjjd	dd\}}}}t
|d
 t
|d t|tj	 t|tj	 tjjddd\}}}}t
|d t
|d t|tj	 t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t
|d W d    d S 1 s[w   Y  d S )Nr$  ro   r  r  r  ra  r  rs         @g?grq@r        @gffffff?gK~?g      2@g۶m۶m?r  UUUUUU?gqq?      $@      @g%I$I?gQ?gUUUUUU@grq?g88Nb@)r(  r)  r*  r+  r3   paretor   rl   r   r   r   r  r   rV  rW  rB   r@   r.   r.   r/   r     s`   











$zTestPareto.test_statsc                 C   s:   d}d}d}t jj||d|d}|| | }t|| d S )Ng    eAr:   ra  r   r7   )r3   r  rI  r   )r   rC   r-   r9   r'  rc   r.   r.   r/   rL  \  s   zTestPareto.test_sfr  r  c                 C   r  r   r  r   r.   r.   r/   r   d  r  zTestPareto.rngz2ignore:invalid value encountered in double_scalars	rvs_shaper   r:   rvs_locr   	rvs_scaler~   c              
   C   s  t jjd||||d}t jj|dddd }t jj|dddd }t jj|dddd }||  kr<|  kr<dks?J  J t jjd|||d |d}t jj|dd	\}	}
}t|d |  |d }|jd }t|	|tt	||    t|
d d S )
Nrh   r   r-   r9   r8   r   r   p=
ף?)r   r   )r   fix_b)r   fbr:   r  )
r3   r  r   r   r   r+  r   rl   r  r:  )r   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ndatar.   r.   r/   r  h  s,   
zTestPareto.test_fitre   fix_shape, fix_loc, fix_scalec                 C      g | ]}d |v r|qS Fr.   rK   r'  r.   r.   r/   rM         zTestPareto.<listcomp>TFr   repeatignoreinvalidc                 C   s|   t jjd||||d}|t j|fg}	t j|	i d }
i }|r%||d< |r+||d< |r1||d< tt j||
fi | d S )Nrh   r  r   r   r   r   )r3   r  r   r  r  r   r   r  r  r  	fix_shaper  r  r   r   r   r   r   r.   r.   r/   test_fit_MLE_comp_optimizer  s   	z&TestPareto.test_fit_MLE_comp_optimizerc                 C   s^   d\}}}t jj|||dtjdd}|t j|fg}t j|i d }tt j|| d S )N)r   r   r   rh   ið& rc  r   )	r3   r  r   rl   r   r   r  r  r   )r   r   locationr9   r   r   r   r.   r.   r/   test_fit_known_bad_seed  s   

z"TestPareto.test_fit_known_bad_seedc                 C   s@   t tj tttjjg ddd tttjjg dddd d S )Nr   r:   r  )r~   r:   r   r   r   r   r   )r   r3   r  assert_raisesr    r   r   r.   r.   r/   test_fit_warnings  s
   

zTestPareto.test_fit_warningsc                 C   s.   t jjddd|d}t|d t j|}d S )Ni~r   rh   )r8   r-   r   r   r   )r3   r  r   r
   r   )r   r   r   rj  r.   r.   r/   test_negative_data  s   
zTestPareto.test_negative_dataN)r  r  r  r  rL  r   r  r   r  filterwarningsr  r  r$   rl   errstater  r  r  r  r.   r.   r.   r/   r    s,    <





r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zejddg dfdddded ejgfdddded d gfd!g d"fgd#d$ Zd%d& Zd'S )(TestGenparetoc                 C   sl   dD ]}t |}tj|\}}t|d tt | qt d}tj|\}}t||gddg d S )Nr  rt   rt          ro   )	rl   asarrayr3   	genpareto_get_supportr   r   isposinfr   )r   rB  r,   r-   r.   r.   r/   test_ab  s   


zTestGenpareto.test_abc                 C   s   t jdd}tddd}t||t j| t||t j| t||t j| tddd}t|	|t j	| d S )Nrt   rB  r   r  r   r  rg   )
r3   r  rl   r  r   r<   r	  rF   rI  rA  r   rvrC   rC  r.   r.   r/   test_c0  s   zTestGenpareto.test_c0c                 C   s   t jdd}tddd}t||t j| t||t j| t||t j| tddd}t|	|t j	| t|
d	d d S )
Nr!  r  r   r  r   rt   r  rg   r   )r3   r  rl   r  r   r<   uniformrF   rI  rA  r   r  r.   r.   r/   test_cm1  s   zTestGenpareto.test_cm1c                 C   s   t jdd}t|tj|tjgddg tt|	tj t jdd}t|tj|tjgddg tt|	tj t jdd}t|tj|tjgddg tt|	tj d S )Nre   r  rt   r  r!  )
r3   r  r   r<   rl   r   rF   r   isneginfr   r   r  r.   r.   r/   
test_x_inf  s   """zTestGenpareto.test_x_infc                 C   s   t ddd}dD ]:}tj||}dD ]}tj||| }t||dd qtj||}dD ]}tj||| }t||dd q0q	d S )	Nr   rg   r   r   r  r  g+rS  r   )r  r  )rl   r  r3   r  r<   r   rF   )r   rC   rB  pdf0dcpdfccdf0cdfcr.   r.   r/   test_c_continuity  s   zTestGenpareto.test_c_continuityc              	   C      t jt jddddt jdddddd	t jdddd f }d
D ]}tj||}dD ]}tj||| }t||dd q*qd S NrS  rq   re   baser   r   Fendpointr  )rt   r!  r'  r   )rl   r  r?  r  r3   r  rA  r   )r   rC  rB  ppf0r)  ppfcr.   r.   r/   test_c_continuity_ppf     z#TestGenpareto.test_c_continuity_ppfc              	   C   r.  r/  )rl   r  r?  r  r3   r  rN  r   )r   rC  rB  isf0r)  isfcr.   r.   r/   test_c_continuity_isf  r7  z#TestGenpareto.test_c_continuity_isfc              	   C   sj   t jt jddddt jdddddd	t jdddd f }d
D ]}ttjtj||||dd qd S )NrS  rq   re   r0  r   r   Fr2  r  )r  gC]r2rw   gV瞯Ҽrw   r   )	rl   r  r?  r  r   r3   r  rF   rA  )r   rC  rB  r.   r.   r/   test_cdf_ppf_roundtrip  s   z$TestGenpareto.test_cdf_ppf_roundtripc                 C   s    t jdddd}t|d d S )Ng    _Brq   r   r   gpEȜ)r3   r  r  r   r  r.   r.   r/   r    s   zTestGenpareto.test_logsfzc, expected_statsr   )r   r   r:   r  r  r  gqq@rg   r:   gqq?g      ?g$I$	?rq?r"  gll0@r  )ro   UUUUUU?r   333333c                 C   s$   t jj |dd}t||ddd d S )Nr  r  r   rw   r  )r3   r  r   )r   rB  expected_statsr  r.   r.   r/   r  !  s   zTestGenpareto.test_statsc                 C   s   t jd}t|ddd d S )Nr  gvǼ
  ?r   rx   )r3   r  r  r   )r   rW  r.   r.   r/   test_var+  s   zTestGenpareto.test_varN)r  r  r  r  r   r"  r%  r-  r6  r:  r;  r  r   r  r  rl   r  r   r  r@  r.   r.   r.   r/   r    s(    

	


r  c                   @   D   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dS )TestPearson3c                 C   r   r   r   r   r.   r.   r/   r   2  r   zTestPearson3.setup_methodc                 C   s   t jjddd}tt|dk t|jjtd v  t jd}tt	|t
 t dd}tt	|tj t|jjtd v  tt|dk d S )Nre   r   r   AllFloatro   r   )r3   r(   r   r   r=   r   r   r   r   r   floatr  r   r   r.   r.   r/   r   5  s   zTestPearson3.test_rvsc                 C   s|   t jdg d}t|tg ddd t jdd}t|tdgdd t jg d	d}t|tg d
dd d S )Nr:   rt   re   ro  )gtT?g+q?g?r  r   r4  re   ND}i?r4  rZ  r  r   r   )rF  gj?gdC?gs?g'M?)r3   r(   r<   r   rl   r   r  r.   r.   r/   r  @  s   
zTestPearson3.test_pdfc                 C   sp   t jdg d}t|tg ddd t jdd}t|dgdd t jg d	d}t|g d
dd d S )Nr:   rE  )grE?gTp]0?g~?r  r   r4  re   g E&"J?rG  )giZ*J?gh+8w?gcK?g|<x6?gG?)r3   r(   rF   r   rl   r   r  r.   r.   r/   r  J  s   

zTestPearson3.test_cdfc                    s@   g d}dd t j|} fdd|D }t|| d S )Nr4  r  r   ro   ro   rY  c                    s$   g | ]}t t|j d  qS rI   )r   r3   r(   r<   )rK   r  neg_infx_evalr.   r/   rM   [  s    z<TestPearson3.test_negative_cdf_bug_11186.<locals>.<listcomp>)r3   r(   rF   r   )r   skewsr=  int_pdfsr.   rI  r/   test_negative_cdf_bug_11186T  s   z(TestPearson3.test_negative_cdf_bug_11186c                 C   sT   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   r:   r   r  )r3   r(   r  r   r   rl   number)r   r  r.   r.   r/   test_return_array_bug_11746_  s   

z(TestPearson3.test_return_array_bug_11746c                 C   s   g d}d}t jt j|||}t|| tdgdgg}tdd}tt j||t j| |  tt j||t j	| |  tt j||t j
||   d S )NrH  ro   ru  ra  rZ  r:   )r3   r(   rA  rF   r   rl   r   r  r<   rI  rN  )r   rL  rK  r   r  rC   r.   r.   r/   test_ppf_bug_17050j  s   
zTestPearson3.test_ppf_bug_17050N)
r  r  r  r   r   r  r  rN  rP  rQ  r.   r.   r.   r/   rB  1  s    

rB  c                   @   rA  )
TestKappa4c                 C   sD   g d}d}dD ]}t j|||}t j|| }t|| qd S )N)rt   re   ro  ro   r  )
gffffffr!  ru  皙ɿ皙re   ro  ro   r  ffffff?)r3   kappa4rF   r  r   r   rC   r"  r@   r   	vals_compr.   r.   r/   test_cdf_genpareto  s   zTestKappa4.test_cdf_genparetoc                 C   sL   t ddd}d}t ddd}tj|||}tj||}t|| d S )Nr  r~   rg   rt   r4  r   )rl   r  r3   rV  rF   
genextremer   rW  r.   r.   r/   test_cdf_genextreme  s   zTestKappa4.test_cdf_genextremec                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr   rg   r  rt   )rl   r  r3   rV  rF   r	  r   rW  r.   r.   r/   test_cdf_expon     zTestKappa4.test_cdf_exponc                 C   @   t ddd}d}d}tj|||}tj|}t|| d S )Nr  r~   rg   rt   )rl   r  r3   rV  rF   r  r   rW  r.   r.   r/   test_cdf_gumbel_r  r]  zTestKappa4.test_cdf_gumbel_rc                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr  r~   rg   r!  rt   )rl   r  r3   rV  rF   r  r   rW  r.   r.   r/   test_cdf_logistic  r]  zTestKappa4.test_cdf_logisticc                 C   r^  )Nr  r~   rg   r  )rl   r  r3   rV  rF   r!  r   rW  r.   r.   r/   test_cdf_uniform  r]  zTestKappa4.test_cdf_uniformc                 C   s   t dd d S r  )r3   rV  r   r.   r.   r/   test_integers_ctor  s   zTestKappa4.test_integers_ctorN)
r  r  r  rY  r[  r\  r_  r`  ra  rb  r.   r.   r.   r/   rR  ~  s    					rR  c                   @   r  )TestPoissonc                 C   r   r   r   r   r.   r.   r/   r     r   zTestPoisson.setup_methodc                 C   s@   t d}tjg d|}d|d |d d g}t|| d S )Nr:   r   r   r:   ro   rG  )rl   r:  r3   poissonr  r   )r   ln2r   rc   r.   r.   r/   test_pmf_basic  s   
zTestPoisson.test_pmf_basicc                 C   s@   t jg dd}g d}t|| t jdd}t|d d S )Nrd  r   )r   r   r   ffffff?r   r   )r3   re  r  r   intervalr   )r   r   rc   rj  r.   r.   r/   test_mu0  s
   
zTestPoisson.test_mu0c                 C   r  )Nro   r   r   r   r   r   )r3   re  r   r   r=   r   r   r   r   r   r   r  r  r   r.   r.   r/   r     r  zTestPoisson.test_rvsc                 C   s   d}t jj |dd}t|||td| d| g tg d}t jj |dd}||tjddtd gtjddgf}t|| d S )	Ng      0@r  r  r  )rt   r  rs   r   r:   ro   )r3   re  r   rl   r  r   r   )r   ry  r  rc   r.   r.   r/   r    s    &zTestPoisson.test_statsN)r  r  r  r   rg  rk  r   r  r.   r.   r.   r/   rc    s    	rc  c                   @   l   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd ZdS )	TestKSTwoc                 C   r   r   r   r   r.   r.   r/   r     r   zTestKSTwo.setup_methodc                 C   s   dD ]W}t dd| d| ddd|  dg}d| | }tj|d }|dkr.t |nd}t dd|| ddtjd|  t	dd|  ddg}tj
||}t|| qd S )Nr   r:   r   rg   rh   r   r   ro   r   r  r:   rt   )rl   r   r2   r   gammalnr   r3   ksonerI  r  kstworF   r   )r   r&  rC   v1lgelgrc   r  r.   r.   r/   r    s   &zTestKSTwo.test_cdfc                 C   s   t ddd}dD ]U}t dd| d| ddd|  dg}d| | }tj|d }|dkr5t |nd}t ddd||  dtj	d| t
d| ddg}tj	||}t|| q	d S )Nr   r   r)  rn  ro   r  r:   )rl   r  r   r2   r   ro  r   r3   rp  rI  r+  rq  r   )r   rC   r&  rr  rs  rt  rc   r  r.   r.   r/   rL    s   &
zTestKSTwo.test_sfc                 C   s\   t ddddd  }g d}|D ]}|t | }tj||}t |}t|d qd S )Nr   r:   r)  r   )r   rh      i  r   r   r  )rl   r  r  r3   rq  rF   diffr
   )r   rC   ns_xxnprobsdiffsr.   r.   r/   test_cdf_sqrtn  s   
zTestKSTwo.test_cdf_sqrtnc                 C   sF   t ddd}dD ]}tj||}tj||}t|d|  q	d S Nr   r   r)  rn  )rl   r  r3   rq  rF   rI  r   )r   rC   r&  r  r  r.   r.   r/   r    s   zTestKSTwo.test_cdf_sfc                 C   sT   t ddd}dD ]}|t | }tj||}tj||}t|d|  q	d S r}  )rl   r  r  r3   rq  rF   rI  r   )r   rC   r&  ry  r  r  r.   r.   r/   test_cdf_sf_sqrtn"  s   zTestKSTwo.test_cdf_sf_sqrtnc                 C   n   t ddd}dD ]+}||d| k }tj||}d|k |dk @ }tj||}t|| || dd q	d S )	Nr   r   r)  rn  ro   r  r  rx   )rl   r  r3   rq  rF   rA  r   r   rC   r&  ry  r  condr   r.   r.   r/   test_ppf_of_cdf*  s   zTestKSTwo.test_ppf_of_cdfc                 C   r  )	Nr   r   r)  rn  ro   r  r  rx   )rl   r  r3   rq  rN  rI  r   )r   rC   r&  ry  vals_isfr  r   r.   r.   r/   test_isf_of_sf4  s   zTestKSTwo.test_isf_of_sfc                 C   t   t ddd}dD ].}|t | |d| k }tj||}d|k |dk @ }tj||}t|| ||  q	d S )Nr   r   r)  rn  ro   r  )rl   r  r  r3   rq  rF   rA  r   r  r.   r.   r/   test_ppf_of_cdf_sqrtn=  s   zTestKSTwo.test_ppf_of_cdf_sqrtnc                 C   r  )Nr   r   r)  rn  ro   rh  )rl   r  r  r3   rq  rI  rN  r   )r   rC   r&  ry  r  r  r   r.   r.   r/   test_isf_of_sf_sqrtnF  s   zTestKSTwo.test_isf_of_sf_sqrtnc                 C   sJ   t ddddd  }dD ]}tj||}tj||}t|| qd S r}  )rl   r  r3   rq  rA  rF   r   )r   rz  r&  ry  r  r.   r.   r/   r  P  s   zTestKSTwo.test_ppfc              	   C   s   g d}t g d}t g dg dg dg dg dg dg}t|D ]%\}}|t d	 t t jd	 |  }tj||}t	||| d
d q&d S )N)rg   r   rh   ru  rt  r   )r  gUUUUUU?ro   r   r:   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$?g qO?)g}+: >gwQ9>gH{?g]qv(?g)~/v?gmJ?)gV27J=gGk(>gWX?gY?g{0`?gZ
H?)g_R=g4>g̪?gT_@?g<e?g2?r:   h㈵>rx   )
rl   r   	enumerater:  r  r>   r3   rq  rF   r   )r   rw  ratiosrc   idxr&  rC   r  r.   r.   r/   test_simard_lecuyer_table1W  s   "z$TestKSTwo.test_simard_lecuyer_table1N)r  r  r  r   r  rL  r|  r  r~  r  r  r  r  r  r  r.   r.   r.   r/   rm    s    
		
rm  c                   @   r6  )TestZipfc                 C   r   r   r   r   r.   r.   r/   r   z  r   zTestZipf.setup_methodc                 C   r  )Nra  r   r   r   r   r   )r3   zipfr   r   r=   r   r   r   r   r   r   r  r  r   r.   r.   r/   r   }  r  zTestZipf.test_rvsc                 C   s\   t jj dd\}}tt| t|tj t jj ddd\}}tt||g   d S )Nffffff@r,   rY  skr,   r  )r3   r  r   rl   r  r   r   r   r  r.   r.   r/   r`    s
   zTestZipf.test_momentsN)r  r  r  r   r   r`  r.   r.   r.   r/   r  y  r;  r  c                   @   r   )
TestDLaplacec                 C   r   r   r   r   r.   r.   r/   r     r   zTestDLaplace.setup_methodc                 C   s   t jjddd}tt|dk t|jjtd v  t jd}tt	|t
 t dd}tt	|tj t|jjtd v  tt jdd u d S )Nra  r   r   r   r   r  )r3   dlaplacer   r   r=   r   r   r   r   r   r  r  r   r.   r.   r/   r     s   zTestDLaplace.test_rvsc                 C   s   d}t |}| d\}}}}d}t| |d }||}	t|	|d  t|	|d  }
}t||fd t||f|
||
d  d fd	d
d d S )Nr  r  %   r   r:   rG  ri  r  r  r  r  )r3   r  rl   r   r  r  r   r   )r   r,   dlrV  rW  rB   r@   rv  rD  ppm2m4r.   r.   r/   r    s   

&(zTestDLaplace.test_statsc                 C   sF   t d}t|}|d\}}}}t||fd t||fd d S )Nrs   r  )rt   rt   )r  g      
@)rl   r:  r3   r  r   r   )r   r,   r  rV  rW  rB   r@   r.   r.   r/   test_stats2  s
   

zTestDLaplace.test_stats2N)r  r  r  r   r   r  r  r.   r.   r.   r/   r    s
    r  c                       sh   e Zd Zdd Zejdddgdd Zejdddg fd	d
Zdd Z	dd Z
dd Z  ZS )TestInvgaussc                 C   r   r   r   r   r.   r.   r/   r     r   zTestInvgauss.setup_methodzrvs_mu,rvs_loc,rvs_scale)r:   r   r   )g
ףp=@g r@gʡE6@c                 C   sB  t jjd|||d}t jj||d\}}}|| }t|}t|t|d |d   }	||	 }
t|
|ddd t|	|ddd t	|| t jjd|||d}t jj||d |d d\}}}t	|d | t	|d | t jj|d	d
d }t jj|d	dd }t jj|d	dd }||  kr|  krd	ksJ  J d S )Nrh   r   ry  r8   r9   r  r  rw   r  r   r  r  )fmur   )fix_mur   )
r3   r   r   r   rl   r,  r   r  r   r   )r   rvs_mur  r  r   ry  r8   r9   mu_temp	scale_mlemu_mle
shape_mle1
shape_mle2
shape_mle3r.   r.   r/   r    s.   



*zTestInvgauss.test_fit)gX9v>@g	@gGz@c           
         s  t jjd|||d}ttt jt jj}||}t j|}t|| ||ddd}t jj|ddd}t|| |t j|fg}t j|i d }	t	t j||	|d t
||d  dks`J t	t j||	|d d t	t j||	dd t	t j||	|t
jdd d d S )	Nrh   r  r   r:   )r   r  r   r  r  )r3   r   r   r   r   r   r   r  r  r   rl   r   r   rand)
r   r  r  r  r   	super_fitsuper_fittedinvgauss_fitr   r   	__class__r.   r/   r    s*   




z(TestInvgauss.test_fit_MLE_comp_optimizerc                 C   sN   t tj tt tjjg ddd W d    d S 1 s w   Y  d S )Nr   r:   r  )r   r3   r   r   r   r    r   r   r.   r.   r/   test_fit_raise_errors	  s   
"z"TestInvgauss.test_fit_raise_errorsc                 C   s   g d}g d}t jjd|d}t|| t jjddd}t|d t jjd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?ry  r  ?gfFn   gr^:g9̗?r  gx_;:g!?gٷ
??)r3   r   rF   r   r   rI  )r   ry  rc   r_   
cdf_actual	sf_actualr.   r.   r/   r  	  s   



zTestInvgauss.test_cdf_sfc                 C   sh   t jjddd}t|d t jdd}t|d t jjddd}t|d t jdd}t|d	 d S )
Nr  r  r  giJ.r  gr^ߺr  gpgFgpQ^L)r3   r   r[  r   r  )r   r[  r  r.   r.   r/   r  *	  s   	


zTestInvgauss.test_logcdf_logsf)r  r  r  r   r   r  r  r  r  r  r  r  __classcell__r.   r.   r  r/   r    s    
&#r  c                       sz   e Zd Zejdg dejdg ddd Zejdg d fd	d
Zdd Zdd Z	dd Z
dd Z  ZS )TestLaplacer  )r  r   r   r:   r  )r   r:   r   rg   c                 C   sL  t jjd||d}t|}tt|| t| }t j|\}}t	||ddd t	||ddd t jj||d\}}t	||ddd t jj||d\}}t	|| |d }tt|| t| }t jj||d\}}t
|| t jj||d\}}t
|| ttt jj|||d ttt jjtjg ttt jjtjg d S )	Nrh   r  rw   r  r  r  r:   r  )r3   r  r   rl   r  r  r   r   r   r   r   r  r   r   r   r   )r   r  r  r   loc_mler  r8   r9   r.   r.   r/   r  >	  s*   



zTestLaplace.test_fitzrvs_scale,rvs_loc))rg   r  )r~   rg   )ro  ro   c                    s   t jjd||d}dd }t j|\}}ttt jt j|\}}||||}	||||}
|	|
k s>tj|	|
ddds@J d S d S )Nr   r  c              	   S   s8   dt | td|  d| tt||     S )Nr  r:   r   )r   rl   r:  r  r   )r8   r9   r   r.   r.   r/   llr	  s   z3TestLaplace.test_fit_MLE_comp_optimizer.<locals>.llrw   r  )r3   r  r   r   r   r   rl   r   )r   r  r  r   r  r8   r9   loc_opt	scale_optll_mlell_optr  r.   r/   r  k	  s   
z'TestLaplace.test_fit_MLE_comp_optimizerc                 C   sZ   t g d}tjj|dd\}}t|dddd tjj|dd\}}t|dddd d S )N)r  r  r  r         @rN  r  r  rG  rw   r  r  )rl   r   r3   r  r   r   )r   r   r8   r9   r.   r.   r/   test_fit_simple_non_random_data	  s
   z+TestLaplace.test_fit_simple_non_random_datac                 C   sl   d}t j| }|dksJ t j|}|dksJ t j|}|dks'J t j| }|dks4J d S )Nr   rt   r  )r3   r  rF   rI  )r   rC   p0p1r.   r.   r/   test_sf_cdf_extremes	  s   z TestLaplace.test_sf_cdf_extremesc                 C   s.   d}t j|}t|t| d dd d S )Nru  r:   r   rx   )r3   r  rI  r   rl   r   )r   rC   r'  r.   r.   r/   rL  	     zTestLaplace.test_sfc                 C   s.   d}t j|}t|td|  dd d S )Ng}:r:   r   rx   )r3   r  rN  r   rl   r:  )r   r'  rC   r.   r.   r/   rP  	  r  zTestLaplace.test_isf)r  r  r  r   r  r  r  r  r  r  rL  rP  r  r.   r.   r  r/   r  =	  s    +	r  c                   @   s   e Zd Zejdddd Zejdg dejdg dejd	g d
ejddd eddgddD dd Z	dd Z
dd ZdS )TestPowerlawr  r  c                 C   r  r   r  r   r.   r.   r/   r   	  r  zTestPowerlaw.rngr  )re   ro   r  r   r:   r  r  r  r  r   c                 C   r  r  r.   r  r.   r.   r/   rM   	  r  zTestPowerlaw.<listcomp>TFr   r  c                 C   s   t jjd||||d}|t j|fg}	t j|	i d }
t }|r&||d< |r4t| tj	 |d< |r:||d< t
t j||
fi | d S )Nr  )r   r,   r8   r9   r   r   r   r   r   )r3   powerlawr   r  r  r   rl   	nextafterr+  r   r   r
  r.   r.   r/   r  	  s   z(TestPowerlaw.test_fit_MLE_comp_optimizerc                 C   sx   d}d}d}t jj|||dtjdd}d| d i}|t j|fg}t j|i d	 }t	t j||fi | d S )
Ng`- @rt   grߟA@rh   r~   )r,   r8   r9   r   r   r   r:   r   )
r3   r  r   rl   r   r   ptpr  r  r   )r   r,   r  r9   r   r   r   r   r.   r.   r/   test_problem_case	  s   
zTestPowerlaw.test_problem_casec                 C   sf  t tj d}tt|d tjjg dddd W d    n1 s#w   Y  d}tt|d tjjg ddd W d    n1 sEw   Y  d}tt|d tjjg dd	d W d    n1 sgw   Y  d
}tt|d tjjg ddd W d    n1 sw   Y  d}tt|d tjjg ddd W d    d S 1 sw   Y  d S )Nz7 Maximum likelihood estimation with 'powerlaw' requiresr   r   r:   rG  r   r   r  r:   r  r   z$Negative or zero `fscale` is outsider4  r  z0`fscale` must be greater than the range of data.)r   r3   r  r  r    r   r   )r   r*   r.   r.   r/   r  	  s*   
"zTestPowerlaw.test_fit_warningsN)r  r  r  r   r  r   r  r  r$   r  r  r  r.   r.   r.   r/   r  	  s    

r  c                   @   r6  )TestInvGammac                 C   s   t  P t dt tjjddd}g d}t|| g d}tjj|dd}g dtjdd	gtj	d
dgtj	tj	dgf}t
||D ]	\}}t|| qBW d    d S 1 sWw   Y  d S )Nr$  g(\O3@r  r  )g~?gCX&?g*7gS?gBqFq @)皙?@gffffff@)r  gEy?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@)r(  r)  r*  r+  r3   r   r   rl   r   r   r   r   )r   r  rc   r,   rC   r  r.   r.   r/   test_invgamma_inf_gh_1866	  s    



"z&TestInvGamma.test_invgamma_inf_gh_1866c                 C   s6   t dd}tj|d}tj|d}t|| d S )Ngr   r   )rl   r?  r3   r   rF   rA  r   r  r.   r.   r/   rE  
  s   zTestInvGamma.test_cdf_ppfc                 C   sR   t jdkrtdd}ntdd}tj|d}tj|d}t||dd d S )N        r:   rh      r   r  rx   )	sysmaxsizerl   r?  r3   r   rI  rN  r   r  r.   r.   r/   r  
  s   
zTestInvGamma.test_sf_isfN)r  r  r  r  rE  r  r.   r.   r.   r/   r  	  s    r  c                   @   r   )
TestFc                 C   s\   t jddgg}|D ]\}}}|j|jg|R  }q	dd |D }dd |D }t|| d S )N)r:   r   r  c                 S   &   g | ]\}}}|j |jg|R  qS r.   r<   r,   rK   _f_argsrj  r.   r.   r/   rM   !
     & z(TestF.test_endpoints.<locals>.<listcomp>c                 S      g | ]\}}}|qS r.   r.   rK   r  r  	_correct_r.   r.   r/   rM   "
      )r3   fr<   r,   r   )r   r   r  r  _correctanscorrectr.   r.   r/   r4  
  s   zTestF.test_endpointsc                 C   sX   t jj dddd\}}}}tt| tt| tt| tt|  d S )Nr)        @r  r  )r3   r  r   rl   r  r  r.   r.   r/   test_f_moments%
  s
   zTestF.test_f_momentsc                 C   sV   t   t dt tjjdgd g ddd W d    d S 1 s$w   Y  d S )Nr$  r)  rG  )r:   rG  r  r  r  dfndfdr  )r(  r)  r*  r+  r3   r  r   r.   r.   r/   test_moments_warnings-
  s   
"zTestF.test_moments_warningsc                 C   sD  t dgdgg}t ddg}tjj||dd\}}}}||d  gd }t|| d|d  || d  | |d d  |d  }t|| d| | d t d|d   |d	 t ||| d    }	t||	 d|d
| d  || d  |d |d d    }
||d	  |d  || d  }|
| }t|| d S )Nr   r)  r	  r  r  r:   rG  r  r  r~      )rl   r   r3   r  r   r  )r   r  r  rV  rW  rB   r@   r  v2s2k2numk2denk2r.   r.   r/   test_stats_broadcast3
  s"   
0
 
 zTestF.test_stats_broadcastN)r  r  r  r4  r  r  r  r.   r.   r.   r/   r  
  s
    
r  c                   C   s   t tjddgddg d S )Nr~   r  g?g?)r   r3   r  r-  r.   r.   r.   r/   test_rvgeneric_stdE
  s   r  c                   C   s   t tjjdddtjtjtjtjf t tjjddddtjtjtjf t tjjddddtjtjtjf t tjjdddddtjtjf t tjjd	d
dtjtjf t tjjdd
ddtjf t tjjdd
ddtjf t tjjdd
dd d S )Nr   r  )rR  r  )\(?rt   r:   gGz @g     i@r   r  gGz@rG  g
ףp=
@)rt   gq    @)r   r3   r  rl   r   r   r.   r.   r.   r/   test_moments_tJ
  s    r  c                  C   s*   g d} g d}t tj| |dd d S )N)r   r:   r  rh   )g?@gTM]?ggY?gU?r   rx   )r   r3   r  rR   )rR  rc   r.   r.   r/   test_t_entropyZ
  s   r  methname)r<   r   rF   rA  rI  rN  
df_infmask)r   r   r   )r   r   r   c                 C   s   t jd t j|td}t jjdd|jd}t jj|j }t j||< t	j
|ddd}t	j
||  ddd}t	jddd}t|| }t|| }t|| }	||}
t|
| |	||  t|
|  |||   d S )	Nr   r   rg   r   r   r   rR  r8   r9   r7   )rl   r   r   r  boolr!  r   randnr   r3   r  r  r   r   )r  r  rR  rC   t_dist
t_dist_ref	norm_distt_meth
t_meth_ref	norm_methr   r.   r.   r/   test_t_inf_dfb
  s   



r  c                 C   s  t jd t j| td} t jjdd| jd}t j|| < tj	j|dddd}tj
jdddd	}tj	j||   dddd}td
D ]}t|| |  ||  t|| |   ||  q@tj	j|ddd}tj
jddd}tj	j||   ddd}t||  | t||   | d S )Nr   r  rg   r   r   r   r  )rR  r8   r9   r  r8   r9   r  rG  r  r7   )rl   r   r   r  r  r!  r   r   r3   r  r  r  r   rR   )r  rR  r   
res_ex_infres_ex_noinfr  r.   r.   r/   test_t_inf_df_stats_entropyy
  s"   
r   c                   @   rl  )TestRvDiscretec                 C   r   r   r   r   r.   r.   r/   r   
  r   zTestRvDiscrete.setup_methodc                 C   s   g d}g d}d}t jd||fd}|j|d}tt|tj t||D ]\}}ttt	||kt
| | dk  q&| }tt|tjsLJ d S )N)r  r   r   r:   r   rG  )rt   333333?r  rt   r  rt   r   sample)namevaluesr   rd  )r3   rO   r   r   r   r=   r  r   r   r  rD  rl   r   r   integer)r   statesprobabilitysamplesrrC   rB   r'  r.   r.   r/   r   
  s   &zTestRvDiscrete.test_rvsc                 C   sr   t g d}tjg d|fd}tt|| }| }t|| tjg dg dfd}| }t|d d S )N)r  rZ  r  rd  r  )r  r   r   rt   )	rl   r   r3   rO   r  r   rR   r   r   )r   rC  r'  r!  r"  r.   r.   r/   r#  
  s   
zTestRvDiscrete.test_entropyc                 C   sT   g d}g d}t j||fd}ddgddgg}t||dd	gd
dggdd d S )Nr  ro   r  ro  r  r  r  r  r:   ro   ro  rt   r  r  r   )r3   rO   r   r  )r   xkpkr  rC   r.   r.   r/   r  
  s   

zTestRvDiscrete.test_pmfc                    d   g d}g d}t j||fd g d}g d}t ||dd t fdd	|D |dd d S )
Nr  r  r  )rZ  r  r  ra  rs   r  rG  r~   )r   ro   ro   ro   r  r  r   r   r  r   c                       g | ]}  |qS r.   )rF   )rK   rD  r  r.   r/   rM   
  r  z+TestRvDiscrete.test_cdf.<locals>.<listcomp>)r3   rO   r   rF   )r   r  r  x_valuesrc   r.   r  r/   r  
     
zTestRvDiscrete.test_cdfc                    r  )
Nr  r  r  )re   ro   333333?r  rm  r  )r   r   r:   r:   rG  rG  r  r   c                    r  r.   )rA  )rK   rC  r  r.   r/   rM   
  r  z+TestRvDiscrete.test_ppf.<locals>.<listcomp>)r3   rO   r   rA  )r   r  r  q_valuesrc   r.   r  r/   r  
  r  zTestRvDiscrete.test_ppfc                 C   sN   g dg df}t j|d}t|||jd d d |jdd   d S )N)r   r:   rG  r"  r  )re   ro  r  r  re   r  r  r  r   )r3   rO   r   rA  rF   r  )r   r   r  r.   r.   r/   test_cdf_ppf_next
  s
   z TestRvDiscrete.test_cdf_ppf_nextc                 C   s`   t dd}t g dg dg dg}tj||fd}t| t |j	|j
 dd d S )Nr	  )r   rG  )re   re   rw  rd  )re   re   rd  rd  r  r  r   )rl   r   r  r   r3   rO   r   r   r  r  r  r   r  r  r  r.   r.   r/   test_multidimension
  s   
$z"TestRvDiscrete.test_multidimensionc                 C   s   g d}ddg}t ttjfi t||fd g d}t ttjfi t||fd g d}g d}t ttjfi t||fd g d}g d}t ttjfi t||fd d S )Nr   ro   r  )ro   333333?gffffff濩r   r:   r   rG  r~   )r  r  r  r  rS  )r  r   r3   rO   r   r   r  r  r.   r.   r/   test_bad_input
  s   "zTestRvDiscrete.test_bad_inputc                 C   s   t ddt dd}}tttjfi t||fd t ddt dd}}tttjfi t||fd t ddt dd}}t	tj||fd
dd d S )	NrG  r:   r:   )r:   r   gUUUUUU?r  r  r   r:   r   )rl   r   r  r  r  r   r3   rO   r   r   r  r  r.   r.   r/   test_shape_rv_sample
  s    z#TestRvDiscrete.test_shape_rv_samplec                 C   sD   g d}g d}t j||fd}t| t|j|j dd d S )N)r   r:   rG  r  r"  r)  )re   ro  ro  ro  ro  re   r  r  r   )r3   rO   r   r   rl   r  r  r  r  r.   r.   r/   test_expect1  s   $zTestRvDiscrete.test_expect1c                 C   s   g d}g d}t j||fd}t| | dd t| tdd t||D dd t|dd	 td
d t||D 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:?rt   gF%uk?g:vz?rt   rt   g.nr?g|гY?rt   rt   rt   g @6*? 4U0*C?g@+?gC6z?g nr?g ?gOjM?g n?g1w-!?g:pΈ?gףp=
?g _Le?rt   g^)p?g~jtx?gJ4q?gGzt?g J4q?g Mb@?g@Psׂ?g@^)ˀ?rt   rt   g N@s?g 1w-!_?r"  gൄ|г?rt   gH}}?rt   g
F%u?rt   rt   g ^)ˀ?g v?rt   r  r  r   c                 s   s    | ]	\}}|| V  qd S rj   r.   rK   rW  wr.   r.   r/   	<genexpr>*  s    z.TestRvDiscrete.test_expect2.<locals>.<genexpr>c                 S      | d S Nr:   r.   r   r.   r.   r/   rX   -      z-TestRvDiscrete.test_expect2.<locals>.<lambda>c                 s   s     | ]\}}|d  | V  qdS )r:   Nr.   r#  r.   r.   r/   r%  .      )r3   rO   r   r   r,  r  r   )r   r  pyr  r.   r.   r/   test_expect2  s   
zTestRvDiscrete.test_expect2N)r  r  r  r   r   r#  r  r  r  r  r  r  r  r   r+  r.   r.   r.   r/   r  
  s    	r  c                   @      e Zd Zdd Zdd ZdS )TestSkewCauchyc                 C   sl   t ddd}ttjj|ddtj| ttjj|ddtj| ttjj|ddtj| d S Nr  r~   rh   r   r  )	rl   r  r   r3   
skewcauchyr<   r  rF   rA  rO  r.   r.   r/   test_cauchy2  s   


zTestSkewCauchy.test_cauchyc                 C   s   t jd t jdd d }t jdd d }g d}g d}ttj||| ttj||| ttj	||| d S )Nr   rg   r:   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?)
rl   r   r   r  r   r3   r/  r<   rF   rA  )r   r,   rC   r<   rF   r.   r.   r/   test_skewcauchy_R;  s   z TestSkewCauchy.test_skewcauchy_RN)r  r  r  r0  r1  r.   r.   r.   r/   r-  1  s    	r-  r:   r~   g@r   gףp=
1@r   gRZ@i   gS㥛Ԋ@re   rf   g&@iQ i'  i0ybi l   HO1Z i3r4  irg   irh   ikru  i1r   i  i4i N  i(  lEI. @ i c                   @   sZ   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Ze	j
dedd Zdd ZdS )TestSkewNormc                 C   s   t d| _d S r   )r   r   r   r.   r.   r/   r        zTestSkewNorm.setup_methodc                 C   s0   t ddd}ttjj|ddtj| d S r.  )rl   r  r   r3   skewnormr<   r  rO  r.   r.   r/   test_normal  s   
zTestSkewNorm.test_normalc                 C   sH   d}t jjd|| jd}t||j t jjd|| jd}t||j d S )N)r   rG  r~   r  )r,   r   r   r4  )r3   r6  r   r   r   r   )r   r   rC   r.   r.   r/   r     s
   zTestSkewNorm.test_rvsc                 C   s   t jjdtddd| jd}t|t|t |t 	|g}t jj ddddd}t
||dd t jjd	tddd| jd}t|t|t |t 	|g}t jj d	dddd}t
||dd d S )
NrG  r  r~   r:   )r,   r   r8   r9   r   r  )r,   r8   r9   r  r
  r>  )r3   r6  r   r  r   rl   r,  r  r  kurtosisr   )r   Xrc   r  r.   r.   r/   r`    s   $$zTestSkewNorm.test_momentsc                 C   sF   t jg dd}t|tddd t jdd}t|ddd d S )	N)rg   r  r   r  r   r  rx   r  r  r  )r3   r6  rF   r   rl   onesr3  r.   r.   r/   test_cdf_large_x  s   zTestSkewNorm.test_cdf_large_xc                 C   sr   g dg dg dg dg dg}|D ]#\}}}t j||}t||dd t j| | }t||dd qd S )N)rh  r   gzbLe9)r>  r:   gn'/2;)rZ  r~   g::)r]  r  g|<)r  r>  Oul2;r  rx   )r3   r6  rF   r   rI  )r   cdfvalsrC   r,   cdfvalr'  r.   r.   r/   test_cdf_sf_small_values  s   z%TestSkewNorm.test_cdf_sf_small_valuesz
a, momentsc                 C   s6   t |ddD ]\}}tj||}t||dd qd S )Nr   )startr  rx   )r  r3   r6  r  r   )r   r,   r  orderrc   momr.   r.   r/   test_noncentral_moments  s   z$TestSkewNorm.test_noncentral_momentsc                 C   s  t jd}d\}}}t|||}|jd|d}tjj|ddd\}}}	tjj|ddd\}
}}||  kr<dks?J  J ||
ksEJ tjj|ddd	d
\}}}|dksXJ t|||}|jdd}t |t|f}t	|| tj
jdd|d}tj|}t t |sJ tjj|d	d\}}}t |sJ t |t |}}t	|||t dt j    t	||d ddt j    d S )Nl   #ke )rZ  r  ro   rh   rc  rs  r   r  gmmr   methodmsr  r   rF  r:   )rl   r   r   r3   r6  r   r   r,  r  r   r  r   r  isinfr  r  r>   )r   r   r,   r8   r9   rL   r   a2loc2scale2a3loc3scale3a4loc4scale4dist4r   r\  a5loc5scale5rV  rW  r.   r.   r/   r    s,   

 zTestSkewNorm.test_fitN)r  r  r  r   r7  r   r`  r;  r?  r   r  r  _skewnorm_noncentral_momentsrC  r  r.   r.   r.   r/   r4    s    	
r4  c                   @   r   )
	TestExponc                 C   s   t tjdd d S r1  )r   r3   r	  r<   r   r.   r.   r/   	test_zero  s   zTestExpon.test_zeroc                 C   s0   t tjdd t tjtjdd d S )NgC]r2<rH  )r   r3   r	  rF   rN  rI  r   r.   r.   r/   	test_tail  s   zTestExpon.test_tailc                 C   ,   t dddddt jg}tttjj| d S No_?46@yX5ͻ@j+?UX@)rl   r   r   r  r   r3   r	  r   rO  r.   r.   r/   test_nan_raises_error     zTestExpon.test_nan_raises_errorc                 C   r[  r\  )rl   r   r   r  r   r3   r	  r   rO  r.   r.   r/   test_inf_raises_error  rc  zTestExpon.test_inf_raises_errorN)r  r  r  rY  rZ  rb  rd  r.   r.   r.   r/   rX    s
    rX  c                   @   r6  )TestNormc                 C   r[  r\  )rl   r   r   r  r   r3   r  r   rO  r.   r.   r/   rb    rc  zTestNorm.test_nan_raises_errorc                 C   r[  r\  )rl   r   r   r  r   r3   r  r   rO  r.   r.   r/   rd  
  rc  zTestNorm.test_inf_raises_errorc                 C   s    g d}t ttjj|dd d S )Nr   shrimp)plate)r  r   r3   r  r   rO  r.   r.   r/   test_bad_keyword_arg  s   zTestNorm.test_bad_keyword_argN)r  r  r  rb  rd  rh  r.   r.   r.   r/   re    s    re  c                   @   s    e Zd ZdZdd Zdd ZdS )TestUniformgh-10300c                 C   r[  r\  )rl   r   r   r  r   r3   r!  r   rO  r.   r.   r/   rb    rc  z!TestUniform.test_nan_raises_errorc                 C   r[  r\  )rl   r   r   r  r   r3   r!  r   rO  r.   r.   r/   rd    rc  z!TestUniform.test_inf_raises_errorN)r  r  r  __doc__rb  rd  r.   r.   r.   r/   ri    s    ri  c                
   @   s   e Zd Zdd Zdd Zdd Zdd Zej	d	g d
dd Z
ej	dg dg dg dg dg dgdd Zej	dg dg dg dg dg dg dgdd ZdS )TestExponNormc                 C   s   dd }d\}}}d||  }t jj |||dd}t||||| d\}}}d||  }t jj |||dd}t||||| d\}}}d||  }t jj |||dd}t||||| d	\}}}d||  }t jj |||dd}t||||| d S )
Nc                 S   sh   dd| | d   }d| | d  |d  }dd| | d  d  }|d|   || d| |    ||gS )Nr  r   r:   r   rs        @rZ  r.   )lamsigry  opK2exp_skewexp_kurtr.   r.   r/   get_moms$  s   $z,TestExponNorm.test_moments.<locals>.get_moms)r   r   r   r  r  r  )r4  r:   re   )r   r   r   )r  r)  r  )r3   	exponnormr   )r   rs  ry  ro  rn  Kstsr.   r.   r/   r`  "  s"   



zTestExponNorm.test_momentsc                 C   2   t dddddt jg}tttjj|ddd d S 	Nr]  r^  r_  r`  ra  r   r   r  )rl   r   r   r  r   r3   rt  r   rO  r.   r.   r/   rb  =     z#TestExponNorm.test_nan_raises_errorc                 C   rw  rx  )rl   r   r   r  r   r3   rt  r   rO  r.   r.   r/   rd  B  ry  z#TestExponNorm.test_inf_raises_errorc                 C   sT   t tjddd t tjddd t tjddd t tjddd d S )Ni|r   rt     rq   )r   r3   rt  r<   r   r.   r.   r/   test_extremes_xG  s   zTestExponNorm.test_extremes_xzx, K, expected))r  rq   g6
N-)r   rq   g՜n+H?)r  rq   gi?)r=  rq   gbJI-)rg   r   gI8?)rg   r1  gQ3|-0?c                 C   s   t tj|||dd d S )Ngdy=rx   )r   r3   rt  r<   )r   rC   ru  rc   r.   r.   r/   test_std_pdfY  s   zTestExponNorm.test_std_pdfzx, K, scale, expected)r   rq   r   gVAҤ?)r  {Gzt?r   g'^>)r  rq   rh   rt   )r  rq   r   gbr ;)r~   r  r   gVMe?c                 C   <   t jj|||d}|dkr|dksJ d S t||dd d S )Nr  rt   r   rx   )r3   rt  rF   r   r   rC   ru  r9   rc   r'  r.   r.   r/   test_cdf_small_Ko  s   zTestExponNorm.test_cdf_small_K)rg   rq   r   ghG}$;)r:   r}  r   g]fJ?)r~   r}  ro   g31"g#;)rg   r}  ro   gf
+-)r  r}  ro   rt   )r4  r  r   ga9S?c                 C   r~  )Nr  rt   g-a=rx   )r3   rt  rI  r   r  r.   r.   r/   test_sf_small_K  s   zTestExponNorm.test_sf_small_KN)r  r  r  r`  rb  rd  r{  r   r  r  r|  r  r  r.   r.   r.   r/   rl  !  s8    

rl  c                   @   r6  )TestGenExponc                 C   s@   ddl m} tjtdddddd}t||dddd d S )	Nr   )simpsrg   rq   ro   rs   )dxr   )scipy.integrater  r3   genexponr<   r=   r   r   )r   r  r'  r.   r.   r/   test_pdf_unity_area  s   z TestGenExpon.test_pdf_unity_areac                 C   s:   t jtdddddd}ttd|k|dk@  d S )Nr   rg   rq   ro   rs   r   )r3   r  rF   r=   r   r   r   )r   rF   r.   r.   r/   test_cdf_bounds  s   zTestGenExpon.test_cdf_boundsc                 C   s$   t jdddd}t|ddd d S )Nr   r   r:   ra  gM <r   rx   )r3   r  rI  r   rK  r.   r.   r/   test_sf_tail  s   zTestGenExpon.test_sf_tailN)r  r  r  r  r  r  r.   r.   r.   r/   r    s    r  c                   @   r/  )TestExponpowc                 C   s6   t tjddd t tjtjdddd d S )N绽|=rs   r  r~   r  )r   r3   exponpowrF   rN  rI  r   r.   r.   r/   rZ    s   zTestExponpow.test_tailN)r  r  r  rZ  r.   r.   r.   r/   r        r  c                   @   s(   e Zd Zdd Zejddd ZdS )TestSkellamc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )Nr  r   rg   r~   )gYjP'?g$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$S?gYjP'?gX_?g+rx?gfSr?gJXx~?r
  )r=   r   r   r   r3   skellamr  )r   r@   mu1mu2skpmfRr.   r.   r/   r    s   zTestSkellam.test_pmfignore::RuntimeWarningc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )Nr  r   r  )gƃQ?gS`X'?gVy)>?g:	 S?gei.f?gȼJ]x?g)?g{^'+i?gLIg>?gnZ?g?rvͪ?gA?g0?g#J?gqSm
.?g~B?gd?gFBD?gQ9?gmF^?gcMy?gGJq?gC^c?g.){?gñݸ?r~   r
  )r=   r   r   r   r3   r  rF   )r   r@   r  r  skcdfRr.   r.   r/   r    s   zTestSkellam.test_cdfN)r  r  r  r  r   r  r  r  r.   r.   r.   r/   r    s    
r  c                   @   r,  )TestLognormc                 C   sZ   t   t dt tjg dd}t|g d W d    d S 1 s&w   Y  d S )Nr$  r   ro   r   r   )rt   g~r?g e3E?)r(  r)  r*  r+  r3   r   r<   r   r   r<   r.   r.   r/   r    s
   
"zTestLognorm.test_pdfc                 C   sn   d\}}}t tjj|| |dtjt|| |  t tjj|| |dtjt|| |  d S )N)g(\5i@   gOn?rW   )r   r3   r   rI  r  rl   r:  r  )r   r  ry  sigmar.   r.   r/   r    s   
zTestLognorm.test_logcdfN)r  r  r  r  r  r.   r.   r.   r/   r    s    r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zejj	e
d	d
dd Zejj	e
d	d
dd Zejj	e
d	d
dd Zdd Zejjedd
dd Zejdejjejjgejdddgdd ZdS )TestBetac                 C   s:   t jddd}t|d t jddd}t|tj d S )Nr   r   ro   g;B.)r3   r  r   r   rl   r   r   r   r.   r.   r/   rq    s   
zTestBeta.test_logpdfc                 C   sV   d\}}t g d}t||}t|| d t||t || d S )Ni  i  ro  ro   r  gƒ)	rl   r   r3   r  r   r   r  r<   r   r   r   r  rC   r-   r.   r.   r/   test_logpdf_ticket_1866   s
    z TestBeta.test_logpdf_ticket_1866c                 C   s$   g d}t ttjj|dddd d S )Nre   ro   r  r   r   rf  )r   r   rg  )r  r   r3   r  r   rO  r.   r.   r/   test_fit_bad_keyword_args  s   
z"TestBeta.test_fit_bad_keyword_argsc                 C   s"   g d}t ttjj|ddd d S )Nr  ro   )fafix_a)r  r   r3   r  r   rO  r.   r.   r/   #test_fit_duplicated_fixed_parameter  s   z,TestBeta.test_fit_duplicated_fixed_parameterzOverflow, see gh-14901reasonc                 C   s$   d\}}}t tj|||d d S )N)g?g     R@g   0xAgx)>)r   r3   r  rA  )r   r'  r,   r-   r.   r.   r/   test_issue_12635  s   
	zTestBeta.test_issue_12635c                 C   sh   t g d}t g d}d}tj||d d| }t|| tj||d d| }t|| d S )N)g@3@?g^?gNC?)rg   rh   r   r  r   r  )rl   r   r3   r  rN  r   rI  )r   inv_R
count_listr'  invr   r.   r.   r/   test_issue_12794  s   
zTestBeta.test_issue_12794c           	      C   sb   d}t dd}d}d| |d || }}}tj|||}tj|||}t|d|  d S )Nh㈵>r   r  r  )rl   r   r3   r  rA  rF   r   )	r   alpha_2count_nobsrC  r,   r-   r  r   r.   r.   r/   test_issue_127960  s   zTestBeta.test_issue_12796c                 C   sD   d\}}t tjd||tj d\}}t tjd||tj d S )Nr  r   )ro  r   r   )r   r3   r  r<   rl   r   )r   r,   r-   r.   r.   r/   r4  <  s   zTestBeta.test_endpointszDoes not convert boost warningc                 C   sJ   d\}}}t t tj||| W d    d S 1 sw   Y  d S )N)gףp=
?g   vH7Bg  @0B)r   warnsr+  r3   r  rA  )r   rC  r,   r-   r.   r.   r/   test_boost_eval_issue_14606G  s   
"z$TestBeta.test_boost_eval_issue_14606rF  a, b)+ph        )@)r  r  c                 C   s,   d}z	|||| W d S  t y   Y d S w )Nrm  )OverflowError)r   rF  r,   r-   r'  r.   r.   r/    test_beta_ppf_with_subnormal_a_bM  s   z)TestBeta.test_beta_ppf_with_subnormal_a_bN)r  r  r  rq  r  r  r  r   r  skipifMACOS_INTELr  r  r  r4  xfailr   r  r  r3   r  rA  rN  r  r.   r.   r.   r/   r    s"    



r  c                   @   r,  )TestBetaPrimec                 C   sZ   d\}}t g d}t||}tt ||  t|	|t 
|| d S )Nr  r  )rl   r   r3   r   r   r  r   r   r   r<   r   r  r.   r.   r/   rq  g  s
    zTestBetaPrime.test_logpdfc                    s   t jddd}t|d d\ tg d}t j| }tt|  t j	j
 fdd|D }t||dd	d
 d S )Nr   ro  r  rt   r  r  c                    s   g | ]
}t j| qS r.   )r3   r   )rK   r   r   r  gen_cdfr.   r/   rM   {      z*TestBetaPrime.test_cdf.<locals>.<listcomp>g-=r  )r3   r   rF   r   rl   r   r   r  r   rP   _cdf_singler   )r   rC   r=  cdfs_gr.   r  r/   r  n  s   
zTestBetaPrime.test_cdfN)r  r  r  rq  r  r.   r.   r.   r/   r  f      r  c                   @   r   )
	TestGammac                 C   s<   t jjdddd}t|d t jjdddd}t|d d S )	NZ   i  ro  r  g
CTb?r   rg   gBΖ?)r3   r  r<   r   r  r.   r.   r/   r    s   
zTestGamma.test_pdfc                 C      t jdd}t|d d S r1  )r3   r  r   r   r  r.   r.   r/   rq    s   zTestGamma.test_logpdfc                 C   s"   g d}t ttjj|ddd d S )Nr  r   rf  )r   rg  )r  r   r3   r  r   rO  r.   r.   r/   r    s   z#TestGamma.test_fit_bad_keyword_argsc                 C   s@   t jtjdddddsJ t jtjdddd	dsJ d S )
Nr_  r   gplC@r  r   gJz5rh   g1}t@r   )rl   iscloser3   r  rN  r   r.   r.   r/   rP    s   
zTestGamma.test_isfN)r  r  r  r  rq  r  rP  r.   r.   r.   r/   r    s
    r  c                   @   r,  )TestChi2c                 C   s4   t tjddddd t tjddddd d S )Nr   gޞw1D?   r
  rh   g6:֜?r   r3   chi2r<   r   r.   r.   r/   rz    s   
zTestChi2.test_precisionc                 C   s|   d}t jd|}t|ddd t jd|}t|ddd d}t jd	|}t|d
dd t jd|}t|ddd d S )NrY  gλm:=6g'bd5 <r  rx   ro   gQ8@   gܐ؆0guu[9=re   g8-*@)r3   r  rA  r   )r   rR  rC   r.   r.   r/   r    s   zTestChi2.test_ppfN)r  r  r  rz  r  r.   r.   r.   r/   r    s    r  c                   @   s>   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	dS )TestGumbelLc                 C   r  Nr  r>  )rl   r  r3   r  rF   rA  r   r  r.   r.   r/   rE    r  zTestGumbelL.test_cdf_ppfc                 C   sH   t dd}tj|}tj|}t |}t| }t	|| d S r  )
rl   r  r3   r  r[  r  r   r   expm1r   )r   rC   r  r  urW  r.   r.   r/   r    s   
zTestGumbelL.test_logcdf_logsfc                 C   r  )Nr=  r~   )rl   r  r3   r  rI  rN  r   r  r.   r.   r/   r    r  zTestGumbelL.test_sf_isfr8   r  r   c                 C   s2   t jjd|d}t jj||d\}}t|| d S )Nrh   )r   r8   r  )r3   r  r   r   r   )r   r8   r   
fitted_locrj  r.   r.   r/   test_fit_fixed_param  s   z TestGumbelL.test_fit_fixed_paramN)
r  r  r  rE  r  r  r   r  r  r  r.   r.   r.   r/   r    s    r  c                   @   r,  )TestGumbelRc                 C      t tjdddd d S )Nr   g?~T}%m;r  rx   )r   r3   r  rI  r   r.   r.   r/   rL       
zTestGumbelR.test_sfc                 C   r  )Nr_  r  r  rx   )r   r3   r  rN  r   r.   r.   r/   rP    r  zTestGumbelR.test_isfN)r  r  r  rL  rP  r.   r.   r.   r/   r    s    	r  c                   @   s  e Zd Zejdd Zejdd Zejdd Zej	de
dej
d	ejjd
gej	dddgej	dg dej	dddgdd Zejjej	dddgdd Zdd Zejjddej	ddd gej	d!ddgd"d# Zd$d% Zd&d' Zd(d) Zej	d*e
g d+g d,g d-ej
g d.g d/g d0ejjd
ej
g d1ed2d3d4ed5dd6ejjd
gd7d8 Zej	d*e
g d+g d,g d-ej
g d.g d/g d0ejjd
ej
g d1ed2d3d4ed5dd6ejjd
gd9d: Zej	d;d<dgej	d=d>d?gd@dA Zej	dBdCdDgdEdDggdFdG Zej	dHdId<ejejejfgdJdKggdLdM Zej	dNg dOej	dPejj dQedRd<dSdTfejj!dQedRd<dSdTfejj dUed<dVdSdQfejj!dUed<dVdSdTfgdWdX Z"dYS )ZTestLevyStablec                 C   ,   t ttjd }t jjj|jd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,pctnames	rl   loadr   __file__parentcorerecords
fromarraysTr   r   r.   r.   r/   nolan_pdf_sample_data  s   z$TestLevyStable.nolan_pdf_sample_datac                 C   r  )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  r.   r.   r/   nolan_cdf_sample_data  s   %z$TestLevyStable.nolan_cdf_sample_datac                 C   s   t ttjd }|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)rl   r  r   r  r  r  r.   r.   r/   nolan_loc_scale_sample_dataC  s   	z*TestLevyStable.nolan_loc_scale_sample_datasample_sizer   rb  )marksparameterizationS0S1z
alpha,beta))r  r   )r  ru  )ra  r   )rU  ro   zgamma,deltar   r   r  c           
      C   sF   |t j_t j||||d}t |j|dd|j\}}	|	dks!J d S )N)r   r  r9   r8   r   rc  rd  )r3   levy_stabler  rg  r   rF   )
r   r  r   r  r  r  r  lsrj  r'  r.   r.   r/   r   R  s   zTestLevyStable.test_rvsr  ro   r   c                 C   sZ   t jd d}d}d}tjj||||dd}tj|d||||fd\}}|d	ks+J d
S )z3Additional test cases for rvs for alpha equal to 1.h:r  ro   ra  i  r8   r9   r   r  rv  rq   N)rl   r   r   r3   r  r   rg  )r   r  r   r8   r9   rC   statr'  r.   r.   r/   test_rvs_alpha1n  s   

zTestLevyStable.test_rvs_alpha1c                 C   s   g d}t j|\}}}}t|dddd t|dd t|dd	 t|d
d |g d }t j|\}}}	}
t|d t|d t|
dd	 t|	dd	 d S )N)wgr  rt   rt   rt   rt   羼 u?r  r  r  r  67',?r  r  r  r  tA}˜.?r  r  r  r  Gz?r   rq   r  )\(̿r:   gۧ1?rG  g9]c?)r  r  r  r  r  r  gv?r  )r3   r  r  r   r   r   r   rC   alpha1beta1loc1scale1r  alpha2beta2rK  rL  r.   r.   r/   r  |  s   

zTestLevyStable.test_fitzUnknown problem with fitstart.r  zalpha,beta,delta,gamma)ra  r  r:   r   )r  r  r:   r   parametrizationc                 C   sZ   |t j_t jj||||ddd}t j|}|\}}	}
}t||||g||	|
|gdd dS )z7Test that fit agrees with rvs for each parametrization.r1  r   r8   r9   r   r   rq   rx   N)r3   r  r   r   r  r   )r   r   r  r  r  r   r   r   	alpha_obsbeta_obs	delta_obs	gamma_obsr.   r.   r/   test_fit_rvs  s   


zTestLevyStable.test_fit_rvsc           
      C   s~   t g d}tj|\}}}}tj| \}}}}	t|d |dks'J t|| t||  t||  t|	| d S )Nr   r   r   r   rg   rg   rg   r   r   rh   rh   r   r   )rl   r   r3   r  r  r   r   )
r   rC   r  r  r  r  r  r  rK  rL  r.   r.   r/   test_fit_beta_flip  s   

z!TestLevyStable.test_fit_beta_flipc                 C   sr   d}t g d}tj| \}}}}tj| | \}}}	}
t|| t|| t|	||  t|
| d S )Nr   r  )rl   r   r3   r  r  r   )r   SHIFTrC   r  r  r  r  r  r  rK  rL  r.   r.   r/   test_fit_delta_shift  s   

z#TestLevyStable.test_fit_delta_shiftc                 C   s   g d}t j|\}}}}|dk sJ d| |t|k s+J dt| d| g d}t j|\}}}	}
|dksDJ d| |	t|ksVJ dt| d|	 d S )	N)r   r   r   r   rg   rg   rg   r   r      r  r   zExpected alpha < 1, got zExpected loc < z, got )r   r   r   r   rg   rg   rg   r   r      r  zExpected alpha > 1, got zExpected loc > )r3   r  r  r+  r  r  r.   r.   r/   test_fit_loc_extrap  s   $(z"TestLevyStable.test_fit_loc_extrapz pct_range,alpha_range,beta_range)rq   ro   r  )re   r   r:   )r  r   r  )rq   rd  ro   rh  r  )re   ro   r   ra  r:   )gru  r   r  r  r   )rq   rd  re   r  ffffff?ro   ?r  rm  rh  r  re   r:   r  r     c                    s  |}t  }|jdko|jdkd|j|j|jg}dd fddgdd	 fd
dgdd	 fddgdd fddgdd fddgdd fddgg}t|D ]\}	\}
}}|
tj_	|durs||| n|}t
 v}|td tjj|d |d |d ddd}tjdd( t|g d|t||d  t||d  t|d  g}W d   n1 sw   Y  ||d |kt|B  }t||d |d |	|
||jj|f d!d" W d   n1 sw   Y  q^dS )#z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnirP  c              	      s  t | d t | d  @ t | d @ | d dk| d dk@ | d dk| d dk@ | d dk@ B | d dkt | d d	d
g@ B | d dkt | d ddg@ B | d dkt | d ddg@ B | d dkt | d ddg@ t t | d g d@ B | d dkt | d dg@ t t | d dg@ B | d dkt | d ddg@ t t | d g d@ B | d dk| d dk@ | d dk@ B | d dk| d dk@ | d dk@ B | d dk| d dk@ | d dk@ B | d dkt | d dg@ t t | d g d@ B | d dkt | d ddg@ t t | d g d@ B | d dkt | d d	d
g@ t t | d ddg@ B | d dkB  @ S )Npctr   r  r   ro   rm  皙?r  rq   r  r  rd  rh  ro  re   r  r  )ro   r  ffffff?r  r  )gٿ333333ӿr  r  ro   r  r  re   ro  r  r  )r  rm  r  rT  r  )rl   isinr   r
  alpha_range
beta_range	pct_ranger.   r/   rX     s   











 
%


*


/


4
9
>
Cz7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>	piecewiser  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr  r   r  ro  r  rl   r  r  r  r.   r/   rX   F     

c                    s:   | d dk @ t | d @ d v @ t | d @ S )Nr   r  r  r  r!  r  r  r  is_linux_32r  r.   r/   rX   Q  s   
g|=c                    s<   t | d t | d  @ t | d @ | d dk@ S )Nr  r   r  ro  r!  r  r  r.   r/   rX   [     
fft-simpsonr  c                    s<   | d dkt | d @ t | d  @ t | d @ S )Nr   rU  r  r  r!  r  r  r.   r/   rX   d  s   
r  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk @ S )Nr  r   r  r   rU  r!  r  r  r.   r/   rX   l  r"  Nz2Density calculations experimental for FFT method.*rC   r   r  r   r   r9   r8   r  overcalcabserrrelerrr'  r-  z8pdf test %s failed with method '%s' [platform: %s]
%s
%sFerr_msgverbose)platformunamesystemmachinejoin	processorr  r3   r  pdf_default_methodr   recordr+  r<   rl   r  r   r   isnanr   r   r  )r   r  r  r  r  r   r2  platform_desctestsixdefault_methodry   filter_funcsubdatasupr'  subdata2failuresr.   r#  r/   test_pdf_nolan_samples  s   
O
	 

z%TestLevyStable.test_pdf_nolan_samplesc                    s  |}dd fddgdd fddgdd fd	dgdd
 fddgdd fddgdd fddgg}t |D ]\}\}}	}
|tj_|
durY||
| n|}t u}|td tjj|d |d |d ddd}tj	dd( t
|g d|t||d  t||d  t|d  g}W d   n1 sw   Y  ||d |	kt|B  }t||d |	d|||jj|f dd W d   n1 sw   Y  qDdS ) z4 Test cdf values against Nolan's stablec.exe output.r   rS  c                    s   t | d t | d  @ t | d @ | d dkt | d g d@ | d dk@ | d dkt | d g d@ | d dk@ B  @ S 	Nr  r   r  r  )r  rS  rT  rq   re   ro  r  r  r!  r  r  r.   r/   rX     s$   



z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>rd  c                    s   t | d t | d  @ t | d @ | d dkt | d g d@ | d dk@ @ | d dkt | d g d@ | d dk@ B S rD  r!  r  r  r.   r/   rX     s"   


	
r&  r  c                    s<   t | d t | d  @ t | d @ | d dk@ S )Nr  r   r  333333?r!  r  r  r.   r/   rX     r%  r  c                    H   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr  r   r  ra  rF  r!  r  r  r.   r/   rX     r"  r  c                    rG  )Nr  r   r  ?ra  r!  r  r  r.   r/   rX     r"  rq   c                    rG  )Nr  r   r  r  rH  r!  r  r  r.   r/   rX     r"  Nz[Cumulative density calculations experimental for FFT method. Use piecewise method instead.*rC   r   r  r   r   r'  r  r(  r*  r'  r-  z)cdf test %s failed with method '%s'
%s
%sFr.  )r  r3   r  cdf_default_methodr   r8  r+  rF   rl   r  r   r   r9  r   r   r  )r   r  r  r  r  r   r;  r<  r=  ry   r>  r?  r@  r'  rA  rB  r.   r  r/   test_cdf_nolan_samples  sz   	

N

z%TestLevyStable.test_cdf_nolan_samplesr   r   r^  r<   rF   c                 C   s   |}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
d}t||| d dS )zGTests for pdf and cdf where loc, scale are different from 0, 1
        r   r   S)r<   rF   r<   rC   r   r  r:   r   r'  r  N)r3   r  rI  r7  r  r<   rF   r   )r   r  r   r^  r   r?  r  rr  r.   r.   r/   test_location_scale6  s   z"TestLevyStable.test_location_scalezmethod,decimal_placesr  rG  r   c              	   C   s   t g d}t g d}t g d}t jddA t %}|jtdd |tj_tjj	|d|dd	d
}t
|||| W d   n1 sGw   Y  W d   dS W d   dS 1 s_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   r:   r:   r:   r:   r   r   r   r   rG  rG  rG  rG  )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   r  ro   r   r   r  ro   r   r   r  ro   r   r   r  ro   r   r   r  ro   r   r  r   zDensity calculation unstable.*)categorymessager   r   r'  N)rl   r   r  r   r]   r+  r3   r  r7  r<   r   )r   rF  decimal_placesxsdensitybetasr@  r<   r.   r.   r/   'test_pdf_alpha_equals_one_beta_non_zeroP  s(   Pz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerozparams,expected)r  r  r   r   )r:   rm  rg   ra  )rg   r  r   r   c                 C   s4   t jj |d |d |d |d dd}t|| d S )Nr   r   r:   r   r  r  )r3   r  r   )r   paramsrc   observedr.   r.   r/   r  w  s
   zTestLevyStable.test_statsr   )r  ro   r  zfunction,beta,points,expectedr  irg   rt   r!  r  c                 C   s@   d|  k rdk sJ  J t ||||dt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   rl   r  r   )r   r   r  r  r  rc   r.   r.   r/   !test_distribution_outside_support  s
   (z0TestLevyStable.test_distribution_outside_supportN)#r  r  r  r   r  r  r  r  r  r  r   r  r   r  r  r  r  r  r
  r  rl   r  xslowrC  rJ  rL  rT  r   NaNr  r3   r  rF   r<   rW  r.   r.   r.   r/   r    s    
!
+

 B
{
 
r  c                   @   r,  )TestArrayArgumentc                 C   r   r   r   r   r.   r.   r/   r     r   zTestArrayArgument.setup_methodc                 C   s.   t jjtdtddd}t|jd d S )Nr~   r  r  )r3   r  r   rl   r   r:  r   r   r   r   r.   r.   r/   test_noexception  s   z"TestArrayArgument.test_noexceptionN)r  r  r  r   r\  r.   r.   r.   r/   rZ        rZ  c                   @   r,  )TestDocstringc                 C   sH   t jjd urtdt jj v  t jjd ur"tdt jj v  d S d S )Nr   r8  )r3   r   rk  r   lowerr8  r   r.   r.   r/   test_docstrings  s
   zTestDocstring.test_docstringsc                 C   s   t   t   d S rj   )r3   rP   rO   r   r.   r.   r/   test_no_name_arg  s   zTestDocstring.test_no_name_argN)r  r  r  r`  ra  r.   r.   r.   r/   r^    r  r^  c                  C   s   t g d} t| dk| d\}}t|g d t|g d tddk| d\}}t|| d  t|dg t| dk| d\}}t||  t|dgt|   d S )N)r   r   r:   r   r:   r   r   r   r:   )r   r:   r:   r   r   )r:   r:   r:   r:   r:   r   )r   r   r   r=   r   r,   r-   rB  r.   r.   r/   TestArgsreduce  s   
rc  c                   @   s   e Zd Zg dZdd Zg dZejde	dd Z
dd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zejjejdddgdd Zejdddgdd ZdS )TestFitMethod)ncfrp  rq  c                 C   r   r   r   r   r.   r.   r/   r     r   zTestFitMethod.setup_method)r	  r  r!  z	dist,argsc                 C   sz   || j v rtd|  tdddddtjg}tdddddtjg}tt|}t	t
|j|dd t	t
|j|dd d	S )
rj  z"%s fit known to fail or deprecatedr]  r^  r_  r`  ra  r   r  N)fitSkipNonFiniter   skiprl   r   r   r   r   r3   r  r   r   )r   rL   r   rC   r  distfuncr.   r.   r/   !test_fit_w_non_finite_data_values  s   

z/TestFitMethod.test_fit_w_non_finite_data_valuesc              	   C   s   t jd t jdd8 tjjddddd}t t |t d d	 	 }t
t tjj|d
dd|d
dgdd W d    d S 1 sGw   Y  d S )Ni90  r  rM  r  rt         4@r  r   r:   r   r  r  r   )rl   r   r   r  r3   r   r   r  r:  r,  r   r   r   )r   rC   expected_shaper.   r.   r/   test_fix_fit_2args_lognorm  s   "
"z(TestFitMethod.test_fix_fit_2args_lognormc                 C   s   t dd}tj|\}}t|d t|t d tjj|dd\}}t|d t|t d tjj|dd\}}t|d t|d d S )Nr   r  r   r:   r  r  )rl   r   r3   r  r   r   r  r   r   rC   r8   r9   r.   r.   r/   test_fix_fit_norm  s   


zTestFitMethod.test_fix_fit_normc                 C   sn  t dd}t | }d}tjj||d\}}}t | | }tt |t	| |dd t
|| t|| | dd d}d}tjj|||d\}}}t
|| t
|| t|| | dd d	}d}tjj|||d\}}}t
|| t
|| t|| | dd d}d	}	tjj|||	d
\}}}t
|| t
||	 |t |	 }
tt	||
 d S )Nr   r  r   r  r~   r
  r  r   r   r:   r  )rl   r   r:  r,  r3   r  r   r   r   digammar   )r   rC   meanlogr   r,   r8   r9   rB   r   r   rB  r.   r.   r/   test_fix_fit_gamma  s6   






z TestFitMethod.test_fix_fit_gammac              	   C   s  dd }t g d}tjj|ddd\}}}}t|d t|d t||||ddgdd t g d}tjj|d	ddd
\}}}}t|d	 t|d t|d ||||\}}t|ddd d| }	tjj|	d	ddd\}
}}}t|d	 t|d t|d ||
||	\}}t|ddd t|
| tt	tjj|ddd t g 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d d S )Nc                 S   sj   t |}t| }td|  }t| | }||| t|    ||| t|   g}|S r   )r   rl   r:  r  r   psi)r,   r-   rC   r&  s1r  psiabr   r.   r.   r/   mlefunc1  s   z0TestFitMethod.test_fix_fit_beta.<locals>.mlefunc)r  r  ro   r   r   r  r  r   r:   )r   r   r   r  )r   r   r   ro   r  )r   r   r   )r   r   r   r   )r   r   r   r   )
rl   r   r3   r  r   r   r   r   r  r   )r   rv  rC   r,   r-   r8   r9   dadbr  rJ  b2rK  rL  r  r.   r.   r/   test_fix_fit_beta.  s:   









zTestFitMethod.test_fix_fit_betac                 C   s   t g d}tj|\}}t|d t|d tjj|dd\}}t|d t|d tjj|dd\}}t|d t|d d S )N)r:   r:   rG  rG  rG  rG  rG  r  r:   r   r  r   r  rG  )rl   r   r3   r	  r   r   rm  r.   r.   r/   test_expon_fite  s   




zTestFitMethod.test_expon_fitc                 C   s   t g d}t |d }tjj|dd\}}}t|| dd t|d t|t 	|
 dd tjj|ddd\}}}t|t |t d d 
 dd t|d t|d tjj|dd	d
\}}}t|d	 t|d t|t 	|
 dd d S )N)ra  r   rg   r      ;   r   r  rS  rx   r  r  r:   r  )r   fix_s)rl   r   r:  r3   r   r   r   r-  r   r   r,  r  )r   rC   lnxm1r   r8   r9   r.   r.   r/   test_lognorm_fitt  s    




zTestFitMethod.test_lognorm_fitc                 C   s   t g d}tj|\}}t||  t||  tjj|dd\}}t|d t||  tjj|dd\}}t|d t|d t	t
tjj|dd t	t
tjj|dd d S )N)r  r  r        "@r   r  rg   r  rs   r  )rl   r   r3   r!  r   r   r+  r  r  r  r   rm  r.   r.   r/   test_uniform_fit  s   


zTestFitMethod.test_uniform_fitrF  MLEMMc              
   C   sl  d\}}t jj||ddd}t jj|d|d}t jj|d|d}t||ddd	 t jj|d|d
}t||ddd	 t jj|d|d}t jj|d|d}t||ddd	 t jj|d|d}t||ddd	 ttt jj|dd|d ttt jj|dddd|d t jj|ddd|d}	|	\}
}}}t|
||gg d d}t jj|dd}t jj|||d\}
}}t|
| d S )N)r  r  rh   r   rc  r  )r   rF  )r  rF  rS  r  )r  rF  r  )r   rF  )r  rF  )r  rF  r   r:   )r  r   rF  r   r   )r  r   r   r   rF  )r  r   r   rF  )r  r   r   r   )	r3   r  r   r   r   r  r   r   r  )r   rF  r,   r-   rC   res_1res_2res_3res_4res_5aabbr  ssr   r.   r.   r/   test_fshapes  s.   zTestFitMethod.test_fshapesc                 C   s@   t j}|jddd}tdd}tt|j|fi |d|i d S )Nr:   rh   )ru  r   i)enikibenikirF  )r3   rt  r   r   r  r   r   )r   rF  rL   r   r   r.   r.   r/   test_extra_params  s   
"zTestFitMethod.test_extra_paramsN)r  r  r  rg  r   rf  r   r  r  r   ri  rl  rn  rr  rz  r{  r  r  r  r  r  r.   r.   r.   r/   rd    s$    

	&7&rd  c                   @   r  )
TestFrozenc                 C   r   r   r   r   r.   r.   r/   r     r   zTestFrozen.setup_methodc                 C   s  t j}t jddd}|d}|jdddd}t|| |d}|jdddd}t|| |d}|jdddd}t|| |d}|jdddd}t|| |d}|jdddd}t|| | }|jddd}t|| |	 }|j	ddd}t|| |
 }|j
ddd}t|| | }|jddd}t|| | }|jddd}t|| |d}|jdddd}t|| t|j|j t|j|j d S )Nr  r  r7   rj  r  r:   )r3   r  r<   r   rF   rA  rN  rI  r  r,  r  r-  rR   r  r,   r-   )r   rL   frozenresult_fr  r.   r.   r/   r     sJ   
















zTestFrozen.test_normc                 C   s  d}t j}t |}|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 )Nrs   rj  r  r  r:   )r3   r  r<   r   rF   rA  rN  rI  r  r,  r  r-  rR   r  r,   rL   r-   )r   r,   rL   r  r  r  r.   r.   r/   
test_gamma  sL   






















zTestFrozen.test_gammac                 C   s8   t d}|d}|j dd |d}t|| d S )Nr   r:   r  r  )r3   r   r  r   )r   r  m1r  r.   r.   r/   test_regression_ticket_1293;  s
   


z&TestFrozen.test_regression_ticket_1293c                 C   sR  d}t j|d}|j|\}}t||gddg d}t jjd|d t|j|dtjg d}t j|d}|j|\}}t||gddg d}t jd| t|jj|jj	ft j| t jdd}t
|j|ju dD ]6}t|}t j|d}|j|j	}}t|d t
t| td}t j|\}}t||gdd	g qpd S )
NrT  r  rt   r  re   r   r  r  ro   )r3   r  rL   r  r   r<   rl   r   r,   r-   r   r  r  r   )r   rB  r  r,   r-   rv1r.   r.   r/   r  J  s4   



zTestFrozen.test_abc                 C   s   t ttjd d S )N	rv_frozen)r   r+   r3   r4   r   r.   r.   r/   test_rv_frozen_in_namespacev  s   z&TestFrozen.test_rv_frozen_in_namespacec                 C   sV   t  }tt|d d|_t|j tj	d  tj	d}|j
d|d d S )Nr   *   r   r  rc  )r3   r  r   r+   r   r   	get_staterl   r   RandomStater   )r   r  rndmr.   r.   r/   test_random_statez  s   
zTestFrozen.test_random_statec           
      C   s   t dd}t d}t jg dg dfd}|||fD ]H}d|_|jdd	 t|}|jdd	}t|}|jdd	}t	|| |
d
|
d
g}	t	|	d |	d  t	||	d ||	d  qd S )Ngdsz@g@e?r  )r   r   r:   r   r  r  r   r  r   ro   r   r   )r3   r  re  rO   r   r   pickledumpsloadsr   rA  rF   )
r   r  poissr  distfnrB   r0	unpickledr1mediansr.   r.   r/   test_pickling  s&   




zTestFrozen.test_picklingc              
   C   s   dd }t jdddd}tjddd |j|d	dd
d}t jj|dddd	dd
d}W d    n1 s4w   Y  t|| t jddd}||}t jj|ddd}t|| d S )Nc                 S      | S rj   r.   r   r.   r.   r/   r        z$TestFrozen.test_expect.<locals>.funcr:   r   rG  )r,   r8   r9   r  )r	  divider   T)r   ubconditionalr:   r   r8   r9   r   r  r  r8   )r   r   r8   )r3   r  rl   r  r   r   re  )r   r   gmgm_val	gamma_valr'  p_valpoisson_valr.   r.   r/   test_expect  s   

zTestFrozen.test_expectN)r  r  r  r   r   r  r  r  r  r  r  r  r.   r.   r.   r/   r    s    34,r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	e
jddd Zdd Zdd Zdd Zdd Zdd Zdd ZdS )
TestExpectc                 C   s   t jjdd ddd}t|ddd t jjd	d ddd}t|ddd t jjd
ddd}t jjdddd}t jjdd dd||d}t|ddd t jjdd dd||dd}t|ddd d S )Nc                 S      | d | d  S )Nr~   r.   r   r.   r.   r/   rX     rY   z&TestExpect.test_norm.<locals>.<lambda>r~   r:   r7   rG  r  r
  c                 S   r  rj   r.   r   r.   r.   r/   rX     r   rd  rh  c                 S   r   r   r.   r   r.   r.   r/   rX     r   r8   r9   r   r  rm  c                 S   r   r   r.   r   r.   r.   r/   rX     r   Tr8   r9   r   r  r  r  )r3   r  r   r   rA  )r   rW  rV  r   r  prob90prob90cr.   r.   r/   r     s   zTestExpect.test_normc              	   C   s   t jjdd dddd}t|ddd	 t jjd
d dddd}t|ddd	 t jjdddddd}t jjdddddd}t jjdd ddd||dd}t|ddd	 t jjdd ddd||dd}t|ddd	 d S )Nc                 S   r  )NUUUUUU@r.   r   r.   r.   r/   rX     rY   z&TestExpect.test_beta.<locals>.<lambda>r  r~   r:   )r   r8   r9   qq?r  r
  c                 S   r  rj   r.   r   r.   r.   r/   rX     r   r  rs   r  rh  rg   r7   rd  c                 S   r   )Nr  r.   r   r.   r.   r/   rX     r   )rg   rg   Fr  rm  c                 S   r   r   r.   r   r.   r.   r/   rX     r   Tr  )r3   r  r   r   rA  )r   rW  rV  r  r   r  r  r.   r.   r/   	test_beta  s    zTestExpect.test_betac           
      C   s&  t jj ddddd\}}t jjdd ddd	}t||d
d t jjdd ddd	}t||dd t jjdd dddd
d}t||dd dt jjdd
gddddd  }t jjdd ddddd}t||d
d t jjdd dddddd}t|ddd t jjdd dddd}	t|	dd
d d S )Nr  rg   r  r  r  c                 S   r  rj   r.   r   r.   r.   r/   rX     r   z+TestExpect.test_hypergeom.<locals>.<lambda>)r  rg   r  r  r  r
  c                 S      | d d S Nr  r:   r.   r   r.   r.   r/   rX         r  c                 S   r  r  r.   r   r.   r.   r/   rX     r  r~   )r   r8   r   r  r   c                 S   r   r   r.   r   r.   r.   r/   rX     r   r  r	  c                 S   r   r   r.   r   r.   r.   r/   rX     r   T)r   r8   r   r  r  c                 S   r   r   r.   r   r.   r.   r/   rX     r   r   )r   r   r  )r3   rs  r   r   r  r  )
r   m_truev_truerV  rW  v_bounds	prob_trueprob_boundsprob_bcprob_br.   r.   r/   test_hypergeom  s2   "zTestExpect.test_hypergeomc                 C   sb   t jjdd dddd}dt jdd }t||d	d
 t jjdd dddd}t|dd	d
 d S )Nc                 S   r   r   r.   r   r.   r.   r/   rX     r   z)TestExpect.test_poisson.<locals>.<lambda>r  r   F)r   r   r  r   r:   r  r
  c                 S   r   r   r.   r   r.   r.   r/   rX     r   T)r3   re  r   rF   r   )r   r  prob_b_trueprob_lbr.   r.   r/   test_poisson  s   zTestExpect.test_poissonc                 C   s<   t j}|jdd}|jdd |jdd}t||dd d S )N)ra  rv  )ro   r  r
  )r3   genhalflogisticr   r   )r   halflogres1r  r.   r.   r/   test_genhalflogistic  s
   zTestExpect.test_genhalflogisticc                 C   sv   t ttj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 d S )	Ni  Gz?c                 S   r   r   r.   r   r.   r.   r/   rX     r   z/TestExpect.test_rice_overflow.<locals>.<lambda>)r  rv  c                 S   r   r'  r.   r   r.   r.   r/   rX     r   c                 S   r   Nr   r.   r   r.   r.   r/   rX     r   )r   rl   r  r3   ricer<   r   r   r.   r.   r/   test_rice_overflow  s   "zTestExpect.test_rice_overflowc                 C   sp   d\}}t jjdd |fd}t|||d  td|  dd t jjdd |f|d	}t||| dd d S )
N)r  r   c                 S   r  rj   r.   r@   r.   r.   r/   rX     r   z(TestExpect.test_logser.<locals>.<lambda>rv  r  rw   r   c                 S   r  rj   r.   r  r.   r.   r/   rX   $  r   r  )r3   r  r   r   rl   r:  )r   r'  r8   res_0res_lr.   r.   r/   test_logser  s   zTestExpect.test_logserr  c                 C   sh   d\}}t jjdd ||fd}t jjdd ||fd}t||| dd t||d  || dd d S )	N)r  r  c                 S   r  rj   r.   r   r.   r.   r/   rX   ,  r   z)TestExpect.test_skellam.<locals>.<lambda>rv  c                 S   r&  r'  r.   r   r.   r.   r/   rX   -  r(  rS  r   r:   )r3   r  r   r   )r   r  p2r  r  r.   r.   r/   test_skellam'  s
   zTestExpect.test_skellamc                 C   sL   d\}}t jdd ||f}t|tdd t||D ||  dd d S )N)r   q   c                 S   r  rj   r.   r   r.   r.   r/   rX   5  r   z)TestExpect.test_randint.<locals>.<lambda>c                 s   s    | ]}|V  qd S rj   r.   rK   rj  r.   r.   r/   r%  7  s    z*TestExpect.test_randint.<locals>.<genexpr>rw   r   )r3   r   r   r   r  r  )r   lohir   r.   r.   r/   test_randint1  s
    
zTestExpect.test_randintc                 C   s   t ttjjdd d d S )Nc                 S   r&  r'  r.   r   r.   r.   r/   rX   <  r(  z&TestExpect.test_zipf.<locals>.<lambda>r  )r	   r+  r3   r  r   r   r.   r.   r/   	test_zipf9  s   
zTestExpect.test_zipfc                 C   s@   t jjdd dd}t jjdd ddddd	}t||d
d d S )Nc                 S   r   r   r.   r   r.   r.   r/   rX   @  r   z/TestExpect.test_discrete_kwds.<locals>.<lambda>r  rv  c                 S   r   r   r.   r   r.   r.   r/   rX   A  r   r0      r  )r   maxcount	chunksize	tolerancer  r
  )r3   re  r   r   )r   n0n1r.   r.   r/   test_discrete_kwds>  s
   zTestExpect.test_discrete_kwdsc                 C   s6   dd }dD ]}t jd|}t|||dd qd S )Nc                 S   s0   | d d| d   d| d   d| d   |  S )Nr~   rg   rG  r  r   r   r:   r.   r  r.   r.   r/   poiss_moment5H  s   0z-TestExpect.test_moment.<locals>.poiss_moment5)r~   r"  r~   r  rx   )r3   re  r  r   )r   r  ry  m5r.   r.   r/   test_momentE  s
   zTestExpect.test_momentc                 C   sn   t tjjdddd t tjjdddd t tjjdddd t tjjddd	 t tjjd
dd
 d S )Nr   r  r7   rH  rg   re   )   rv  r  U   r  )r   r3   r  r   r  r  r   r.   r.   r/   test_challenging_cases_gh8928O  s
   z(TestExpect.test_challenging_cases_gh8928c                 C   s   t j}|jddd}t|jddd| t|jddddd| t|jddddd|d	  t|jddddd
d| t|jdddddd t|jdddddd t|jddddd
dd d S )Nrg   r~   r7   rj  r  r  r)  r  r  Tr  r  g433333@g433333r	  )r3   r!  r,  r   r   )r   rL   r\  r.   r.   r/   test_lb_ub_gh15855X  s"   zTestExpect.test_lb_ub_gh15855N)r  r  r  r   r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r.   r.   r.   r/   r    s     "
	

	
	r  c                   @   r  )TestNctc                 C   s@   t dd}t|dd t dd}t|dddd d S )Nr~   r   ro   r  g K?rg   r
  )r3   nctr   rF   r   r$  r.   r.   r/   test_nc_parametero  s   zTestNct.test_nc_parameterc              	   C   sZ   t jdtddd d d f tddd}tg dg dg dg}t||d	d
 d S )Nr~   rG  r"  re   r   )gMp^j?g6].ftv?gȳ'ς?gu?)g!Y<a?g]d1p?go|?g?)gHdY?g2Ԥg?g}o/u?g .mr?r  rx   )r3   r  r<   rl   r   r  r   r   )r   r   rc   r.   r.   r/   test_broadcastingw  s   zTestNct.test_broadcastingc                 C   s   t dd}t| d d S )NrG  r   rs   )r3   r  r   r  r$  r.   r.   r/   test_variance_gh_issue_2401  s   z#TestNct.test_variance_gh_issue_2401c                 C   s   t jj dddd\}}}}t||||gtjtjtjtjg t jj dddd\}}}}tt| t|||gtjtjtjg t jj dddd\}}}}tt|||g  t|tj d S )Nrm  r  r  )rR  ncr  rU  r  )r3   r  r   rl   r   r   r  r   r  r.   r.   r/   test_nct_inf_moments  s   "zTestNct.test_nct_inf_momentsc                 C   s   t jdd}t j dd}ddg}t||d dd t||dd t jdd}t j dd}d	d
g}t||d dd t||dd d S )Nr   r:   g@ @g*dn?r   r  rx   r  gqI  @gL) ?r  )r3   r  r,  r   )r   nct_mean_df_1000nct_stats_df_1000expected_stats_df_1000nct_mean	nct_statsr?  r.   r.   r/   test_nct_stats_large_df_values  s   
z&TestNct.test_nct_stats_large_df_valuesN)r  r  r  r  r  r  r  r  r.   r.   r.   r/   r  n  s    r  c                   @   r   )
TestRecipInvGaussc                 C   s   t jdd}|dksJ d S )Nr   r  rt   )r3   recipinvgaussr<   r3  r.   r.   r/   test_pdf_endpoint  s   z#TestRecipInvGauss.test_pdf_endpointc                 C   s"   t jdd}|tj ksJ d S )Nr   r  )r3   r  r   rl   r   r  r.   r.   r/   test_logpdf_endpoint  rM  z&TestRecipInvGauss.test_logpdf_endpointc                 C   s$   t jdd}d}t||dd d S )Nrd  ro   g9V9s;r  rx   )r3   r  rF   r   r   r'  rc   r.   r.   r/   test_cdf_small_x  s   z"TestRecipInvGauss.test_cdf_small_xc                 C   s"   t jdd}d}t||d d S )NP   ro   glH<+<)r3   r  rI  r   r  r.   r.   r/   test_sf_large_x  s   z!TestRecipInvGauss.test_sf_large_xN)r  r  r  r  r   r  r  r.   r.   r.   r/   r    s
    r  c                   @   r6  )TestRicec                 C   s   g d}t ttjj|dd  t ttjj|dd  t ttjj|dd  t ttjj	|dd  g d}t ttjj
|dd  tjjddd}t t|  d}ttj|dtj|||dd	 d S )
N)ro  r  r  rt   r-   )re   re   ro   rm  r   r  r  r  r  )r   rl   r  r3   r  r<   r   r   rF   r[  rA  r   )r   rC   rC  r  r-   r.   r.   r/   test_rice_zero_b  s   
zTestRice.test_rice_zero_bc                 C   s2   t jj}t|ddjd t|dddjd d S )Nr  r  r   )r   r~   )r-   r   )r3   r  r   r   r   r   r[  r.   r.   r/   test_rice_rvs  s   zTestRice.test_rice_rvsc                 C   s   t jtdddtddd}g d}t|| tddd}t jj|ddd}g d	}t|| tj jd
tddd}g d}t|| d S )Nrg      )g/Ƹ?g[jǊ\?g 	?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?re   r   g     @_@rG  r  )	g<~@gwd
@gC?@gb
0@g` A@@g'NxP@g33-a@g4pv@g$F@ro      )gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g<
uQ@giff T@g9r[V@g3bXQ Y@gqxJ[@g`*DD ^@g@`@gdAa@)r3   r  rF   rl   r   r   rA  r2   )r   rF   cdf_expprobabilitiesrA  ppf_expr.   r.   r/   test_rice_gh9836  s   "

zTestRice.test_rice_gh9836N)r  r  r  r  r	  r  r.   r.   r.   r/   r    s    r  c                   @   r6  )
TestErlangc                 C   r   r   r   r   r.   r.   r/   r     r   zTestErlang.setup_methodc              	   C   s   t  6 t dt tttjjddddd g d}tjj|dd}tj	j|dd}t
||d	d
 W d    d S 1 s=w   Y  d S )Nr$  rH  r   r   rG  r  )ro   r  rs   r  r  r  rx   )r(  r)  r*  r+  r  r3   erlangr   r   r  r   )r   r   result_erlangresult_gammar.   r.   r/   test_erlang_runtimewarning  s   
"z%TestErlang.test_erlang_runtimewarningc                 C   s.   t tjjdddgdtjjdddgd d S )Nro   r   r  r  )r   r3   r  r<   r  r   r.   r.   r/   test_gh_pr_10949_argcheck,  s   z$TestErlang.test_gh_pr_10949_argcheckN)r  r  r  r   r  r  r.   r.   r.   r/   r    s    r  c                   @   sp   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	ejdddgddggdd Z
dd Zdd ZdS )TestRayleighc                 C   r   )Nr  r   r   r.   r.   r/   r   2  r   zTestRayleigh.setup_methodc                 C   r  )Nr   g)Zx)r3   r   r   r   r   r  r.   r.   r/   rq  6     zTestRayleigh.test_logpdfc                 C   r  )Nr   i)r3   r   r  r   r  r.   r.   r/   r  :  r  zTestRayleigh.test_logsfzrvs_loc,rvs_scale)gB)Q?got|?)gS2P?g3?c                 C   s   t jjd||d}dd }|||}t jj||d\}}t|| t|| t jj|dd\}}t|d t j|\}}t|||| d S )Nr  r  c                 S   s"   t | | d dt|   d S )Nr:   ro   )rl   r  r   )r   r   r.   r.   r/   r  C  s   "z(TestRayleigh.test_fit.<locals>.scale_mler  r  r  )r3   r   r   r   r   )r   r  r  r   r  scale_expectr8   r9   r.   r.   r/   r  >  s   



zTestRayleigh.test_fitr  rq   g̡=E?g@1d?c                 C   sH   t jjd||d}|t j|fg}t j|i d }tt j|| d S )Nr  r  r   )r3   r   r   r  r  r   )r   r  r  r   r   r   r.   r.   r/    test_fit_comparison_super_methodW  s   z-TestRayleigh.test_fit_comparison_super_methodc                 C   s   t tj d S rj   )r   r3   r   r   r.   r.   r/   r  d  r5  zTestRayleigh.test_fit_warningsc           	      C   s   t jd}d\}}}tjj||||d}tj|\}}|t |k s&J tjj||d\}}|t |k s9J ||ks?J d S )Ni  )r   r  rt  rc  r  )rl   r   r   r3   r   r   r   r+  )	r   r   r8   r9   r   r   loc_fitrj  	scale_fitr.   r.   r/   test_fit_gh17088g  s   
zTestRayleigh.test_fit_gh17088N)r  r  r  r   rq  r  r   r  r  r  r  r  r  r.   r.   r.   r/   r  1  s    


r  c                   @   r6  )TestExponWeibc                 C   sB   d}d}d}t j|||}t j|||}t||gddg d S )Nre   r  g      Y@g:23W+g~`9k)r3   	exponweibr<   r   r   )r   rC   r,   rB  r'  rp  r.   r.   r/   test_pdf_logpdfv  s   zTestExponWeib.test_pdf_logpdfc                 C   sj   t ddd}d}d}tj|||}tj||}t|| tj|||}tj||}t|| d S )Nr>  r  rG  r   rh   )rl   r?  r3   r  r<   weibull_minr   r   r   rC   r,   rB  r'  rc   rp  r.   r.   r/   test_a_is_1  s   
zTestExponWeib.test_a_is_1c                 C   sf   t ddd}d}d}tj|||}tj|}t|| tj|||}tj|}t|| d S )Nrh  r   rg   )rl   r?  r3   r  r<   r	  r   r   r"  r.   r.   r/   test_a_is_1_c_is_1  s   
z TestExponWeib.test_a_is_1_c_is_1N)r  r  r  r   r#  r$  r.   r.   r.   r/   r  t  s    r  c                   @   r,  )TestFatigueLifec                 C   r  )Nr!  r  X9r   rx   )r3   r   rI  r   rK  r.   r.   r/   r    s   zTestFatigueLife.test_sf_tailc                 C   s$   d}t j|d}t|ddd d S )Nr&  r  r!  r   rx   )r3   r   rN  r   )r   r'  rC  r.   r.   r/   test_isf_tail  s   zTestFatigueLife.test_isf_tailN)r  r  r  r  r'  r.   r.   r.   r/   r%    s    r%  c                   @   r6  )TestWeibullc                 C   r  r1  )r3   r!  r   r   r  r.   r.   r/   rq       zTestWeibull.test_logpdfc           
      C   sP  d}d}d}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|t	
d  t jj|||d}t|tt	
d  t jj|||d}t|td t jj|||d}	t|	d t jjdddd}t|td	 t jjdddd}	t|	d	 d
}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|td t jj|||d}t|d t jj|||d}t|t	
d  t jj|||d}	t|	tt	
d  t jjdddd}t|t	
d  t jjdddd}	t|	tt	
d  d S )Nra  rs   r  r  r9  r   r   r:   r  rs  g&.gCe )r3   r!  r<   r   rl   r   r   r:  rF   r   r  r[  rI  r  weibull_max)
r   rC   r,   r-   r'  r  rB  lcrB   r  r.   r.   r/   test_with_maxima_distrib  sH   


z$TestWeibull.test_with_maxima_distribc                 C   s   t jd}d\}}}t|||}|jd|d}tjj|ddd\}}}	tjj|ddd\}
}}||  kr<dks?J  J ||
ksEJ tjj|ddd	d
\}}}|dksXJ t|||}|jdd}t |t|f}t	|| d S )Nl   > )r:   r  ro   rh   rc  ra  r   r  r  rD  rE  rG  r  )
rl   r   r   r3   r!  r   r   r,  r  r   )r   r   rB  r8   r9   rL   r   c2rK  rL  c3rN  rO  c4rQ  rR  rS  r   r\  r.   r.   r/   test_fit_min  s   
zTestWeibull.test_fit_minN)r  r  r  rq  r,  r0  r.   r.   r.   r/   r(    s    Tr(  c                   @   r  )TestTruncWeibullc                 C   s(   t jddgddd}t|ddg d S )Nre   rs   g)\(?gףp=
?rt   )r3   truncweibull_minr<   r   r  r.   r.   r/   test_pdf_bounds,     z TestTruncWeibull.test_pdf_boundsc                 C   s>   t jdddtj}t|d t jdddd}t|d d S )Nrs   r  rt   r  g~?)r3   r2  r   rl   r   r   r   r  r.   r.   r/   rq  1  s   
zTestTruncWeibull.test_logpdfc                 C   s(   t jddgddd}t|ddg d S )Nrt   r  rs   re   )r3   r2  rA  r   r  r.   r.   r/   test_ppf_bounds9  r4  z TestTruncWeibull.test_ppf_boundsc                 C   :   g d}t j|ddd}t j|ddd}t|| d S N)rt   re   r  ro   r  rm  r  rs   rt   r  )r3   r2  rA  rF   r   r   rC  rC   q_outr.   r.   r/   test_cdf_to_ppf>     z TestTruncWeibull.test_cdf_to_ppfc                 C   r6  r7  )r3   r2  rN  rI  r   r8  r.   r.   r/   test_sf_to_isfD  r;  zTestTruncWeibull.test_sf_to_isfc                    s  dd d fddt jd }t|d t jd }tfdd	 \}}t|| t jd
 }tfdd	 \}}t|| t jd }tfdd	 \}}t|| t jd }	tfdd	 \}
}t|	|
 d S )Nrs   r  r  c                    s   | | t j|   S rj   )r3   r2  r<   )rC   r&  rb  r.   r/   xnpdfO  s   z)TestTruncWeibull.test_munp.<locals>.xnpdfr   r   c                    
    | dS r   r.   r   r=  r.   r/   rX   V     
 z,TestTruncWeibull.test_munp.<locals>.<lambda>r:   c                    r>  r'  r.   r   r?  r.   r/   rX   Z  r@  r   c                    r>  r  r.   r   r?  r.   r/   rX   ^  r@  rG  c                    r>  )NrG  r.   r   r?  r.   r/   rX   b  r@  )r3   r2  r  r   r   r   )r   rR  r  m1_expectedrj  r  m2_expectedm3m3_expectedr  m4_expectedr.   )r,   r-   rB  r=  r/   	test_munpJ  s$   



zTestTruncWeibull.test_munpc                 C   s   d}d}d}t dt dt dt d    }tj||||}t|d tj||||}t|t d  tj	d|||}t|| tj
||||}t|d tj||||}	t|	t d  tjd|||}
t|
| d S )Nr  r  rs   r   ro   r  )rl   r  r:  r   r3   r2  rF   r   r[  rA  rI  r  rN  )r   r,   r-   rB  x_medrF   r+  rA  rI  r  rN  r.   r.   r/   test_reference_valuese  s    *


z&TestTruncWeibull.test_reference_valuesc                 C   s  d}d}d}t j}d}tjj|||d}tjj|||||d}t|| tjj|||d}tjj|||||d}	t||	 tjj|||d}
tjj|||||d}t|
| tjj	|||d}tjj	|||||d}t|| tjj
|||d}tjj
|||||d}t|| tjj|||d}tjj|||||d}t|| tjj
dd||dd}t|t d	 tjjdd||dd}t|d	 d S )
Nra  rs   rt   r  r  r   r:   r   r  )rl   r   r3   r!  r<   r2  r   r   rF   r[  rI  r  r   )r   rC   rB  r,   r-   r9   r'  p_truncr  lp_truncrF   	cdf_truncr+  lc_truncrB   s_truncr  ls_truncr.   r.   r/   test_compare_weibull_min}  s6   





z)TestTruncWeibull.test_compare_weibull_minc           
      C   s   d\}}}t ||d}tj||||}tj||||}tj||tj|| }tj||| }tj||tj|| | }	t j|| t j||	 d S )N)r  r        ?rh   )	rl   r  r3   r2  r<   rF   r!  testingr   )
r   rB  r,   r-   rC   r  r  r  r  r  r.   r.   r/   test_compare_weibull_min2  s   
 z*TestTruncWeibull.test_compare_weibull_min2N)r  r  r  r3  rq  r5  r:  r<  rF  rH  rO  rR  r.   r.   r.   r/   r1  *  s    )r1  c                   @   r,  )	TestRdistc                 C   s0   t j}g d}t|||dd|dd d S )Nr  g     @r~   r
  )r3   rdistr   rF   rA  )r   r  r  r.   r.   r/   test_rdist_cdf_gh1285  s
   
zTestRdist.test_rdist_cdf_gh1285c                 C   sN   t ddd}d}tdt|d |d |d d  t|| d S )NgGzr  rg   g@ro   r:   r   )rl   r  r   r3   r  r<   rT  )r   rC   rB  r.   r.   r/   test_rdist_beta  s
   &zTestRdist.test_rdist_betaN)r  r  r  rU  rV  r.   r.   r.   r/   rS    r  rS  c                   @   <   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestTrapezoidc                 C   s`   g d}|D ]'}d|dg}t tj|||tj|| t tj|||tj|| qd S )N)r   r  ro   r   r   r   )r   r3   r   r<   triangrF   )r   modesmoderC   r.   r.   r/   test_reduces_to_triang  s   
z$TestTrapezoid.test_reduces_to_triangc                 C   sN   t ddd}ttj|ddtj| ttj|ddtj| d S Nr   r   rg   )rl   r  r   r3   r   r<   r!  rF   rO  r.   r.   r/   test_reduces_to_uniform  s   "z%TestTrapezoid.test_reduces_to_uniformc                 C   s  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   r:   r   ro   r  r<  ro  r  re   g      ?rP  rm  g      ?r  g      ?)r   r3   r   r<   rF   r   r.   r.   r/   
test_cases  s    zTestTrapezoid.test_casesc           	         sf  d\              f\}}}}d      fdd}|d}|d|d  }d          t d      }ttj|||||dd ttj|||||dd ttj|||||dd ttjd	d	d
dddd ttjd	dd
dd	dd ttjd	dd
dddd d S )N)r4  r  r:   r   r:   c                    sT   | d  | d     | d   | d        | d  | d  S )Nr:   r   r.   )r&  r,   r-   rB  dr"  r.   r/   r    s    z6TestTrapezoid.test_moments_and_entropy.<locals>.momentr   ro   r  r
  r   r4  r  r  r   )rl   r:  r   r3   r   r,  r  rR   )	r   r  r  r8   r9   r  r,  r  rR   r.   r`  r/   test_moments_and_entropy  s&   0> z&TestTrapezoid.test_moments_and_entropyc                 C   s`  t g d}t ddgd d d f }t g d}tj|||}t |||\}}}t j|j|jd}t 	|j}	t
|	| | | D ]\}
}}}tj|||||
< qIt|||jdd t tjj||dd	}t ||\}}t |jd
f}t 	|j}	t
|	| | D ]\}
}}tjj||dd	||
< qt||j|jdd d S )NrE  ro   r  )rw  r  rm  r  rw   r   r  r  rG  )rl   r   r3   r   r<   broadcast_arraysemptyr   r   r   r   ravelr   r  r   r  r  )r   rB  ra  rC   rW  ccddrD  r   indr  r  c1d1r.   r.   r/   test_trapezoid_vect  s"   &z!TestTrapezoid.test_trapezoid_vectc                 C   s0   t ddd}ttj|ddtj| d S r]  )rl   r  r   r3   rS   r<   r!  rO  r.   r.   r/   
test_trapz  s   "zTestTrapezoid.test_trapzN)	r  r  r  r\  r^  r_  rb  rk  rl  r.   r.   r.   r/   rX    s    	rX  c                   @   r/  )
TestTriangc                 C   s"  t j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 ttjddd W d    d S 1 sw   Y  d S )NraiserM  r   rs   ro   r  r   rt   r:   r  r  )rl   r  r   r3   rY  r<   rF   r   r.   r.   r/   test_edge_cases&  s   "zTestTriang.test_edge_casesN)r  r  r  ro  r.   r.   r.   r/   rm  %  r  rm  c                   @   r,  )
TestMielkec                 C   s\   d\}}t t||dtj t t|ddtj ttt|dd d S )N)g rh@gv?r   r  r  )r   r3   mielker  rl   r   r   r  )r   r@   rB   r.   r.   r/   r`  :  s    zTestMielke.test_momentsc                 C   s@   t ddd}d\}}ttj|||| tj||| d S )Nrq   rh   r   )g@gHzG@)rl   r  r   r3   burrr<   rq  )r   rC   r@   rB   r.   r.   r/   test_burr_equivalenceA  s   *z TestMielke.test_burr_equivalenceN)r  r  r  r`  rs  r.   r.   r.   r/   rp  9  r  rp  c                   @   r6  )TestBurrc              	   C   s   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d |D }t|| dd |D }dd |D }t|| d S )N)r   r   )ro   r:   )r   r   )r:   ro   r  ro   r  )r   r:   rs   c                 S   r  r.   r  r  r.   r.   r/   rM   T  r  z0TestBurr.test_endpoints_7491.<locals>.<listcomp>c                 S   r  r.   r.   r  r.   r.   r/   rM   U  r  c                 S   r  r.   )r   r,   r  r.   r.   r/   rM   X  r  c                 S   s   g | ]
\}}}t |qS r.   )rl   r:  r  r.   r.   r/   rM   Y  r  )r3   fiskrr  burr12r   )r   r   r  r  r.   r.   r/   test_endpoints_7491H  s   






	
zTestBurr.test_endpoints_7491c                 C   s<   d\}}t ||  \}}d\}}t|| t|| d S )N)r  r   )g4U?g&MI?)r3   rr  r   )r   rB  ra  r,  variancemean_hcvariance_hcr.   r.   r/   test_burr_stats_9544\  s
   
zTestBurr.test_burr_stats_9544c           	      C   sF  d\}}t ||  \}}tt| tt| d\}}t ||  \}}tt| tt| d\}}t jtg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d S )N)ro   r   )ra  r   )r   r:   r   rG  )r  r   )r  r   )r  r   )r3   rr  r   rl   r9  r  _munpr   )	r   rB  ra  r,  rx  e1e2e3e4r.   r.   r/   test_burr_nan_mean_var_9544g  sL   "z$TestBurr.test_burr_nan_mean_var_9544N)r  r  r  rw  r{  r  r.   r.   r.   r/   rt  G  s    rt  c                   @   s  e Zd Zg dZg dZg dZeeeefZg dZ	ddddd	ej
gZg d
Zeeee	eeeZddddej
dfddej
dfddej
dfgZdd Zejjdd ZejeZdZeejeedZe !eZ"W d   n1 sxw   Y  ej#de"d dd Z$ej#de"d dd Z%ejjej&dej#de"d  d!d" Z'd#d$ Z(ejj)d%d& Z*ej#d'ed(d) Z+ejjej&dd*d+ Z,ejj)d,d- Z-d.d/ Z.d0d1 Z/d2d3 Z0dS )4TestStudentizedRange)gQ1@g33333F@g
ףp=*K@gHzM@g/$@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@)rh  r  r  r   r   rg   r  x   )r:   r  r  r  )re   r   i)#  gupm1f?)r   rg   r   g?<-=A?gv"?rG  gd暕?ga-A?c                 C   s<   | j D ]\}}|\}}}tj|||}t||dd qd S )Nr  rx   )r   r3   studentized_rangerF   r   )r   pvkrC  
p_expectedrW  r@   res_pr.   r.   r/   test_cdf_against_tables  s
   
z,TestStudentizedRange.test_cdf_against_tablesc                 C   s<   | j D ]\}}|\}}}tj|||}t||dd qd S )NMb@?rx   )r   r3   r  rA  r   )r   r  
q_expectedr'  rW  r@   res_qr.   r.   r/   test_ppf_against_tables  s
   
z,TestStudentizedRange.test_ppf_against_tablesz&data/studentized_range_mpmath_ref.jsonr
  Ncase_resultcdf_datac                 C   N   |d }|d }|d |d |d f}t jj| }t|||d |d d d S 	Nsrc_case	mp_resultrC  r@   rW  expected_atolexpected_rtolr  )r3   r  rF   r   r   r  r  r  qkvr   r.   r.   r/   test_cdf_against_mp     
z(TestStudentizedRange.test_cdf_against_mppdf_datac                 C   r  r  )r3   r  r<   r   r  r.   r.   r/   test_pdf_against_mp  r  z(TestStudentizedRange.test_pdf_against_mpz+intermittent RuntimeWarning: invalid value.moment_datac                 C   sz   |d }|d }|d |d |d f}t jdd tjj| }W d    n1 s*w   Y  t|||d |d	 d
 d S )Nr  r  rV  r@   rW  r  r  r  r  r  )rl   r  r3   r  r  r   )r   r  r  r  mkvr   r.   r.   r/   test_moment_against_mp  s   
z+TestStudentizedRange.test_moment_against_mpc                 C   s4   d\}}t tjjdtj||fd}t|d d d S )Nr   rg   r   rv  r   )r   r3   r  r<   rl   r   r   )r   r@   rW  r   r.   r.   r/   test_pdf_integration  s   z)TestStudentizedRange.test_pdf_integrationc                 C   s\   d\}}t jdddd}tj|||dd  }tj|||}t||}t||dd d S )	Nr  r   rg   rq   )stepr   r  rx   )rl   r   r3   r  rF   r<   r   r   )r   r@   rW  rC   y_cdf	y_pdf_rawy_pdf_cumulativer.   r.   r/   test_pdf_against_cdf  s   
z)TestStudentizedRange.test_pdf_against_cdfr_case_resultc                 C   sV   |\}}}}t jdd tj|||}W d    n1 sw   Y  t|| d S )Nr  r  )rl   r  r3   r  rF   r   )r   r  rC  r@   rW  r_resr   r.   r.   r/   test_cdf_against_r  s
   z'TestStudentizedRange.test_cdf_against_rc                 C   s   t jdd tjddgddgddg}W d    n1 sw   Y  t|jd	 tjt	d
d tjdddgg d W d    d S 1 sIw   Y  d S )Nr  r  r   r:   rG  r~   rg   r)  r  z...could not be broadcast...r   )rg   r)  r	  )
rl   r  r3   r  r|  r   r   r   r   r   r  r.   r.   r/   test_moment_vectorization  s   "z.TestStudentizedRange.test_moment_vectorizationc              	   C   s   t  /}tjdd |t tjg d\}}}}W d    n1 s&w   Y  W d    n1 s5w   Y  ttj	|| d S )Nr  r  r   )
r   rl   r  r]   r   r3   r  r  r   	_argcheck)r   r@  r@   rR  rj  r.   r.   r/   test_fitstart_valid$  s   
 z(TestStudentizedRange.test_fitstart_validc                 C   sh   t jddtj}t jddd}t||ddd t jddtj}t jddd}t||ddd d S )Nr   rg   韆 r  r  )r3   r  r<   rl   r   r   rF   )r   r   
res_finiter.   r.   r/   test_infinite_df,  s   z%TestStudentizedRange.test_infinite_dfc                 C   s   t jddd}t jddd}t jddd}ttt||ddd t||ddd t jddd}t jddd}t jddd}ttt||ddd t||ddd d S )Nr   rg   r  r  i r  r  )r3   r  r<   r  AssertionErrorr   rF   )r   r   r  
res_sanityr.   r.   r/   test_df_cutoff7  s   

z#TestStudentizedRange.test_df_cutoffc                 C   s8   d\}}}t j|||}t|ddd |dksJ d S )N)gaRA@r   iS  r   r  r   )r3   r  rI  r   )r   rC  r@   rW  r'  r.   r.   r/   test_clippingL  s   
z"TestStudentizedRange.test_clipping)1r  r  r  q05q01q001rl   r  qspsr   vskslistr   r$   r   r_datar  r   r  r  r  ospathdirnamer  path_prefixrelative_pathopenr5  filejsonr  pregenerated_datar  r  r  xfail_on_32bitr  r  rX  r  r  r  r  r  r  r  r.   r.   r.   r/   r    sX    









r  c                   C   sR   t tjddddd t tjddddd t tjjdd	d
ddddd d S )Ng2g?rg   test_540_567)r  r/  g2gk?g;B.?gͣh?gHŎ*?r7   g.y?)r   r3   r  rF   r.   r.   r.   r/   r  V  s   
r  c                   C   s   t jjdd d S )Nr  r  )r3   _continuous_distns	gamma_genr.   r.   r.   r/   test_regression_ticket_1316b  s   r  c                   C   s   t tjdddd d S )Nrt   r:   ro   r  r  r.   r.   r.   r/   test_regression_ticket_1326h  s   r  c               	   C   s  t ddd} t jddE dddt dgdgdggfD ]}tj| |}t|dk  tt 	|   qt dgdgd	gg}tj| |}W d    n1 sUw   Y  tt 	|   t|d
 dk  t|d dk  t|d dk
  t|d dk
  d S )N      r  rf   r  r  rt   r!  r  rs   r   r   r:   )rl   r  r  r   r3   r'   r<   r   r   r9  any)rC   rn  r'  r.   r.   r/   test_regression_tukey_lambdam  s   "	r  zdocstrings strippedr  c                   C   s$   t dtjjv t dtjjv  d S )Nzpdf(x, mu, loc=0, scale=1)zpmf(x,)r   r3   re  rk  r.   r.   r.   r/   test_regression_ticket_1421  s   r  c                   C   s  t jdd tt tjdt j tt tjdt j tt tj	dt j tt tj
dt j tt tjdt j tt tjdt j tt tjdt j tt tjdt j tt tjt jd tt tjt jd tt tj	t jd tt tj
t jd tt tjt jd tt tjt jd tt tjt jd tt tjt jd W d    d S 1 sw   Y  d S )Nr  r  r   ro   )rl   r  r   r9  r3   r  r[  r   rF   r  rI  r<   r   rA  rN  r8  r  rX  r.   r.   r.   r/    test_nan_arguments_gh_issue_1362  s$   "r  c                  C   sj  t jd t g d} tjj| d | d | d dd}t jdd	 t tjj|d
d}W d    n1 s9w   Y  t	|| dd t tjj|ddd}t	|| dd t tjj|ddd}t	|| dd t tjj|ddd}t	|| dd t jd d}d}tj
j|ddd}t tj
j||d}t |t || d  g}t	||dd d S )Ni.  )r  rt   ro   r   r   r:   rh   r   r  r  rt   r  r
  ro   )r   r8   r  )r   r8   ro  rm  rs   rG  )rl   r   r   r   r3   r   r   r  r   r   r  r  r,  )truerC   rU  r8   r   rc   r.   r.   r/   test_frozen_fit_ticket_1536  s(     r  c                  C   s<   t jd tjjdd} tj| }d}t||dd d S )Ni	 rh   r   )g
ףp=
?gʡE?r   r
  )rl   r   r   r3   r  r   r   r   )r   rU  rc   r.   r.   r/   test_regression_ticket_1530  s
   r  c                  C   sV   t jd t jd} dD ]}tj| | \}}t||dd t|ddd qd S )Nr   r  )r  g   6Ar  r   r  )rl   r   r   r  r3   r  r   r   )rC   offsetr8   r9   r.   r.   r/   test_gh_pr_4806  s   r  c                  C   s   t jj ddd} dtjd d ddg}t| |dd t jj d	dd} g d
}t| |dd t jj ddd} g d}t| |dd d S )Nr   r  r  r:   r   r  rg   r
  g
ףp=
	@)r   gz5v?r   gRTgQ?)r   gNg @r   gJFٻ)r3   r'   rl   r>   r   )ra  rc   r.   r.   r/   "test_tukeylambda_stats_ticket_1545  s   r  c                   C   s   t ttjdd d S )Nrb  ru  )r   rl   r  r3   re  rX  r.   r.   r.   r/   test_poisson_logpmf_ticket_1436  s   r  c                  C   s4   ddg} | D ]\}}t jj |dd}t|| qd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))
    )r  )ro   r=  rt   r>  )rs   )gUUUUUU?r  g^cQg333333r  r  N)r3   r  r   )casesr,   
exact_mvskr  r.   r.   r/   test_powerlaw_stats  s   r  c                  C   s   t jdd} t| d d S )Nr   r   rt   )r3   r  r   r   r'  r.   r.   r/   test_powerlaw_edge
  r)  r  c                  C   sh   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   rt   )r  r  ra  r  )r3   r  r   r   r<   rl   r   r  r.   r.   r/   test_exponpow_edge  s   
r  c                  C   s   t jddd} t| d d S )Nr   r   r  )r3   gengammar<   r   r  r.   r.   r/   test_gengamma_edge  s   r  c                  C   s@   t jddd} | dksJ t jddd}|tj ksJ d S )Nr   r   r  rt   )r3   r  r<   r   rl   r   )r'  rp  r.   r.   r/   !test_gengamma_endpoint_with_neg_c"  s   r  c                  C   s8   t jddd} t| d t jddd} t| d d S )NrZ  ru  r  g>rg   gqq?)r3   r  r|  r   r  r.   r.   r/   test_gengamma_munp)  s   
r  c               	   C   s   t g d} t jdd6 t }|td |td tj	|  W d    n1 s.w   Y  W d    d S W d    d S 1 sFw   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)
rl   r   r  r   r]   r   r+  r3   rp  r   )ra  r@  r.   r.   r/   test_ksone_fit_freeze2  s    "r  c                  C   s   t ttddd } g d}tt | |dd tt | d j|dd tj| d d	 j	}t 
tj| tj|  }t||d	d d S )
Nr   r  rG  )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  )rl   r  r  r  r   r3   r  r[  realimagr   r   )rC   rc   derivderiv_expectedr.   r.   r/   test_norm_logcdfJ  s   	r  c                  C   sT   t g d} t g d}tj| }t||dd tj|}t|| dd d S )N)r   r  ro   re   rq   r  )g~V1?g|N?gba"?g܄4ťY?r<  g$%+Ir  rx   r   )rl   r   r3   r   rF   r   rA  )rC   rc   r  rD  r.   r.   r/   test_levy_cdf_ppfc  s   r  c                  C   :   t g d} t g d}tj| }t||dd d S )N)  4&kCg(,* EgMraB3Ggd~QJ)gep[>g}XEQ=gѭEG<g?_%~:r  rx   )rl   r   r3   r   rI  r   rC   rc   r  r.   r.   r/   test_levy_sf{     r  zp, expected_isf))r  gj1e2H)r  g6C)g      ?gnE@)r  g!^x1?)r  gZ?)g   ?g:}!Nu?c                 C   r   )Nr  r   )r3   r   rN  r   )r'  expected_isfrC   r.   r.   r/   test_levy_isf  s   r  c                  C   r  )N)gMbg{Gzg{Gztg~jtX)g#]<gOul2;gޢا6g̅7=!r   rx   )rl   r   r3   r   rI  r   r  r.   r.   r/   test_levy_l_sf  r  r  c                  C   s8   t g d} tj| }tj|}t|| dd d S )N)g [n<r  r  gvIh%,=rx   )rl   r   r3   r   rN  rI  r   )r'  rC   rC  r.   r.   r/   test_levy_l_isf  s   r  c                   C   s|   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 )Nrh  i i  i  )g      c@g     h@g=
ףp=?Gz?)g      c@g     h@{Gz?rh   r  r   )r   r3   rs  rj  rA  r.   r.   r.   r/   test_hypergeom_interval_1802  s   r  c                  C   sr  t jd t jdd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 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 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 tttjj| d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j	dddd tj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	 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ttjj| dd
ddddd	 tj| dd
ddd d S )Nr   re   r  r~   numr:   r   r  r  rG  ro   r7   rs   ra  r"  r   r  r  )rl   r   r   r  r  r   r3   r  r<   r   rF   rA  rR   r   r  r  r	  r  re  r   r.   r.   r/   test_distribution_too_many_args  s8   r  r  c                  C   sH   t jtddddd} t jtddddd}t| |ddd d S )	Nr  r  ro  r:   gYZ@r  r   r  )r3   ncx2rF   rl   r   _cdfvecr   r  r.   r.   r/   test_ncx2_tails_ticket_955  s   r  c               	   C   s   t  ) t dt ttjdt	dddd tj
dt	ddd} W d    n1 s0w   Y  tt|   t  % t dt ttjddd	d ttj
ddd	d
 W d    d S 1 sjw   Y  d S )Nr$  r   iT  i^  r:   r   r1  r   r	  gsq6)r(  r)  r*  r+  r   r3   r  r<   rl   r   r   r   r#  r   r   )logvalr.   r.   r/   test_ncx2_tails_pdf  s   

"r  zmethod, expectedrF   gu%>g	;Q=r<   g<x>gRz\R>r   gʎK$/gԆX1rA  gfHu@ge:@c                 C   s,   t tj| dddgdd}t||dd d S )Nre   r   rG  rg   )r  rR  rw   r   )r   r3   r  r   )rF  rc   r  r.   r.   r/   test_ncx2_zero_nc  s   r  c                  C   s4   t jjdddd} t jjddd}t| |dd d S )Nrg   r   r   )rR  r  r   )rR  r   rw   r   )r3   r  r   r  r   )r  rc   r.   r.   r/   test_ncx2_zero_nc_rvs  s   r  c                  C   s,   dt dd } ttjjdd| dd d S )Nrg   r~   r  r   rR  r  r   )rl   r   r   r3   r  rF   )r  r.   r.   r/   test_ncx2_gh12731  s   r   c                  C   sB   t g d} d\}}tjj| ||d}g d}t||d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  )r  r  r  r  r  g?gy[qD?rt   rt   rt   rt   rt   rt   rS  r   )rl   r   r3   r  rI  r   )rC   nurn  rI  sf_expectedr.   r.   r/   test_ncx2_gh8665&  s
   
r  c               	   C   sx   d} d}t jtjd| |tjd| |dd}tj|| |}tj|| | t d|  d|  }t||d	d
 d S )Ni,  i  r  r  r1  r  r:   rG  r  r   )	rl   r  r3   r  rA  r<   r  r  r   )rR  r  rC   ncx2_pdfgauss_approxr.   r.   r/   test_ncx2_gh11777B  s   &r  c                  C   s"   t jddd} t| dd d S )Nr   r   r  )r3   foldnormr   rF   r  r.   r.   r/   test_foldnorm_zeroQ  s   r  c                  C   s   t j g ddd} t j ddgdd}tdd |D }t||  t j g d} t j dd	g}td
d |D }t||  d S )N)rt   ro   r  r   ro   r  c                 s   s     | ]}t jt j|f V  qd S rj   rl   r  r   r  r.   r.   r/   r%  \  r)  z-test_stats_shapes_argcheck.<locals>.<genexpr>)r:   r  r  r:   r  c                 s   s     | ]}t j|t jf V  qd S rj   r	  r  r.   r.   r/   r%  b  r)  )r3   r   tupler   r   )mv3mv2mv2_augmentedr.   r.   r/   test_stats_shapes_argcheckW  s   
r  c                   @   r/  )
_distr_genc                 C   r   Nr  r.   r   rC   r,   r.   r.   r/   _pdfm  r  z_distr_gen._pdfNr  r  r  r  r.   r.   r.   r/   r  l  r  r  c                   @   r/  )_distr2_genc                 C      d| | S r  r.   r  r.   r.   r/   _cdfr     z_distr2_gen._cdfN)r  r  r  r  r.   r.   r.   r/   r  q  r  r  c                   @   r,  )_distr3_genc                 C   s   || S rj   r.   r   rC   r,   r-   r.   r.   r/   r  w  s   z_distr3_gen._pdfc                 C   r  r  r.   r  r.   r.   r/   r  z  s   z_distr3_gen._cdfNr  r  r  r  r  r.   r.   r.   r/   r  v  r]  r  c                   @   r,  )_distr6_genc                 C   s   || | S rj   r.   r  r.   r.   r/   r    r  z_distr6_gen._pdfc                 C   r  r  r.   r  r.   r.   r/   r    r  z_distr6_gen._cdfNr  r.   r.   r.   r/   r    s    r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#S )$TestSubclassingExplicitShapesc                 C   s$   t ddd}t|jdddd d S )Ndummyr,   r  r   r   r  r  r  r   r<   r   dummy_distrr.   r.   r/   test_correct_shapes  s   z1TestSubclassingExplicitShapes.test_correct_shapesc                 C   s,   t ddd}tt|jdfi tdd d S )Nr  Ar  r   r  )r  r  r   r<   r   r   r.   r.   r/   test_wrong_shapes_1  s    z1TestSubclassingExplicitShapes.test_wrong_shapes_1c                 C   s4   t ddd}tdddd}tt|jdfi | d S )Nr  za, b, cr  r   r:   r   rb  )r  r   r  r   r<   )r   r!  r   r.   r.   r/   test_wrong_shapes_2  s   z1TestSubclassingExplicitShapes.test_wrong_shapes_2c                 C   "   t ddd}tttfi | d S )Nr  r  r  )r   r  r   r  r   r   r.   r.   r/   test_shapes_string     z0TestSubclassingExplicitShapes.test_shapes_stringc                 C   r&  )Nr  z(!)r  r   r  SyntaxErrorr  r'  r.   r.   r/   test_shapes_identifiers_1  r)  z7TestSubclassingExplicitShapes.test_shapes_identifiers_1c                 C   r&  )Nr  4chanr  r*  r'  r.   r.   r/   test_shapes_identifiers_2     z7TestSubclassingExplicitShapes.test_shapes_identifiers_2c                 C   r&  )Nr  zm(fti)r  r*  r'  r.   r.   r/   test_shapes_identifiers_3  r/  z7TestSubclassingExplicitShapes.test_shapes_identifiers_3c                 C   r&  )Nr  za=2r  r*  r'  r.   r.   r/   "test_shapes_identifiers_nodefaults  r/  z@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaultsc                 C   r&  )Nr  z*argsr  r*  r'  r.   r.   r/   test_shapes_args  r/  z.TestSubclassingExplicitShapes.test_shapes_argsc                 C   r&  )Nr  z**kwargsr  r*  r'  r.   r.   r/   test_shapes_kwargs  r/  z0TestSubclassingExplicitShapes.test_shapes_kwargsc                 C   r&  )Nr  za, b, c, lambdar  r*  r'  r.   r.   r/   test_shapes_keywords  r)  z2TestSubclassingExplicitShapes.test_shapes_keywordsc                 C   s@   G dd dt j}|dd}t|jdddt jdd  d S )Nc                   @   r/  )zFTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_genc                 S      t j|| S rj   r3   r  r  r  r.   r.   r/   r    r   zKTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_gen._pdfNr  r.   r.   r.   r/   	_dist_gen  r  r7  r,   r   ro   r:   r  r3   rP   r   r<   r  r   r7  rL   r.   r.   r/   test_shapes_signature  s   
$z3TestSubclassingExplicitShapes.test_shapes_signaturec                 C   s>   G dd dt j}|dd}tt|jdfi tddd d S )	Nc                   @   r/  )zSTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_genc                 S   r5  rj   r6  r  r.   r.   r/   r    r   zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_gen._pdfNr  r.   r.   r.   r/   r7    r  r7  r  r8  ro   r   r:   r  )r3   rP   r  r   r<   r   r:  r.   r.   r/   "test_shapes_signature_inconsistent  s   
"z@TestSubclassingExplicitShapes.test_shapes_signature_inconsistentc                 C   sz   G dd dt j}|dd}t|jdddt jdd  t|ddt jdd  tt|jdfi tdd d S )	Nc                   @   r/  )z?TestSubclassingExplicitShapes.test_star_args.<locals>._dist_genc                 W   s   |d }t j|| S Nr   r6  )r   rC   r   extra_kwargr.   r.   r/   r    s   zDTestSubclassingExplicitShapes.test_star_args.<locals>._dist_gen._pdfNr  r.   r.   r.   r/   r7    r  r7  r>  r8  ro   !   r>  )xxx)r3   rP   r   r<   r  r  r   r   r:  r.   r.   r/   test_star_args  s
   
  z,TestSubclassingExplicitShapes.test_star_argsc                 C   sj   G dd dt j}|dd}t|jddddt jdd d  t|dddt jdd d  d S )	Nc                   @   r/  )zATestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_genc                 W   s   |d }t j|| | S r=  r6  )r   rC   r  r   r>  r.   r.   r/   r    s   zFTestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_gen._pdfNr  r.   r.   r.   r/   r7    r  r7  zoffset, extra_kwargr8  ro   o   r?  )r  r>  r9  r:  r.   r.   r/   test_star_args_2  s   
z.TestSubclassingExplicitShapes.test_star_args_2c                 C   s<   G dd dt j}|dd}t|jdddt jd d S )Nc                   @   r/  )zBTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_genc                 _   s   | dd}tj|| S )Nr>  r   )popr3   r  r  )r   rC   r   kwargsr>  r.   r.   r/   r    s   zGTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_gen._pdfNr  r.   r.   r.   r/   r    r  r  r>  r8  r   r   r@  r9  )r   r  rL   r.   r.   r/   test_extra_kwarg  s   
 z.TestSubclassingExplicitShapes.test_extra_kwargc                 C   s8   G dd dt j}|dd}t|dt jd d S )Nc                   @   r/  )zDTestSubclassingExplicitShapes.shapes_empty_string.<locals>._dist_genc                 S   s   t j|S rj   )r3   r  r<   rO  r.   r.   r/   r    r  zITestSubclassingExplicitShapes.shapes_empty_string.<locals>._dist_gen._pdfNr  r.   r.   r.   r/   r7    r  r7   r8  ro   r9  r:  r.   r.   r/   shapes_empty_string  s   
z1TestSubclassingExplicitShapes.shapes_empty_stringN)r  r  r  r"  r$  r%  r(  r,  r.  r0  r1  r2  r3  r4  r;  r<  rB  rD  rG  rI  r.   r.   r.   r/   r    s$    		r  c                   @   sl   e Zd Zdd Zdd Zejjedddd Z	ejjeddd	d
 Z
dd Zdd Zdd Zdd ZdS )TestSubclassingNoShapesc                 C   s"   t dd}t|jdddd d S )Nr  r  r   r  r  r  r   r.   r.   r/   test_only__pdf  s   
z&TestSubclassingNoShapes.test_only__pdfc                 C   s"   t dd}t|jdddd d S )Nr  r  r   r  )r  r   r<   r   r.   r.   r/   test_only__cdf  s   
z&TestSubclassingNoShapes.test_only__cdfdocstring strippedr  c                 C   sD   t dd}t|jd t|jd td|j}tt|dk d S )Nr  r  r   r,   zlogpdf\(x, a, loc=0, scale=1\))	r  r   numargsr   refindallrk  r   r   r   r!  r   r.   r.   r/   test_signature_inspection  s   
z1TestSubclassingNoShapes.test_signature_inspectionc                 C   sD   t dd}t|jd t|jd td|j}tt|dk d S )Nr  r  r:   r  z!logpdf\(x, a, b, loc=0, scale=1\)r   )	r  r   rN  r   rO  rP  rk  r   r   rQ  r.   r.   r/   test_signature_inspection_2args  s   
z7TestSubclassingNoShapes.test_signature_inspection_2argsc                 C   s   t ttdd d S )Nr  r  )r  r   r  r   r.   r.   r/   0test_signature_inspection_2args_incorrect_shapes"  r6   zHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapesc                 C   .   G dd dt j}tt|fi tdd d S )Nc                   @   s   e Zd ZdddZdS )z>TestSubclassingNoShapes.test_defaults_raise.<locals>._dist_genr  c                 S   r   r  r.   r  r.   r.   r/   r  )  r  zCTestSubclassingNoShapes.test_defaults_raise.<locals>._dist_gen._pdfN)r  r  r.   r.   r.   r/   r7  (  s    r7  r  r  r3   rP   r  r   r   r   r7  r.   r.   r/   test_defaults_raise&     z+TestSubclassingNoShapes.test_defaults_raisec                 C   rU  )Nc                   @   r/  )z>TestSubclassingNoShapes.test_starargs_raise.<locals>._dist_genc                 W   r   r  r.   )r   rC   r,   r   r.   r.   r/   r  0  r  zCTestSubclassingNoShapes.test_starargs_raise.<locals>._dist_gen._pdfNr  r.   r.   r.   r/   r7  /  r  r7  r  r  rV  rW  r.   r.   r/   test_starargs_raise-  rY  z+TestSubclassingNoShapes.test_starargs_raisec                 C   rU  )Nc                   @   r/  )z<TestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_genc                 [   r   r  r.   )r   rC   r,   rF  r.   r.   r/   r  7  r  zATestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_gen._pdfNr  r.   r.   r.   r/   r7  6  r  r7  r  r  rV  rW  r.   r.   r/   test_kwargs_raise4  rY  z)TestSubclassingNoShapes.test_kwargs_raiseN)r  r  r  rK  rL  r   r  r  DOCSTRINGS_STRIPPEDrR  rS  rT  rX  rZ  r[  r.   r.   r.   r/   rJ    s    


	rJ  rM  c                  C   sT   g d} t jD ] }tt |}t|t jt jfr'| D ]}tt||j	d u  qqd S )N)z,\s*,z\(\s*,z^\s*:)
r3   r\   r   r   rO   rP   r   rO  searchrk  )badonesdistnamerL   regexr.   r.   r/   r`  <  s   

r`  c                   C   s4   t tjtjddd t tjtjddd d S )Nrg   r)  r   r  re   r   )r   r3   r  rI  rl   r   r  r  r.   r.   r.   r/   test_infinite_inputF  s   ra  c                  C   &   t jt jddd} t| d d S Ng0.++r   )r3   lomaxrA  rF   r   r  r.   r.   r/   test_lomax_accuracyK     re  c                  C   rb  rc  )r3   gompertzrA  rF   r   r  r.   r.   r/   test_gompertz_accuracyQ  rf  rh  c                  C   rb  rc  )r3   
truncexponrA  rF   r   r  r.   r.   r/   test_truncexpon_accuracyW  rf  rj  c                  C   s*   t jt jddd} t| ddd d S )Nrj  r   r  r   r
  )r3   r   rN  rI  r   r  r.   r.   r/   test_rayleigh_accuracy]  s   rk  c                  C   s   t jdd5} t d tjdd tjdd tjdd tjt	j
 d t| }t|d W d   dS 1 s>w   Y  dS )zregression test for gh-6219T)r8  alwaysro   r   rt   N)r(  r)  r*  r3   rZ  rF   r<   rA  r   rl   r   r   r   )r$  number_of_warnings_thrownr.   r.   r/    test_genextreme_give_no_warningsc  s   
"rn  c                  C   s   d} t jd}t|d|  d dd t jd}t|| d dd t jd}t|d t jjd	d
d}t|| d td
 d dd t jd
}t|d|  d dd t jd}t|d|  d dd d S )Ngox?r!  r:   r   r  rx   r   r  r  rg   r  r   r]  r  r)  )r3   rZ  rR   r   r   rl   r:  )euler_gammar"  r.   r.   r/   test_genextreme_entropyq  s   
 rp  c                  C   s   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 )	Ng    חAg      g'b%4gQ@r  gؗҜ;r   g.l6?)r3   rZ  rI  r   rN  )rC   rB   r  r.   r.   r/   test_genextreme_sf_isf  s   




rq  c                  C   s"   d} t j| dd}t|d d S )Nr  r:   r   gH&8>)r3   rv  rA  r   )probr  r.   r.   r/   test_burr12_ppf_small_arg  s   	rs  c                  C   s6  t ddddd } tjj| ddd}t g d	}t||d
d tjj| ddd}t g d}t||d
d tjj| ddddd}t g d}t||d
d tjj| ddd}t g d}t||d
d tjj| ddd}t g d}t||d
d tjj| ddddd}t g d}t||d
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.
    r  r  r  Nr  r  rs   )r  rV  )gC,d	Ɣ?gH㸘?g5?gM"M#w?gɫs^?g @?gƴ?g@w?ɫs^?|?q ?g C?ru  rt  gJó?g,BV\ۤ?g;?g#ek?g%ǓE?g(Ȍx?g>J>r  rx   r  )g#{`?gdf?g Jq?gSS){?g'	w?uL? T)?cAJ?GTn?R1#?gA]P?rz  ry  rx  rw  gvӢ?gKq?gL?g
	N<!?gAw>ro   )r  rV  r8   r9   )g=aO}?gI8?g#T?aW)?ǓI?
J?E?d۳?GTn?8?R1#?kP?g(*T?r  r  r  r  r~  r}  r|  r{  )gD
)?g:3P?g9?g?S[?rt  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?rv  ğ@ _?y}D?焂Rr/?N?YjhG?a0L?4f?<@?@CH?g	ސF?g5+-#?g?g?q ?r  )g}'v?rv  g*V?r  gr/0+?r  g[8	?r  gΥ?r  gY?r  g#)a?r  g?̔?r  g]ؚ?r  g|c ?r  )rl   r  r3   crystalballr<   r   r   rF   )r9  
calculatedrc   r.   r.   r/   test_crystalball_function  s&   r  c                  C   s  t g d} t g d}t g d}tjd| |}t||dd t g d}t dd	t jd
dg}|| }tjd| |}t||dd t t jt jt jddg}|| }tjd| |}	t||	dd t t jt jt jt jdg}|| }
tjd| |}t|
|dd t t jt jt jt jdg}|| }tjd| |}t||dd t t jt jt jt jdg}|| }tjd| |}t||dd dS )zg
    All values are calculated using the pdf formula and the integrate function
    of Mathematica
    )rs   r  r  rs   r  )r  r  rs   r  r  )r  r  r  r  r  r   r  rx   )gԚh@g[&@gͪ@g2dQ@gn6-@g?ޫV&̿g BgQCRgQF\ jr   g
@gn(@r:   g?Җ)r   gMg'#@rG  g('UHr~   N)rl   r   r3   r  r|  r   r   )r  rV  expected_0th_momentcalculated_0th_momentr  r,   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_momentr.   r.   r/   !test_crystalball_function_moments	  s4   r  c                  C   sR   t dd} |  }d\}}}t|||}tt| ||}t||dd d S )Nr:   r   )ir   r3  rP  rx   )	r3   r  rR   rl   r  r   r   r<   r   )cbr  r  r  rv  rC   r  r.   r.   r/   test_crystalball_entropy7  s   
r  c                  C   s\   ddd} t g d}tjj|d| d\}}}t|ddd	 |dks%J t|d
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                 S   s   t | |||dddS )NrS  )r   dispxtolftol)r#   )r   x0r   r  r.   r.   r/   	optimizerY  s   z&test_invweibull_fit.<locals>.optimizer)r   rP  r:   r  r  r   r}  rG  r~   r  rg   r	  @   c   )r   r  g`?r  rx   g [@N)r.   r   )rl   r   r3   r   r   r   )r  rC   rB  r8   r9   r.   r.   r/   test_invweibull_fitB  s   
r  zx, c, expected))r   ra  g7Ըh?)r   ra  gz]r>)r   g     "@goBڱ9)r  ra  g$=cC;c                 C   ru   rv   )r3   r   rI  r   )rC   rB  rc   r  r.   r.   r/   test_invweibull_sfd  s   r  zp, c, expected)ro   r  g9?)geK<r~   g@c                 C   ru   rv   )r3   r   rN  r   )r'  rB  rc   r  r.   r.   r/   test_invweibull_isfo  s   r  z	df1,df2,x)ru  ro  r  r`  rG  r)  r"  r  r  c                 C   sh   d}t j|| |}t j|| ||}t||dd t j|| |}t j|| ||}t||dd d S )Nr   r  rx   r  )r3   r  rF   re  r   r<   )df1df2rC   r  expected_cdfcalculated_cdfr{   calculated_pdfr.   r.   r/   test_ncf_edge_casew  s   
r  c                  C   s"   t jddd} t| ddd d S )Nr:   r  rG  g     `E@r  rx   )r3   re  r  r   )rW  r.   r.   r/   test_ncf_variance     r  c                  C   s.   t jdddd} d}t|tj| dd d S )Nr  r  r?  gffffff>@g&4I,)?)decimals)r3   re  rF   r   rl   round)	scipy_val	check_valr.   r.   r/   test_ncf_cdf_spotcheck  s   r  r  z(On some 32-bit the warning is not raisedc                     sx   t ddd} d| d< d tt tjj| g R  } fdd| D }W d    n1 s0w   Y  t|| d S )Nr   r   r  r  )re   r:   r~   r   r   c                    s    g | ]}t jj|g R  qS r.   )r3   re  rA  )rK   xiparr.   r/   rM     s     z,test_ncf_ppf_issue_17026.<locals>.<listcomp>)	rl   r  r   r  r+  r3   re  rA  r   )rC   rC  q0r.   r  r/   test_ncf_ppf_issue_17026  s   r  c                   @   rW  )TestHistogramc                 C   s\   t jd t jg ddd}t|| _tjjddddd	}t j|d
d}t|| _	d S )Nr   )r   r:   r:   r   r   r   rG  rG  rG  rG  r~   r~   r~   r~   r~   r  r  r  r  r"  r"  r"  r  r  rj  r  binsr  r  r1  {   r  r   )
rl   r   r   	histogramr3   rQ   templater  r   norm_template)r   r  r   norm_histogramr.   r.   r/   r     s   
zTestHistogram.setup_methodc                 C   s   t g d}t g d}t| j|| t| jdd t| jdd t| jdd t| jdd t d	d
d}t| j|t	j
j|ddddd d S )Nrt   ro   r  ra  rs   r  r  r  r  r  r        @rm  r        @ri  r        !@r  g      #@)rt   rt   r  r  {Gz?r  Q?r  {Gz?r  ro  ro  r  r  r  r  r  r  rt   rt   r  r  r  r  rt   r  rZ  r:   rg   r  r  r7   re   rx   )rl   r   r  r   r  r<   r   r  r  r3   r  )r   r  
pdf_valuesrC   r.   r.   r/   r    s   
zTestHistogram.test_pdfc                 C   s   t g d}t g d}t| j|| t| j|dd |dd  t ddd}t| j| j|| t ddd}t| j| j|| t d	dd
}t| j|t	j
j|ddddd d S )Nr  )rt   rt   rt   r  r  r  r  
ףp=
?Q?{Gz?r  ro   r  (\?RQ?=
ףp=?)\(?r  r  r  r:   r  r  r  rh   rt   rZ  rg   r  r7   re   rx   )rl   r   r  r   r  rF   rA  r  r  r3   r  )r   r  
cdf_valuesrC   r.   r.   r/   rE    s   "
zTestHistogram.test_cdf_ppfc                 C   s   d}| j j|dd}tt|dk d tt|dkd| dd	 tt|d
kd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|dkd| dd	 tt|d kd!| dd	 tt|d"kd#| dd	 tt|d$kd%| dd	 tt|d&kd| dd	 tt|d&kd| dd	 tt|d&kd d S )'Nr1  r  rc  r  rt   rs   r  ro  rx   r  r  r  r  re   r  r  r  r  r  r  r  r  rd  r  ro   rm  r  r  r  r  r  ri  r  r  r  r  r  r  )r  r   r   rl   r  r   )r   rv  r  r.   r.   r/   r     s(   zTestHistogram.test_rvsc                 C   s6   t dD ]}t| j|tdd|dd qd S )NrG  r  r  rd  rx   )r  r   r  r|  r3   r  r  )r   r&  r.   r.   r/   rF    s
   zTestHistogram.test_munpc                 C   s$   t | j tjjddddd d S )Nr  r  r7   rd  rx   )r   r  rR   r3   r  r   r.   r.   r/   r#    s   

zTestHistogram.test_entropyN)	r  r  r  r   r  rE  r   rF  r#  r.   r.   r.   r/   r    s    r  c                  C   s   ddgg d} }t j| |fdd}tj|ddgddg | dks(J t j| |fdd}tj|ddgd	 | d
ksEJ d}tt|d t | |f}| d
ks]J W d    n1 sgw   Y  t | g df}| dks}J d S )Nr   )r   r   r0  F)rR  ro   ru  r  Tg'^P?g     H@z(Bin widths are not constant. Assuming...r   rd  )	r3   rQ   rl   rQ  r   r<   r  r	   r+  )countsr  rL   rO  r.   r.   r/   test_histogram_non_uniform  s   r  c                   @   s.   e Zd Zdd Zejdddgdd ZdS )	TestLogUniformc                 C   s   t jd}tdd}|jd|d}t jd}tdd}|jd|d}t|| t jt 	|dd\}}d|
   krK|   krKd	ksNJ  J t t |d
 dks\J d S )N   0o[ r  r   r1  rc  rg   r  rz  iL  r   )rl   r   r   r3   
loguniformr   
reciprocalr   r  log10r+  r  r   r  )r   r   r  r   rv2r   r   rj  r.   r.   r/   
test_alias(  s   
. zTestLogUniform.test_aliasrF  mlerD  c                 C   sn   t jd}tjjddd|d}tjj||d\}}}}|dks"J tjj|d|d\}}}}|dks5J d S )	Nr  re   r   r   rc  rH  r:   rE  )rl   r   r   r3   r  r   r   )r   rF  r   r   r,   r-   r8   r9   r.   r.   r/   test_fit_override9  s   z TestLogUniform.test_fit_overrideN)r  r  r  r  r   r  r  r  r.   r.   r.   r/   r  '  s    r  c                   @   s  e Zd Zdd Zejdddgddgdd	ggd
d Zejdddgdd Zejdg ddd Z	ejdg ddd Z
ejdg ddd Zejdg ddd  Zejdg d!d"d# Zejdg d$d%d& Zejdg d'd(d) Zd*S )+	TestArgusc                 C   s2   t jjdddd}tt d | dd d S )Nr   rt  E  rc  rG  r
  )r3   argusr   r   r,  rO  r.   r.   r/   test_argus_rvs_large_chiH  s    z"TestArgus.test_argus_rvs_large_chizchi, random_statere   r  rH     r     c                 C   s6   t jj|d|d}t |d|f\}}t|dk d S )Nrt  rc  r  rd  r3   r  r   rg  r   )r   rH  r   rC   rj  r'  r.   r.   r/   r   M  s   zTestArgus.test_rvsrH  r  r  c                 C   s6   t jj|ddd}t |dd \}}t|dk d S )Nrt  ie rc  c                 S   s   dd| d  d  S )Nr   r:   ra  r.   r   r.   r.   r/   rX   ]  rN   z.TestArgus.test_rvs_small_chi.<locals>.<lambda>rd  r  )r   rH  r
  rj  r'  r.   r.   r/   test_rvs_small_chiW  s   zTestArgus.test_rvs_small_chizchi, expected_mean))r   g щi?)rg   g.憃?)rH  g\paP?)<   g	?)r  g,6?c                 C   s"   t jj|dd}t||dd d S )Nr   r  r   rx   )r3   r  r,  r   )r   rH  expected_meanrV  r.   r.   r/   rU  a  r  zTestArgus.test_meanzchi, expected_var, rtol))r   gLH'B?r   )rg   go$?r  )rH  g
=>r  )r  g2W>r  )r  gb~P>r  c                 C   s"   t jj|dd}t|||d d S )Nr   r  rx   )r3   r  r  r   )r   rH  expected_varry   rW  r.   r.   r/   r@  l  r  zTestArgus.test_varzchi, expected, rtol))rm  gwM?r  )ro   gj?r  )re   gHEA`!?r  )rq   gcف>rw   )r  gF=r  )r  g߹Q#B=r  )r  g0ޟ<r  )r  g*W%:rw   c                 C   s   t t|||d d S r  )r   r!   )r   rH  rc   ry   r.   r.   r/   test_argus_phi_small_chiw  s   
z"TestArgus.test_argus_phi_small_chizchi, expected))ro   )g-\/?g+p7c?g5Ϧ\?)ro  )g
f?gi{?ٸ?gZ@7?)re   )gB	?g]?gR{?)rq   )glͅw?g,?g[Z=?)r  )gz,?g]?gѪ1?)r  )g8<?gE-?gI?)r  )g~7?g7B.?g9?)r  )g;?g9B.?g}5?c                 C   *   t g d}ttj|||dd d S )Nre   ro   rm  r   rx   )rl   r   r   r3   r  r<   r   rH  rc   rC   r.   r.   r/   test_pdf_small_chi     zTestArgus.test_pdf_small_chi))ro   )gQ߹?e?grJ,?g򺗄?)ro  )gΎd?g?gh?)re   )g|
o?gvb?g+@?)rq   )g̈́On?ge?gC|[3?)r  )g!?m?g{jiH?gu53?)r  )g~m?g0-.?g3?)r  )g~m?g7;B.?gŗ3?)r  )g~m?g9B.?gŗ3?c                 C   r  )Nr  r  rx   )rl   r   r   r3   r  rI  r  r.   r.   r/   test_sf_small_chi  r  zTestArgus.test_sf_small_chi))ro   )g+&?gk?gμm/?)ro  )g?CL\f?g^N?g]AͭR?)re   )ga>$?g;Lf?gaW?)rq   )gx?g 43n?gwY?)r  )go7🤎?g
+-oGn?gIQ9Y?)r  )gT?gGn?g@̋Y?)r  )gU?g{Gn?giG͋Y?)r  )gDU?g {Gn?gH͋Y?c                 C   r  )Nr  rS  rx   )rl   r   r   r3   r  rF   r  r.   r.   r/   test_cdf_small_chi  r  zTestArgus.test_cdf_small_chi))ro   )gQ)?g6{?rS  )gB`"۹?)g?g8%?r  )re   )g388?gV%?r   )rq   )g*j?gRS%?r   )r  )g!|?gZ%?r   )r  )gy[|?gG%?r   )r  )g"3|?gW%?r   )r  )g!3|?gW%?r   c                 C   s"   t jj |dd}t|||d d S )Nra  r  rx   )r3   r  r   )r   rH  rc   ry   r   r.   r.   r/   test_stats_small_chi  s   zTestArgus.test_stats_small_chiN)r  r  r  r  r   r  r  r   r  rU  r@  r  r  r  r  r  r.   r.   r.   r/   r  G  sT    

	


	






r  c                   @   s   e Zd Zdd Zdd Zejjddejdg dejd	g d
ejdg ddd Z	ejd	g d
ejdg ddd Z
dS )TestNakagamic                 C   s$   d}d}t j||}t|d d S )Nr  r  gM+)r3   nakagamir   r   )r   r  rC   rp  r.   r.   r/   rq    s   zTestNakagami.test_logpdfc                 C   sD   d}d}t j||}t|ddd t j||}t||dd d S )Nr  r  g"S+:r   rx   )r3   r  rI  r   rN  )r   r  r  rI  r  r.   r.   r/   r    s   zTestNakagami.test_sf_isfz+Fit of nakagami not reliable, see gh-10908.r  r  )r  r  r~  r8   )rr   rg   #   r9   )r  r~   r  c           
         s   d t jj |||ddt j\}}}t||dd t||dd t||dd fdd} fdd	} fd
d}	t||||ddd t||||ddd t|	|||ddd d S )Nrh   9  r   r  r8   r9   r   ro  rx   c                    s<   d|  d t d |   d|  |d  t  |   S )NrZ  r   r:   rl   r  r  r8   r9   )r	  r.   r/   	dlogl_dnu  s   z(TestNakagami.test_fit.<locals>.dlogl_dnuc                    sN    dt |  td|   dt t | |   t | | d  S )Nr   r   r:   )rl   r:  r   r  r  rv  r	  r.   r/   
dlogl_dloc  s
   z)TestNakagami.test_fit.<locals>.dlogl_dlocc                    s2   d  |  | d|  |d  t | d   S )NrZ  r:   r   r  r  r  r.   r/   dlogl_dscale  s    z+TestNakagami.test_fit.<locals>.dlogl_dscaler   r  r   )r3   r  r   r   r   )
r   r  r8   r9   nu_estloc_est	scale_estr  r  r  r.   r  r/   r    s   zTestNakagami.test_fitc                 C   s   d}d}t jj||||dd}t jj||d\}}}t|}	tt|| d }
t||dd t||	dd t||
dd d S )	Nro   rh   r  r  r  r:   rP  rx   )	r3   r  r   r   rl   r+  r  r,  r   )r   r8   r9   r  r&  r	  r  r  r  loc_theo
scale_theor.   r.   r/   test_fit_nu  s   
zTestNakagami.test_fit_nuN)r  r  r  rq  r  r   r  r  r  r  r  r.   r.   r.   r/   r    s    r  c                   @   r6  )TestWrapCauchyc                 C   sr   t ddgddgg}t dgdgg}tj||}|jdks"J dd	 t ||fD }t| |d
d d S )NQ?r  ro   r  r  r  r  c                 S   s   g | ]\}}t j||qS r.   )r3   
wrapcauchyrF   )rK   r  ri  r.   r.   r/   rM   $  s    z>TestWrapCauchy.test_cdf_shape_broadcasting.<locals>.<listcomp>r   rx   )	rl   r   r3   r  rF   r   nditerr   re  )r   rB  rC   r'  scalar_valuesr.   r.   r/   test_cdf_shape_broadcasting  s   z*TestWrapCauchy.test_cdf_shape_broadcastingc                 C   s"   t jtjd}t|ddd d S )Nr  ro   r  rx   )r3   r  rF   rl   r>   r   r3  r.   r.   r/   test_cdf_center(  rQ  zTestWrapCauchy.test_cdf_centerc                 C   s   d}d}d}t j||g|}d| d|  }t|d t|t|d  tj  t|d dt|ttj|d   tj   d S )Nr  r  r  r   r   r:   )r3   r  rF   r   rl   arctantanr>   )r   r  r  rB  r'  crr.   r.   r/   r  ,  s   (6zTestWrapCauchy.test_cdfN)r  r  r  r  r	  r  r.   r.   r.   r/   r    s    r  c                  C   sV   G dd dt j} | dd}ttdd |  W d    d S 1 s$w   Y  d S )Nc                   @   r/  )z/test_rvs_no_size_error.<locals>.rvs_no_size_genc                 S   r   r   r.   r   r.   r.   r/   _rvs9  r  z4test_rvs_no_size_error.<locals>.rvs_no_size_gen._rvsN)r  r  r  r  r.   r.   r.   r/   rvs_no_size_gen8  r  r  rvs_no_sizer  z_rvs\(\) got (an|\d) unexpectedr   )r3   rP   r  r   r   )r  r  r.   r.   r/   test_rvs_no_size_error6  s
   

"r  zdistname, argsc                 C   s   | t v rtd|  d tt| }t|tjrQt|dkr1|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   rg  r   r3   r   rP   r   supportr   rl   r   )r_  r   rL   a0b0r  r  a1b1r,   r-   r.   r.   r/   test_support_gh13294_regressionB  s"   

r  c                  C   sX  t jg dg d\} }ttj tj tj tjg}ttjtjtjtjg}t| | t|| | j|jks<J |j|jksDJ t jg g \}}tg tg }}t|| t|| |j|jksjJ |j|jksrJ t jg ddg\}}	tdtjg }
tdtjg }t||
 t|	| |j|
jksJ |	j|jksJ d S )N)r   r   r   r   )r   r   r   r  r  rG  )	r3   r  r  rl   r   r   r   r   r   )r  r  ex_a0ex_b0r  r  ex_a1ex_b1rJ  ry  ex_a2ex_b2r.   r.   r/   ,test_support_broadcasting_gh13294_regression]  s(    





r  c                  C   sn   ddg} dgdgdgg}t tj| |ddgddgddgg td} td}tj| |jdks5J d S )	Nrt   r  rs   r  r  r  rI   r  )r   r3   r  r  rl   rd  r   r7   r.   r.   r/   *test_stats_broadcasting_gh14953_regressionv  s   &

r   rn  )gn!	g:I"<)gQ	@gE?c                 C   s*   t tj| | t tj|  | d S rj   )r   r3   cosinerF   rI  )rC   rc   r.   r.   r/   test_cosine_cdf_sf  s   r"  zp, expected))r  gkM6O)r_  g0ӭ!	)g333333?g;'u(@c                 C   s*   t tj| | t tj| |  d S rj   )r   r3   r!  rA  rN  )r'  rc   r.   r.   r/   test_cosine_ppf_isf  s   r#  c                  C   s0   t jtj tjg} t| tj tj g d S rj   )r3   r!  r   rl   r>   r   r   )rp  r.   r.   r/   test_cosine_logpdf_endpoints  s   r$  c                  C   sT   dd t D } dd tD }| |ksJ dd tD }dd tD }||ks(J d S )Nc                 S   s   h | ]\}}t |tr|qS r.   )r   rU   rK   r  rj  r.   r.   r/   	<setcomp>  s    
z*test_distr_params_lists.<locals>.<setcomp>c                 S      h | ]\}}|qS r.   r.   r%  r.   r.   r/   r&    rN   c                 S   r'  r.   r.   r%  r.   r.   r/   r&    rN   c                 S   r'  r.   r.   r%  r.   r.   r/   r&    rN   )r   r   r   r   )discrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamesr.   r.   r/   test_distr_params_lists  s   r,  c                   C   sB   t jjddd t jjddddksJ t jdddksJ d S )Nr   r@   r  rG  )rA  r,   r  )r3   r6  _statsr  r|  r.   r.   r.   r/   test_moment_order_4  s   r.  rj   )rk  r(  rO  r  r  pathlibr   r  r  r1  numpy.testingr   r   r   r   r   r   r	   r
   r   r   r   r   r  r=   rl   r   r   numpy.lib.recfunctionsr   r2   r   scipy._lib._utilr   r  r   r   r   r   scipy.statsr3   !scipy.stats._distn_infrastructurer   scipy.stats.distributionsscipy.specialr   r   r   scipy.stats._distr_paramsr   r   test_discrete_basicr   r   scipy.stats._continuous_distnsr    r!   scipy.optimizer"   r#   	itertoolsr$   flagsoptimizer\  r4  r  r  r0   r5   rE   rG   rd   ri   rm   rp   r  r  r|   r   r   r   r   r   r   r   r   r  r0  r7  r<  rF  rV  r^  r  r  r  r  r  r  r  r  rm  rr  r  r  r  r  r  r  rB  rR  rc  rm  r  r  r  r  objectr  r  r  r  r  r  r  r   r  r-  r  r>   rW  r4  rX  re  ri  rl  r  r  r  r  r  r  r  r  r  r  r  rZ  r^  rc  rd  r  r  r  r  r  r  r  r  r%  r(  r1  rS  rX  rm  rp  rt  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  rP   r  r  r  r  r  rJ  r`  ra  re  rh  rj  rk  rn  rp  rq  rs  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r"  r#  r$  r,  r.  r.   r.   r.   r/   <module>   s~   0



.	
H $d>*# h 5U() wM?* $ lH)+


 !5		$hv-n*     E
 p i <=%EC,s ^K E	
&	
(

	x;	,G.
"

a yZ

