o
    Ge                    @   s
  d Z ddlZddlZddlZddl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 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$m%Z% dd
l&m'Z' ddl(Zddl)m*Z*m+Z+m,Z, ddl-m.Z.m/Z/ ddl0m1Z1m2Z2 ddl3m4Z4m5Z5 ddl6m7Z7m8Z8 ddl9m:Z: ej;j<dkZ=ejdkoe> dkZ?ddgZ@ddddZAdd ZBdd ZCdd ZDdd ZEd d! ZFd"d# ZGd$d% ZHejIJd&g d'd(d) ZKd*d+ ZLd,d- ZMejIJd.g d/d0d1 ZNG d2d3 d3ZOG d4d5 d5ZPG d6d7 d7ZQG d8d9 d9ZRG d:d; d;ZSG d<d= d=ZTG d>d? d?ZUG d@dA dAZVG dBdC dCZWG dDdE dEZXG dFdG dGZYG dHdI dIZZG dJdK dKZ[G dLdM dMZ\G dNdO dOZ]G dPdQ dQZ^G dRdS dSZ_G dTdU dUZ`G dVdW dWZaG dXdY dYZbG dZd[ d[ZcG d\d] d]ZdG d^d_ d_ZeG d`da daZfG dbdc dcZgG ddde deZhG dfdg dgZiG dhdi diZjG djdk dkZkG dldm dmZlG dndo doZmG dpdq dqZnG drds dsZoG dtdu duZpdvdw Zqdxdy Zrdzd{ ZsG d|d} d}ZtG d~d dZuG dd dZvG dd dZwG dd dZxG dd dZyG dd dZzG dd dZ{G dd dZ|G dd dZ}G dd dZ~G dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZdd 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 dZG dd dZG dd dZG ddÄ dÃZG ddń dŃZddǄ ZddɄ Zdd˄ Zdd̈́ ZejIje=ddύddф Zddӄ ZddՄ Zddׄ Zddل Zddۄ Zdd݄ Zdd߄ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZejIJddeddgfdedd gfdeddgfdeddgfgdd Zd	d
 Zdd Zdd Zdd Zdd ZG dd de%jZG dd de%jZG dd de%jZG dd de%jZG dd dZG dd dZejIje=ddύd d! Zd"d# Zd$d% Zd&d' ZÐd(d) ZĐd*d+ ZŐd,d- ZƐd.d/ Zǐd0d1 ZȐd2d3 Zɐd4d5 Zʐd6d7 Zːd8d9 Z̐d:d; ZejIJd<d=d=g d>fd?d@g d>fdAdBg dCfgdDdE ZΐdFdG ZG dHdI dIZАdJdK ZG dLdM dMZG dNdO dOZG dPdQ dQZԐdRdS ZejIJdTe2e/ dUdV Z֐dWdX ZejIJdYdZd[gd\d] ZejIJd^g d_d`da Zِdbdc ZdS (e  z!
Test functions for stats module
    N)	assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_assert_warnsassert_array_lesssuppress_warnings)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,   n/var/www/html/SPIRAL.web.tool/spiral_venv/lib/python3.10/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattr3   s   r.   c                   C   s   t tjjd d S )Nf_gen)r.   scipystatsdistributionsr,   r,   r,   r-   test_api_regression9      r3   c                 C   s8   t j| ||d}t||||dtj |   d S )Nlocscale   )r1   vonmisesr   pdfnumpypikLsxvmr,   r,   r-   check_vonmises_pdf_periodic>   s   (rC   c                 C   s@   t j| ||d}t||d ||dtj |  d  d S )Nr5   r   r8   )r1   r9   r   cdfr;   r<   r=   r,   r,   r-   check_vonmises_cdf_periodicC   s   0rE   c                  C   s`   t tjjj} dd tD }dd tD }g d}|| | }t tdd |}| |ks.J d S )Nc                 S      g | ]}|d  qS r   r,   .0distr,   r,   r-   
<listcomp>J       z0test_distributions_submodule.<locals>.<listcomp>c                 S   rF   rG   r,   rH   r,   r,   r-   rK   K   rL   )rv_discreterv_continuousrv_histogramentropytrapzc                 S   s   t | d S )N<)str
startswithr@   r,   r,   r-   <lambda>R       z.test_distributions_submodule.<locals>.<lambda>)setr0   r1   r2   __all__r   r   filter)actual
continuousdiscreteotherexpectedr,   r,   r-   test_distributions_submoduleH   s   r`   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<   rC   rE   )r>   rA   r,   r,   r-   test_vonmises_pdf_periodicW   s   re   c                   C   s&   t tjjtj  t tjjtj d S N)r   r1   vonmises_liner*   npr<   r+   r,   r,   r,   r-   test_vonmises_line_supportc   s   ri   c                  C   s   t d} t| dd d S )N   r         ?)r1   r9   r   rD   )rB   r,   r,   r-   test_vonmises_numericalh   s   
rl   zx, kappa, expected_pdf))ra   {Gz?g|65?)ra         9@g?U?)ra   rj   g"?)       @rm   gDfI?)ro   rn   g1<)ro   rj           c                 C   s    t j| |}t||dd d S )NV瞯<rtol)r1   r9   r:   r   )rA   kappaexpected_pdfr:   r,   r,   r-   test_vonmises_pdfw   s   rv   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.
    rq   rr   N)fitsupertyperh   allclose)rJ   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   r8      z3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:r8   )extra_keywordzToo many positional arguments.r   )shapeslensplitdictziprh   arangepytestr   RuntimeErrorrw   naninf	TypeError)rJ   paramnshapes	all_fixedr{   r,   r,   r-   assert_fit_warnings   s6   ""r   rJ   )alpha	betaprimefatiguelifeinvgammainvgauss
invweibull	johnsonsblevylevy_llognormgilbrat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   getattrr1   r   r:   r*   r   logpdfrh   r   r+   )rJ   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  rh   randomseed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 )N      rd   sizer8   2   
AllInteger   .   r'   r   )r1   randintrvsr   r;   allr   shapedtypecharr   
isinstance
ScalarTypereprry   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_wherer1   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   rd   r   r         ?      @r   rn      decimal)	rh   linspacer;   floorselectr1   r   rD   r   )r   rA   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 Nrc         ?r   r   r   r   r   )r1   binomr   r   r;   r   r   r   r   r   r   intndarrayr   r,   r,   r-   r      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 )Nrd   r   r   r   rq   rs   atol)r1   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 )Nr8   rk   )      ?rk   r   rp   r   )	r1   r   rh   r   sumr   rP   r   r   )r   r+   
expected_p
expected_hhr,   r,   r-   test_entropy   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errorr8   r   )np)	warningscatch_warningssimplefilterRuntimeWarningr   r1   r   meanstdr   r,   r,   r-   test_warns_p0  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   )r1   arcsiner:   r   rh   r   r   r   r,   r,   r-   test_endpoints  s   zTestArcsine.test_endpointsN)r   r   r   r  r,   r,   r,   r-   r  	      r  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     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   )r1   	bernoullir   r   r;   r   r   r   r   r   r   r   r   r   r,   r,   r-   r     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   rp   r   )r1   r
  rh   logrP   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-   r	        r	  c                   @   r  )TestBradfordc                 C   s:   d}t dd}tj||}tj||}t|| d S )Nra   )rh   logspacer1   bradfordrD   ppfr   )r   crA   qxxr,   r,   r-   test_cdf_ppf3  s
   zTestBradford.test_cdf_ppfN)r   r   r   r  r,   r,   r,   r-   r  1  r  r  c                   @       e Zd ZdZdd Zdd ZdS )TestChignT9;c                 C   s"   t jdd}t|| jdd d S )Nrc      rq   rr   )r1   chisfr   CHI_SF_10_4r   r@   r,   r,   r-   test_sfA  s   zTestChi.test_sfc                 C   s"   t j| jd}t|ddd d S )Nr  rc   rq   rr   )r1   r  isfr  r   r   rA   r,   r,   r-   test_isfE     zTestChi.test_isfN)r   r   r   r  r  r"  r,   r,   r,   r-   r  ;  s    r  c                   @   r  )
TestNBinomc                 C   r   r   r   r   r,   r,   r-   r   K  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   )r1   nbinomr   r   r;   r   r   r   r   r   r   r   r   r   r,   r,   r-   r   N  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   rh   expr1   r%  logpmfr   r0   r   )r   r   r,   r,   r-   r   Y  s
   zTestNBinom.test_pmfN)r   r   r   r   r   r   r,   r,   r,   r-   r$  J  r  r$  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   c  r   zTestGenInvGauss.setup_methodc                 C   :   t dd}t |jddd|j\}}t|dkd d S )Nffffff@      ?  r   r   random_state皙?Tr1   geninvgausskstestr   rD   r   r   gig_r   r,   r,   r-   test_rvs_with_mode_shiftf     z(TestGenInvGauss.test_rvs_with_mode_shiftc                 C   r)  )N?r   r,  r   r-  r/  Tr0  r3  r,   r,   r-   test_rvs_without_mode_shiftm  r7  z+TestGenInvGauss.test_rvs_without_mode_shiftc                 C   r)  )Nra   皙?r,  r   r-  r/  Tr0  r3  r,   r,   r-   test_rvs_new_methodt  r7  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 )Nr,  r   r-  r   r/  )r1   r1  r   r2  rD   )r   r+   r4  r   r,   r,   r-   my_ks_check}  s   z4TestGenInvGauss.test_rvs_p_zero.<locals>.my_ks_checkr   r:  Tr8  r+  )r   )r   r<  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      r8   rc   r   r-  r   r+  )r   r1   r1  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 )Nr,        r   r   )r   r   r+   r.  r   r   333333?Trd   rm   rc   )r   r+   r7   )r1   r1  r   r   r2  rh   r   r:   r   r   rD   )r   igmurA   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?rm   r   rc   rk   r   )rh   r   r   r   r1   r1  r:   )r   vals_RrA   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   rk   g    >Ar   r8   )r   r1   r1  r:   r   r,   r,   r-   test_pdf_zero  s   zTestGenInvGauss.test_pdf_zeroN)r   r   r   r   r   markslowr6  r9  r;  r=  r?  rG  rI  rJ  r,   r,   r,   r-   r(  b  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?r8   r8   r   rk   r+  r5   rc   r   vIh%<=r   rs   )rh   r   r1   genhyperbolicr   r   r:   
r   rH  lmbdar   betarD  deltar   ghrA   r,   r,   r-   
test_pdf_r     
zTestGenHyperbolic.test_pdf_rc           
      C   rO  )
N)
g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?rP  rQ  r5   rR  rc   r   ư>rT  )rh   r   r1   rU  r   r   rD   rV  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@rP  rQ  c                    s$   g | ]}t j d |qS )r5   )r1   rU  moment)rI   ir   rY  rD  r,   r-   rK     s    z4TestGenHyperbolic.test_moments_r.<locals>.<listcomp>r   r   r   rS  rT  )ranger   )r   rH  rW  r   rX  vals_usr,   ra  r-   test_moments_r  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 )	NrP  rQ  r5   r,  r   r-  r/  T)r1   rU  r2  r   rD   r   )
r   rW  r   rX  rD  rY  r   rZ  r5  r   r,   r,   r-   r     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   rc   r8   r   r5   rm   Gz?r   r]  rT  )rh   r   float_powerfinfofloat32epssqrtr1   rU  r  newaxisr   r:   t)	r   dfr   rX  rD  rY  r   rZ  rA   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 )
Nr@  r   )r   r   r5   rm   re  r   r]  rT  )rh   rg  rh  ri  r1   rU  r   r  rk  r   r:   cauchy)	r   rW  r   rX  rD  rY  r   rZ  rA   r,   r,   r-   test_pdf_cauchy  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 )NrR  rc   )r   r   r   r5   r     r   r   r   dy=rT  )rh   r   rg  rh  ri  r1   rU  rk  r   r:   laplace)	r   r6   rY  rW  r   rX  r   rZ  rA   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   rq  rc   r      rd   r@  r5   rm   re  r   )r*   r+   r6   r7   rS  rT  )rh   r   rf  rb  r1   rU  r  rk  r   r:   norminvgauss)	r   r   rX  rY  rD  rW  r   rZ  rA   r,   r,   r-   test_pdf_norminvgauss6  s   (

z'TestGenHyperbolic.test_pdf_norminvgaussN)r   r   r   r   r[  r^  rd  r   rn  rp  rt  ry  r,   r,   r,   r-   rN    s    rN  c                   @   r   )TestNormInvGaussc                 C   r   r   r   r   r,   r,   r-   r   N  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   rk   r*   r+   &.>r   )rh   r   r1   rx  rD   r   )r   r_cdfx_testvals_cdfr,   r,   r-   
test_cdf_RQ  s   zTestNormInvGauss.test_cdf_Rc                 C   r{  )N)gp϶>g\H55$?geСt&?go NiH?g]u>r|  r   rk   r  r  r  )rh   r   r1   rx  r:   r   )r   r_pdfr  vals_pdfr,   r,   r-   rI  ]  s   zTestNormInvGauss.test_pdf_Rc                 C   s   d\}}t |d |d  }|| |d |d  d| |t |  ddd|d  |d    | f}t|tjj||dd d S )	Nr   rk   r8   r         @r   r  mvskmoments)rh   rj  r   r1   rx  )r   r*   r+   gammav_statsr,   r,   r-   
test_statse  s   (zTestNormInvGauss.test_statsc                 C   s@   d\}}t g d}tj|||}t|tj||| d S )Nr  MbP?rk   +?)rh   r   r1   rx  r  r   rD   )r   r*   r+   r  r   r,   r,   r-   test_ppfl  s   zTestNormInvGauss.test_ppfN)r   r   r   r   r  rI  r  r  r,   r,   r,   r-   rz  M  s    rz  c                   @   sL   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dS )TestGeomc                 C   r   r   r   r   r,   r,   r-   r   t  r   zTestGeom.setup_methodc                 C      t jjddd}tt|dk tt|dk t|jjt	d v  t jd}tt
|t t dd}tt
|tj t|jjt	d v  d S )Nr   r   r   r   r   r   )r1   geomr   r   r;   r   r   r   r   r   r   r   r   r   r,   r,   r-   r   w     zTestGeom.test_rvsc                 C   s$   t jg dd}t|g d d S )Nr   rk   )rk   r         ?)r1   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   rk   rq   r   r   r   rp   )rh   r  r1   r  r   r'  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   rk   rk   r   g      ?r   )r1   r  rD   r  r   r   r   r   vals_sfr_   r,   r,   r-   test_cdf_sf  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   rk   r  )	r1   r  logcdflogsfr   r   rh   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  rk   )r   ro   r  )r1   r  r  r   r   r   r   r_   r,   r,   r-   r       zTestGeom.test_ppfc                 C   s   t tjddddd d S )N#B;r   +=r  )r   r1   r  r  r   r,   r,   r-   test_ppf_underflow  s   zTestGeom.test_ppf_underflowN)r   r   r   r   r   r   r  r  r  r  r  r,   r,   r,   r-   r  s  s    
r  c                   @   r  )
TestPlanckc                 C   r   r   r   r   r,   r,   r-   r     r   zTestPlanck.setup_methodc                 C   r  )Nr   r   )g|dy?g8'\>ggrU!>)r1   planckr  r   r   r  r,   r,   r-   r    s   zTestPlanck.test_sfc                 C   r  )N)     @@     @@     p@r  )g    P.g    h>g    TF)r1   r  r  r   r   r  r,   r,   r-   
test_logsf  r  zTestPlanck.test_logsfN)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 )TestGennormc                 C   0   g d}t j|d}t j|}t|| d S Nr   r   )r1   gennormr:   rs  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   r8   g;f?r7   )r1   r  r:   normr   r  r,   r,   r-   	test_norm     zTestGennorm.test_normN)r   r   r   r  r  r,   r,   r,   r-   r        r  c                   @   r  )TestHalfgennormc                 C   r  r  )r1   halfgennormr:   exponr   r  r,   r,   r-   
test_expon  r  zTestHalfgennorm.test_exponc                 C   r  r  )r1   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
(?r8   )r1   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                   @   r  )TestLaplaceasymmetricc                 C   s6   t g d}tj|d}tj|}t|| d S r  )rh   r   r1   laplace_asymmetricr:   rs  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   r8   r   )rh   r   r1   r  r:   r   )r   r  rt   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   rc   r8   ra   gMbp?r:  gV-?皙?gMb`?)rh   r   r  r1   r  r:   rD   r  r  r   r   concatenate)r   r  rt   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dZ
ejddd Zdd Zdd Zdd Zdd ZdS )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r@  r   -C6?rk   gH.?r   r8         r   r      r8   r5   r   fO?l@r   )r1   	truncnormr  rh   r   r   r   r  r,   r,   r-   test_ppf_ticket1131  
   
z!TestTruncnorm.test_ppf_ticket1131c              	   C   r  )Nr  r  r   r   r  r8   r5   r   r  r  r   )r1   r  r   rh   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)irR  r   r   rc   r   )rc      r1   r  r   r   minmaxr   lowhighrA   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)rd   rb   r   r   rc   r   )    )'  i'  )ii)r1   r  r   r   r  r  rS   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   r  r  ro   r   r   r   r   r   r   rp   rp   )r   d._MT
@BKg?r   r   )r   r  r  r   r   r8   rk   r   rk   r   gĖy	@gdv*?g,mj%V?r   )rh   r   r   r1   r  rD   r  r:   r   r  r  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_values0  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'   (   ro   r  r  )r   pGC@Ff<r   r   )r   r  r  r   r   r8   rk   r  gEC@g i?gspXio)>r   r  rv  )rh   r   r   r1   r  rD   r  r:   r   r  r  r  r   )r   r  r  r  r  r  r  r  r  r  r  r  r   r  r:   xvals2r,   r,   r-   test_gh_9403_medium_tail_valuesS  sd   




 z-TestTruncnorm.test_gh_9403_medium_tail_valuesr  c                 C   s^   |d d \}}}}t jj ||dd\}	}
}}t|	| t|
| t|||d t|| d S )Nr  r  r  r   )r1   r  r   )r   r*   r+   r_   	decimal_sm0v0s0k0mvr@   r>   r,   r,   r-   _test_moments_one_range  s   

z%TestTruncnorm._test_moments_one_rangez&reduced accuracy with 32bit platforms.c                 C   s   |  ddg d |  ddg d |  ddg d |  d	d
g d |  dtjg d |  tj dg d |  ddg d |  ddg d |  ddg d |  ddg d | j ddg ddd |  ddg d |  dd g d! d S )"Nr   )r   r   rp   rp   rR  rc   r  r   )rp   gMFmz%?rp   gſr8   )rp   ghI}?rp   gHNMr   )gQ63E?nl$A?gv1"D?<8L?)gQ63Er  gv1"Dr  rv  )gU*? bn?gnA?!c3TXʿr   )gU*ҿr  gnAr  )gH$7"g͢xr?gN8`gp=#K@r  i)gif3g6oRf?gg+15|@i)go=gqXS?gCØsgm@   )r  r  r  )gGC&SԍuE?gynw@r  r  )gGC@r  gy?r  )r  rh   r   r   r,   r,   r-   test_moments  s   	zTestTruncnorm.test_momentsc                 C   s0   t jj dtjdd\}}t|d t|d d S )Nr   mvr  g e3E?g:&A?)r1   r  rh   r   r   )r   r  r  r,   r,   r-   test_9902_moments  s   
zTestTruncnorm.test_9902_momentsc                 C   sV   d\}}t jj||dddd}t||   k o%|   k o%|k  d S    d S )N)rc   r   r   r   rc   r   r  r  r,   r,   r-   test_gh_1489_trac_962_rvs  s   8z'TestTruncnorm.test_gh_1489_trac_962_rvsc                 C   s   ddt j dt j t j dddddg}dddt jddddd	t jt jg}tjj||dt|fd
}t |dt|fks=J tt ||j	ddk tt |j
dd|k d S )NrR  rc   r}  ir  r  r   r  -   r   r   )axis)rh   r   r1   r  r   r   r   r   r   r  r  r  r,   r,   r-   test_gh_11299_rvs  s   & zTestTruncnorm.test_gh_11299_rvsc                 C   s.   t tjdrtjjdddtj d d S d S )Ndefault_rngrR  r}  r   r-  )r)   rh   r   r1   r  r   r$  r   r,   r,   r-   test_rvs_Generator  s
   
z TestTruncnorm.test_rvs_GeneratorN)r  )r   r   r   r   r  r  r  r  r  r
  r  r   rK  xfail_on_32bitr  r  r   r#  r%  r,   r,   r,   r-   r    s    
#
/

7
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
=)rd   gh@X)r  gh<c                 C   s$   d}t j||}t||dd d S )Nr+  rS  rr   )r1   genlogisticr   r   )r   rA   r_   r  logpr,   r,   r-   test_logpdf  s   zTestGenLogistic.test_logpdfN)r   r   r   r   rK  parametrizer+  r,   r,   r,   r-   r'    s    r'  c                   @   rM  )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 )Nrq  rc   r   r   r   r   r   )r1   	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     r8   gkㅒP?r  )r1   r.  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   r8   r   r   r  rp   )r   r1   r.  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   r1   r.  rD   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@r  gffffff@g@r        @     @c                    s"   g | ]}t j   |qS r,   )r1   r.  r  )rI   eatenorangespearsquantiler,   r-   rK     s    z1TestHypergeom.test_precision2.<locals>.<listcomp>)r   gpR(g㘍R2gJޱ p9g?Mf=
G?r   r   gƠ>rT  )g     @r;  g     @g     @g     @)r   rA  g)9g"1)rh   r   r   r1   r.  r  )r   fruits_eatenresr_   	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 )Nr  r   r   r   rp   )	r1   r.  rP   rh   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   @  iX  ,  g_7	j$r   )r1   r.  r  r   r   r>   r0  r   r1  resultr_   r,   r,   r-   r  2  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   rI  rJ  rK  g)\Ur   r   r  rL  r   rM  g*@Vr   }      r/  gר)r  r  r  )r1   r.  r  r   rh   r   fullrN  r,   r,   r-   test_logcdfJ  s8   zTestHypergeom.test_logcdfN)r   r   r   r   r   r5  r6  r7  rG  r   r  rS  r,   r,   r,   r-   r-    s    
	r-  c                   @   s6   e Zd Zejdddgdd Zdd Zdd	 Zd
S )TestLoggammazx, c, sf)r  r+  gQOu3;)r  rd   g\Z{0c                 C   s<   t j||}t||dd t j||}t||dd d S N-q=rr   )r1   loggammar  r   r   )r   rA   r  r  r@   yr,   r,   r-   test_sf_isf  s   zTestLoggamma.test_sf_isfc                 C       t jdd}t|ddd d S )Nir8   g     @r  rr   )r1   rW  r   r   )r   lpr,   r,   r-   r+    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)rk   g"~jg46<@g oŏ      @r   g	h"lxgQ?gZd;333333@g      (@g{/L@g??gгYҿgh|?5?rv  r   msvkr  r  r   )rh   r   reshaper1   rW  r   )r   tabler  r   varskewkurtcomputedr,   r,   r-   r    s   zTestLoggamma.test_statsN)	r   r   r   r   rK  r,  rY  r+  r  r,   r,   r,   r-   rT  y  s    

rT  c                   @   st   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zej	
dejdgdd Zej	
dejdgdd ZdS )TestLogisticc                 C   2   t dd}tj|}tj|}t|| d S Nr  rq  )rh   r   r1   logisticrD   r  r   r   rA   rX  r  r,   r,   r-   r       zTestLogistic.test_cdf_ppfc                 C   rf  rg  )rh   r   r1   rh  r  r   r   ri  r,   r,   r-   rY    rj  zTestLogistic.test_sf_isfc                 C   s4   d}d}t tjd| | t tj|| d S )Ng      <gg|EA@r   )r   r1   rh  r  r   )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   rc   )gm\  .g9B.gO& $rS  rr   )r1   rh  r   r   )r   r*  r_   r,   r,   r-   test_logpdf_basic  s   zTestLogistic.test_logpdf_basicc                 C   s"   t jddg}t|ddg d S )Nrj   i)r1   rh  r   r   r   r*  r,   r,   r-   test_logpdf_extreme_values  s   z'TestLogistic.test_logpdf_extreme_valuesloc_rvs,scale_rvsr8   c                 C   sR   t jjd||d}dd }t|t j||fdj}t j|}t||dd d S )Nrd   r   r6   r7   c                 S   s   | \}}t |}tt|| | dt|| |   |d  }t|| | t|| | d t|| | d   | }||fS Nr   r8   )r   rh   r   r&  )inputr{   r*   r+   r   x1x2r,   r,   r-   r|     s   z#TestLogistic.test_fit.<locals>.funcrA  gKH9r  )r1   rh  r   r    	_fitstartrA   rw   r   )r   loc_rvs	scale_rvsr{   r|   expected_solution
fit_methodr,   r,   r-   test_fit  s   
zTestLogistic.test_fitc                 C   H   t jjd||d}|t j|fg}t j|i d }tt j|| d S Nrd   rq  r   )r1   rh  r   rv  _reduce_funcr   )r   rw  rx  r{   r   r|   r,   r,   r-   test_fit_comp_optimizer  s   z$TestLogistic.test_fit_comp_optimizerN)r   r   r   r  rY  rl  rm  ro  r   rK  r,  rh   r   randr{  r  r,   r,   r,   r-   re    s    
re  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   )r1   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 )Nr  r  g&Y3)r1   r  r   r   r   r  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  ?)r1   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                   @   sp   e Zd Zdd Zejdejej	gejde
jdgdd Zejdejd	fej	d
fgdd ZdS )TestGumbel_r_lc                 C   r   r   r   r   r,   r,   r-   r     r   zTestGumbel_r_l.setup_methodrJ   rp  r8   c                 C   s@   |j d||d}|||fg}||i d }t||| d S r}  )r   rv  r~  r   )r   rJ   rw  rx  r{   r   r|   r,   r,   r-   r    s   z&TestGumbel_r_l.test_fit_comp_optimizerz	dist, sgnr   rv  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]  rr   )rh   r   rw   r   )r   rJ   sgnzr6   r7   r,   r,   r-   r{    s   zTestGumbel_r_l.test_fitN)r   r   r   r   r   rK  r,  r1   gumbel_rgumbel_lrh   r   r  r  r{  r,   r,   r,   r-   r    s    
r  c                   @   s   e Zd Zdd Z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ejdddgejd	d
dgejdddg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   rk   r  r  r   r+  r  ro         @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   r1   paretor   rh   r   r   r   rj  r   r  r  r@   r>   r,   r,   r-   r  )  s`   











$zTestPareto.test_statsc                 C   s:   d}d}d}t jj||d|d}|| | }t|| d S )Ng    eAr8   r+  r   r5   )r1   r  r  r   )r   rA   r+   r7   r   r_   r,   r,   r-   r  e  s   zTestPareto.test_sfz2ignore:invalid value encountered in double_scalars	rvs_shaper   r8   rvs_locr   	rvs_scaler   c                 C   s  t jjd|||d}t jj|dddd }t jj|dddd }t jj|dddd }||  kr;|  kr;dks>J  J t jjd|||d d}t jj|dd	\}}	}
t|
d |  t|d
d
t|d  tt	|d | d     t|	d d S )Nrd   r   r+   r7   r6   r   p=
ף?r   r   )r   fix_b)r   fbr8   r   r   )
r1   r  r   rw   r   r  r   rh   r   r  )r   r  r  r  r{   shape_mle_analytical1shape_mle_analytical2shape_mle_analytical3shape_mle_a	loc_mle_ascale_mle_ar,   r,   r-   r{  m  s0   

zTestPareto.test_fitc                 C   s   t jjd|||d}|t j|fg}t j|i d }tt j|||d tt j||dd tt j||ddd tt j||d|d d	 d S )
Nrd   r  r   r  r   r  r  r8   r   r   )r1   r  r   rv  r~  r   )r   r  r  r  r{   r   r|   r,   r,   r-   test_fit_MLE_comp_optimzer  s   
z%TestPareto.test_fit_MLE_comp_optimzerc                 C   s@   t tj tttjjg ddd tttjjg dddd d S )Nr   r8   r  )r   r8   r   r   r   r  )r   r1   r  assert_raisesr   rw   r   r,   r,   r-   test_fit_warnings  s
   

zTestPareto.test_fit_warningsN)r   r   r   r  r  r   rK  filterwarningsr,  r{  r  r  r,   r,   r,   r-   r  (  s    <

r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zejddg dfdddded ejgfdddded d gfd!g d"fgd#d$ 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   rp   rp          rk   )	rh   asarrayr1   	genpareto_get_supportr   r   isposinfr   )r   r  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 )Nrp   r  r   r  r   r   rc   )
r1   r  rh   r   r   r:   r  rD   r  r  r   rvrA   r  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   rp   r   rc   r   )r1   r  rh   r   r   r:   uniformrD   r  r  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 )Nra   r  rp   r   r  )
r1   r  r   r:   rh   r   rD   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   rc   r   r   rv  r  g+rV  r  )r  r  )rh   r   r1   r  r:   r   rD   )r   rA   r  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 NrV  rm   ra   baser   r   Fendpointr   )rp   r  r  r  )rh   r   r  r   r1   r  r  r   )r   r  r  ppf0r  ppfcr,   r,   r-   test_c_continuity_ppf     z#TestGenpareto.test_c_continuity_ppfc              	   C   r  r  )rh   r   r  r   r1   r  r   r   )r   r  r  isf0r  isfcr,   r,   r-   test_c_continuity_isf  r  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 )NrV  rm   ra   r  r   r   Fr  r   )r  gC]r2rq   gV瞯Ҽrq   r  )	rh   r   r  r   r   r1   r  rD   r  )r   r  r  r,   r,   r-   test_cdf_ppf_roundtrip  s   z$TestGenpareto.test_cdf_ppf_roundtripc                 C   s    t jdddd}t|d d S )Ng    _Brm   r   r   gpEȜ)r1   r  r  r   rn  r,   r,   r-   r    s   zTestGenpareto.test_logsfzc, expected_statsr   )r   r   r8   r  r   r  gqq@rc   r8   gqq?g      ?g$I$	?rq?r  gll0@rv  )rk   UUUUUU?r   333333c                 C   s$   t jj |dd}t||ddd d S )Nr  r  rS  rq   r   )r1   r  r   )r   r  expected_statsrO  r,   r,   r-   r    s   zTestGenpareto.test_statsc                 C   s   t jd}t|ddd d S )Nr  gvǼ
  ?rS  rr   )r1   r  ra  r   )r   r  r,   r,   r-   test_var  s   zTestGenpareto.test_varN)r   r   r   r  r  r  r  r  r  r  r  r  r   rK  r,  rh   rj  r   r  r  r,   r,   r,   r-   r    s(    

	


r  c                   @   <   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestPearson3c                 C   r   r   r   r   r,   r,   r-   r   $  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 )Nra   r   r   AllFloatrk   r   )r1   r&   r   r   r;   r   r   r   r   r   floatr   r   r   r,   r,   r-   r   '  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 )Nr8   rp   ra   r:  )gtT?g+q?g?r]  r  r  ra   ND}i?r  r  rv  r   r   )r  gj?gdC?gs?g'M?)r1   r&   r:   r   rh   r   r  r,   r,   r-   r   2  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 )Nr8   r  )grE?gTp]0?g~?r]  r  r  ra   g E&"J?r  )giZ*J?gh+8w?gcK?g|<x6?gG?)r1   r&   rD   r   rh   r   r  r,   r,   r-   r   <  s   

zTestPearson3.test_cdfc                    s@   g d}dd t j|} fdd|D }t|| d S )N)r  rv  r   rk   rk   r  c                    s$   g | ]}t t|j d  qS rG   )r   r1   r&   r:   )rI   rb  neg_infx_evalr,   r-   rK   M  s    z<TestPearson3.test_negative_cdf_bug_11186.<locals>.<listcomp>)r1   r&   rD   r   )r   skewsr  int_pdfsr,   r  r-   test_negative_cdf_bug_11186F  s   z(TestPearson3.test_negative_cdf_bug_11186c                 C   sP   t jdd}t|d tt|t t jdd}t|d tt|t d S )Nr   r8   r   r]  )r1   r&   r_  r   ry   r  )r   r_  r,   r,   r-   test_return_array_bug_11746Q  s   

z(TestPearson3.test_return_array_bug_11746N)	r   r   r   r   r   r   r   r  r  r,   r,   r,   r-   r  #  s    

r  c                   @   sD   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 )
TestKappa4c                 C   sD   g d}d}dD ]}t j|||}t j|| }t|| qd S )N)rp   ra   r:  rk   r   )
gffffffr  r@  皙ɿ皙ra   r:  rk   r   ffffff?)r1   kappa4rD   r  r   r   rA   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   rc   rp   r  r   )rh   r   r1   r  rD   
genextremer   r  r,   r,   r-   test_cdf_genextremei  s   zTestKappa4.test_cdf_genextremec                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr   rc   r   rp   )rh   r   r1   r  rD   r  r   r  r,   r,   r-   test_cdf_exponr     zTestKappa4.test_cdf_exponc                 C   @   t ddd}d}d}tj|||}tj|}t|| d S )Nr}  r   rc   rp   )rh   r   r1   r  rD   r  r   r  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   rc   r  rp   )rh   r   r1   r  rD   rh  r   r  r,   r,   r-   test_cdf_logistic  r  zTestKappa4.test_cdf_logisticc                 C   r  )Nr}  r   rc   r   )rh   r   r1   r  rD   r  r   r  r,   r,   r-   test_cdf_uniform  r  zTestKappa4.test_cdf_uniformc                 C   s   t dd d S rr  )r1   r  r   r,   r,   r-   test_integers_ctor  s   zTestKappa4.test_integers_ctorN)
r   r   r   r  r  r  r  r  r  r  r,   r,   r,   r-   r  ]  s    					r  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 )Nr8   r   r   r8   rk   r  )rh   r  r1   poissonr   r   )r   ln2r   r_   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 )Nr  r   )r   r   r   ffffff?r   r   )r1   r  r   r   intervalr   )r   r   r_   r  r,   r,   r-   test_mu0  s
   
zTestPoisson.test_mu0c                 C   r  )Nrk   r   r   r   r   r   )r1   r  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   )rp   r   ro   r   r8   rk   )r1   r  r   rh   rj  r   r   )r   rD  rO  r_   r,   r,   r-   r    s    &zTestPoisson.test_statsN)r   r   r   r   r  r  r   r  r,   r,   r,   r-   r    s    	r  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   r8   r   rc   rd   r  r   rk   r   r   r8   rp   )rh   r   r0   r   gammalnr&  r1   ksoner  r  kstworD   r   )r   r   rA   v1lgelgr_   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  r  rk   r   r8   )rh   r   r   r0   r   r   r&  r1   r  r  r  r  r   )r   rA   r   r  r  r  r_   r  r,   r,   r-   r    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   r8   r  r   )r   rd      i  r  i  r  )rh   r   rj  r1   r  rD   diffr	   )r   rA   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  r  )rh   r   r1   r  rD   r  r   )r   rA   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  )rh   r   rj  r1   r  rD   r  r   )r   rA   r   r
  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  r  rk   re  r  rr   )rh   r   r1   r  rD   r  r   r   rA   r   r
  r  condr   r,   r,   r-   test_ppf_of_cdf	  s   zTestKSTwo.test_ppf_of_cdfc                 C   r  )	Nr   r   r  r  rk   r   r  rr   )rh   r   r1   r  r   r  r   )r   rA   r   r
  vals_isfr  r   r,   r,   r-   test_isf_of_sf  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  r  rk   r   )rh   r   rj  r1   r  rD   r  r   r  r,   r,   r-   test_ppf_of_cdf_sqrtn  s   zTestKSTwo.test_ppf_of_cdf_sqrtnc                 C   r  )Nr   r   r  r  rk   r  )rh   r   rj  r1   r  r  r   r   )r   rA   r   r
  r  r  r   r,   r,   r-   test_isf_of_sf_sqrtn%  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  )rh   r   r1   r  r  rD   r   )r   r  r   r
  r  r,   r,   r-   r  /  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)rc   r   rd   r  r/  r  )r   gUUUUUU?rk   r   r8   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?r8   h㈵>rr   )
rh   r   	enumerater  rj  r<   r1   r  rD   r   )r   r  ratiosr_   idxr   rA   r  r,   r,   r-   test_simard_lecuyer_table16  s   "z$TestKSTwo.test_simard_lecuyer_table1N)r   r   r   r   r   r  r  r  r  r  r  r  r  r  r  r,   r,   r,   r-   r    s    
		
r  c                   @   r  )TestZipfc                 C   r   r   r   r   r,   r,   r-   r   Y  r   zTestZipf.setup_methodc                 C   r  )Nr+  r   r   r   r   r   )r1   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*   333333@skr*   r  )r1   r  r   rh   isfiniter   r   r   r  r,   r,   r-   r  g  s
   zTestZipf.test_momentsN)r   r   r   r   r   r  r,   r,   r,   r-   r  X  r  r  c                   @   r   )
TestDLaplacec                 C   r   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 )Nr+  r   r   r   r   r  )r1   dlaplacer   r   r;   r   r   r   r   r   r   r   r   r,   r,   r-   r   u  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   r8   r  r  r  r  r  rT  )r1   r'  rh   r   r   r   r   r   )r   r*   dlr  r  r@   r>   r1  r  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 )Nro   r  )rp   rp   )r\  g      
@)rh   r  r1   r'  r   r   )r   r*   r)  r  r  r@   r>   r,   r,   r-   test_stats2  s
   

zTestDLaplace.test_stats2N)r   r   r   r   r   r  r-  r,   r,   r,   r-   r&  q  s
    r&  c                       s   e Zd Zdd Zejddej	dd gdd Z
ejddej	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)r8   r   r   r   rc   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 )Nrd   r   rD  r6   r7   r  rv  rq   rT  r   r  r  )fmur   )fix_mur   )
r1   r   r   rw   rh   r   r   r   r   r   )r   rvs_mur  r  r{   rD  r6   r7   mu_temp	scale_mlemu_mle
shape_mle1
shape_mle2
shape_mle3r,   r,   r-   r{    s.   



*zTestInvgauss.test_fitc           
         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 )	Nrd   r/  r   r8   )r   r0  r   r  r  )r1   r   r   rx   ry   rw   r   rv  r~  r   rh   r   r   r  )
r   r3  r  r  r{   	super_fitsuper_fittedinvgauss_fitr   r|   	__class__r,   r-   r    s*   




z'TestInvgauss.test_fit_MLE_comp_optimzerc                 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   r8   r  )r   r1   r   r   r   r   rw   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?rD  r  ?gfFn   gr^:g9̗?r  gx_;:g!?gٷ
??)r1   r   rD   r   r   r  )r   rD  r_   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  rB  rA  giJ.rC  gr^ߺr  gpgFgpQ^L)r1   r   r  r   r  )r   r  r  r,   r,   r-   r  	  s   	


zTestInvgauss.test_logcdf_logsf)r   r   r   r   r   rK  r,  rh   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   r8   r  )r   r8   r   rc   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 )	Nrd   rq  rq   rT  r  r   r8   r  )r1   rs  r   rh   medianr   absr   rw   r   r   r  r   r   r   )r   r  r  r{   loc_mler5  r6   r7   r,   r,   r-   r{    s*   



zTestLaplace.test_fitzrvs_scale,rvs_loc))rc   r}  )r   rc   )r:  rk   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  rq  c              	   S   s8   dt | td|  d| tt||     S )Nrv  r8   r   )r   rh   r  r   rJ  )r6   r7   r{   r,   r,   r-   llQ  s   z2TestLaplace.test_fit_MLE_comp_optimzer.<locals>.llrq   rT  )r1   rs  r   rw   rx   ry   rh   rz   )r   r  r  r{   rL  r6   r7   loc_opt	scale_optll_mlell_optr=  r,   r-   r  J  s   
z&TestLaplace.test_fit_MLE_comp_optimzerc                 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          @g      ,@r  r  r  rq   rT  rH  )rh   r   r1   rs  rw   r   )r   r{   r6   r7   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  rp   r   )r1   rs  rD   r  )r   rA   p0p1r,   r,   r-   test_sf_cdf_extremesh  s   z TestLaplace.test_sf_cdf_extremesc                 C   s.   d}t j|}t|t| d dd d S )Nr  r8   rS  rr   )r1   rs  r  r   rh   r&  )r   rA   r   r,   r,   r-   r  }     zTestLaplace.test_sfc                 C   s.   d}t j|}t|td|  dd d S )Ng}:r8   rS  rr   )r1   rs  r   r   rh   r  )r   r   rA   r,   r,   r-   r"    rV  zTestLaplace.test_isf)r   r   r   r   rK  r,  r{  r  rR  rU  r  r"  rF  r,   r,   r=  r-   rG    s    +	rG  c                   @   r  )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   r1   r   r   rh   r   r   r   r   )r   r  r_   r*   rA   rX  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   )rh   r  r1   r   rD   r  r   ri  r,   r,   r-   r    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 )Nl        r8   rd      r   r   rr   )	sysmaxsizerh   r  r1   r   r  r   r   ri  r,   r,   r-   rY    s   
zTestInvGamma.test_sf_isfN)r   r   r   rZ  r  rY  r,   r,   r,   r-   rW    s    rW  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)r8   r   r   c                 S   &   g | ]\}}}|j |jg|R  qS r,   r:   r*   rI   _f_argsr5  r,   r,   r-   rK        & z(TestF.test_endpoints.<locals>.<listcomp>c                 S      g | ]\}}}|qS r,   r,   rI   rb  rc  	_correct_r,   r,   r-   rK         )r1   fr:   r*   r   )r   r{   rb  rc  _correctanscorrectr,   r,   r-   r    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  )r1   ri  r   rh   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  r  )r8   r  r  r~  r  dfndfdr  )r   r   r   r   r1   ri  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  ro  r8   r  r~  r  r      )rh   r   r1   ri  r   rj  )r   rp  rq  r  r  r@   r>   r+  v2s2k2numk2denk2r,   r,   r-   test_stats_broadcast  s"   
0
 
 zTestF.test_stats_broadcastN)r   r   r   r  rn  rr  ry  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   r1   rl  r   r,   r,   r,   r-   test_rvgeneric_std  s   rz  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  )rm  r  )\(?rp   r8   gGz @g     i@r   r#  gGz@r  g
ףp=
@)rp   gq    @)r   r1   rl  rh   r   r   r,   r,   r,   r-   test_moments_t  s    r|  c                  C   s*   g d} g d}t tj| |dd d S )N)r   r8      rd   )g?@gTM]?ggY?gU?rS  rr   )r   r1   rl  rP   )rm  r_   r,   r,   r-   test_t_entropy  s   r~  c                   @   r  )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 d S )N)rv  r   r   r8   r   r  )rp   333333?r@  rp   r  rp   r  sample)namevaluesr   r/  )r1   rM   r   r   r   r;   r   r   rJ  r   r  r   )r   statesprobabilitysamplesrrA   r@   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   g?r  r  r  )r   r   r   rp   )	rh   r   r1   rM   r   r   rP   r   r   )r   r  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 )Nr   r8   r  rk   r  r:  r  r   r\  r  r8   rk   r:  rp   r  r  r  )r1   rM   r   r   )r   xkpkr  rA   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  )r  r   rX  r+  ro   r  r  r   )r   rk   rk   rk   r  r  r   r   r  r  c                       g | ]}  |qS r,   )rD   )rI   r  r  r,   r-   rK   ,	  rh  z+TestRvDiscrete.test_cdf.<locals>.<listcomp>)r1   rM   r   rD   )r   r  r  x_valuesr_   r,   r  r-   r   "	     
zTestRvDiscrete.test_cdfc                    r  )
Nr  r  r  )ra   rk   333333?r  r8  r   )r   r   r8   r8   r  r  r  r  c                    r  r,   )r  )rI   r  r  r,   r-   rK   9	  rh  z+TestRvDiscrete.test_ppf.<locals>.<listcomp>)r1   rM   r   r  )r   r  r  q_valuesr_   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   r8   r  r  r~  )ra   r:  r  r  ra   r  rv  r  r   )r1   rM   r   r  rD   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   r  )ra   ra   rB  r/  )ra   ra   r/  r/  r  r  r  )rh   r   r_  r   r1   rM   r   expectr   r  r  r   r  r  r  r,   r,   r-   test_multidimensionD	  s   
$z"TestRvDiscrete.test_multidimensionc                 C   s   g d}ddg}t ttjfi t||fd g d}t ttjfi t||fd g d}g d}t ttjfi t||fd g d}g d}t ttjfi t||fd d S )Nr   rk   r  )rk   333333?gffffff濩r   r8   r   r  r   )r  r  r  r  r  )r  
ValueErrorr1   rM   r   r   r  r  r,   r,   r-   test_bad_inputM	  s   "zTestRvDiscrete.test_bad_inputc                 C   s   t ddt dd}}tttjfi t||fd t ddt dd}}tttjfi t||fd t ddt dd}}t	tj||fd
dd d S )	Nr  r8   r8   )r8   r   gUUUUUU?r  r  )r   r8   r   )rh   r   r_  rR  r  r  r1   rM   r   r   r   r  r,   r,   r-   test_shape_rv_sample]	  s    z#TestRvDiscrete.test_shape_rv_samplec                 C   sD   g d}g d}t j||fd}t| t|j|j dd d S )N)r   r8   r  r  r  r  )ra   r:  r:  r:  r:  ra   r  r  r  )r1   rM   r   r  rh   r   r  r  r  r,   r,   r-   test_expect1l	  s   $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:?rp   gF%uk?g:vz?rp   rp   g.nr?g|гY?rp   rp   rp   g @6*? 4U0*C?g@+?gC6z?g nr?g ?gOjM?g n?g1w-!?g:pΈ?gףp=
?g _Le?rp   g^)p?g~jtx?gJ4q?gGzt?g J4q?g Mb@?g@Psׂ?g@^)ˀ?rp   rp   g N@s?g 1w-!_?r  gൄ|г?rp   gH}}?rp   g
F%u?rp   rp   g ^)ˀ?g v?rp   r  r  r  c                 s   s    | ]	\}}|| V  qd S rf   r,   rI   r  wr,   r,   r-   	<genexpr>	  s    z.TestRvDiscrete.test_expect2.<locals>.<genexpr>c                 S      | d S Nr8   r,   rA   r,   r,   r-   rV   	      z-TestRvDiscrete.test_expect2.<locals>.<lambda>c                 s   s     | ]\}}|d  | V  qdS )r8   Nr,   r  r,   r,   r-   r  	      )r1   rM   r   r  r   r   r   )r   rX  pyr  r,   r,   r-   test_expect2s	  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                   @   r  )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   rd   r   r!  )	rh   r   r   r1   
skewcauchyr:   ro  rD   r  r!  r,   r,   r-   test_cauchy	  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   rc   r8   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?)
rh   r   r   r  r   r1   r  r:   rD   r  )r   r*   rA   r:   rD   r,   r,   r-   test_skewcauchy_R	  s   z TestSkewCauchy.test_skewcauchy_RN)r   r   r   r  r  r,   r,   r,   r-   r  	  s    	r  c                   @   r  )TestSkewNormc                 C   s   t d| _d S r   )r   rngr   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  )rh   r   r   r1   skewnormr:   r  r!  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   r  r   r   )r*   r   r.  r  )r1   r  r   r  r   r   )r   r   rA   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 )
Nr  rJ  r   r8   )r*   r   r6   r7   r.  r  )r*   r6   r7   r  r   r  )r1   r  r   r   r  rh   r   ra  rb  kurtosisr   )r   Xr_   rd  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)rc   rq  r   rv  r   r  rr   r}  r  r   )r1   r  rD   r   rh   onesr  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)r   gzbLe9)r  r8   gn'/2;)r  r   g::)r  rv  g|<)rR  r  Oul2;r  rr   )r1   r  rD   r   r  )r   cdfvalsrA   r*   cdfvalr   r,   r,   r-   test_cdf_sf_small_values	  s   z%TestSkewNorm.test_cdf_sf_small_valuesN)	r   r   r   r   r  r   r  r  r  r,   r,   r,   r-   r  	  s    	r  c                   @   r   )
	TestExponc                 C   s   t tjdd d S r  )r   r1   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<r  )r   r1   r  rD   r   r  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@)rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   test_nan_raises_error
     zTestExpon.test_nan_raises_errorc                 C   r  r  )rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   test_inf_raises_error
  r  zTestExpon.test_inf_raises_errorN)r   r   r   r  r  r  r  r,   r,   r,   r-   r   
  s
    r  c                   @   r  )TestNormc                 C   r  r  )rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   r  
  r  zTestNorm.test_nan_raises_errorc                 C   r  r  )rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   r  
  r  zTestNorm.test_inf_raises_errorc                 C   s    g d}t ttjj|dd d S )Nr   shrimp)plate)r  r   r1   r  rw   r!  r,   r,   r-   test_bad_keyword_arg
  s   zTestNorm.test_bad_keyword_argN)r   r   r   r  r  r  r,   r,   r,   r-   r  
  s    r  c                   @   r  )TestUniformgh-10300c                 C   r  r  )rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   r  %
  r  z!TestUniform.test_nan_raises_errorc                 C   r  r  )rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   r  *
  r  z!TestUniform.test_inf_raises_errorN)r   r   r   __doc__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	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   r8   r   r>        @r  r,   )lamsigrD  opK2exp_skewexp_kurtr,   r,   r-   get_moms3
  s   $z,TestExponNorm.test_moments.<locals>.get_moms)r   r   r   r   r  r6   r7   r  )r  r8   ra   )r   r   r   )r}  r  r  )r1   	exponnormr   )r   r  rD  r  r  Kstsr,   r,   r-   r  1
  s"   



zTestExponNorm.test_momentsc                 C   2   t dddddt jg}tttjj|ddd d S 	Nr  r  r  r  r  r   r   r  )rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   r  L
     z#TestExponNorm.test_nan_raises_errorc                 C   r  r  )rh   r   r   r  r   r1   r  rw   r!  r,   r,   r-   r  Q
  r  z#TestExponNorm.test_inf_raises_errorc                 C   sT   t tjddd t tjddd t tjddd t tjddd d S )Ni|r   rp     rm   )r   r1   r  r:   r   r,   r,   r-   test_extremes_xV
  s   zTestExponNorm.test_extremes_xzx, K, expected))rq  rm   g6
N-)r   rm   g՜n+H?)rv  rm   gi?)r  rm   gbJI-)rc   r   gI8?)rc   r  gQ3|-0?c                 C   s   t tj|||dd d S rU  )r   r1   r  r:   )r   rA   r  r_   r,   r,   r-   test_std_pdfh
  s   zTestExponNorm.test_std_pdfzx, K, scale, expected)r   rm   r   gVAҤ?)r}  {Gzt?r   g'^>)     rm   rd   rp   )r  rm   r  gbr ;)r   r  r   gVMe?c                 C   <   t jj|||d}|dkr|dksJ d S t||dd d S )Nr  rp   rS  rr   )r1   r  rD   r   r   rA   r  r7   r_   r   r,   r,   r-   test_cdf_small_K~
  s   zTestExponNorm.test_cdf_small_K)rc   rm   r   ghG}$;)r8   r  r   g]fJ?)r   r  rk   g31"g#;)rc   r  rk   gf
+-)rq  r  rk   rp   )r  r  r   ga9S?c                 C   r  )Nr  rp   g-a=rr   )r1   r  r  r   r  r,   r,   r-   test_sf_small_K
  s   zTestExponNorm.test_sf_small_KN)r   r   r   r  r  r  r  r   rK  r,  r  r  r  r,   r,   r,   r-   r  0
  s8    

r  c                   @   r  )TestGenExponc                 C   s@   ddl m} tjtdddddd}t||dddd d S )	Nr   )simpsrc   rm   rk   ro   )dxr   )scipy.integrater  r1   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   rc   rm   rk   ro   r   )r1   r  rD   r;   r   r   r   )r   rD   r,   r,   r-   test_cdf_bounds
  s   zTestGenExpon.test_cdf_boundsc                 C   s$   t jdddd}t|ddd d S )Nr   r   r8   r+  gM <rS  rr   )r1   r  r  r   r  r,   r,   r-   test_sf_tail
  s   zTestGenExpon.test_sf_tailN)r   r   r   r  r  r  r,   r,   r,   r-   r  
  s    r  c                   @   r  )TestExponpowc                 C   s6   t tjddd t tjtjdddd d S )N绽|=ro   r  r   r  )r   r1   exponpowrD   r   r  r   r,   r,   r-   r  
  s   zTestExponpow.test_tailN)r   r   r   r  r,   r,   r,   r-   r  
      r  c                   @   r  )TestSkellamc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )NrR  r   rc   r   )gYjP'?g$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$S?gYjP'?gX_?g+rx?gfSr?gJXx~?r   )r;   r   r   r   r1   skellamr   )r   r>   mu1mu2skpmfRr,   r,   r-   r   
     zTestSkellam.test_pmfc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )NrR  r   r  )gƃQ?gS`X'?gVy)>?g:	 S?gei.f?gȼJ]x?g)?g{^'+i?gLIg>?gnZ?g?rvͪ?gA?g0?g#J?gqSm
.?g~B?gd?gFBD?gQ9?gmF^?gcMy?gGJq?gC^c?g.){?gñݸ?r   r   )r;   r   r   r   r1   r  rD   )r   r>   r  r  skcdfRr,   r,   r-   r   
  r  zTestSkellam.test_cdfN)r   r   r   r   r   r,   r,   r,   r-   r  
  s    r  c                   @   r  )TestLognormc                 C   sZ   t   t dt tjg dd}t|g d W d    d S 1 s&w   Y  d S )Nr   r   rk   r   r   )rp   g~r?g e3E?)r   r   r   r   r1   r   r:   r   r   r:   r,   r,   r-   r   
  s
   
"zTestLognorm.test_pdfc                 C   sn   d\}}}t tjj|| |dtjt|| |  t tjj|| |dtjt|| |  d S )N)g(\5i@   gOn?rU   )r   r1   r   r  r  rh   r  r  )r   ru  rD  sigmar,   r,   r-   rS  
  s   
zTestLognorm.test_logcdfN)r   r   r   r   rS  r,   r,   r,   r-   r  
  s    r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zejj	e
d	d
dd Zejj	e
d	d
dd Zejj	e
d	d
dd Zdd Zdd ZdS )TestBetac                 C   s:   t jddd}t|d t jddd}t|tj d S )Nr   r   rk   g;B.)r1   rX  r   r   rh   r   r   r   r,   r,   r-   r+    s   
zTestBeta.test_logpdfc                 C   sV   d\}}t g d}t||}t|| d t||t || d S )Ni  i  r:  rk   r  gƒ)	rh   r   r1   rX  r   r   r   r:   r&  r   r   rX  rA   r+   r,   r,   r-   test_logpdf_ticket_1866  s
    z TestBeta.test_logpdf_ticket_1866c                 C   s$   g d}t ttjj|dddd d S )Nra   rk   r  r   r   r  )r   r   r  )r  r   r1   rX  rw   r!  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
  rk   )fafix_a)r  r  r1   rX  rw   r!  r,   r,   r-   #test_fit_duplicated_fixed_parameter  s   z,TestBeta.test_fit_duplicated_fixed_parameterzOverflow, see gh-14901reasonc                 C   s$   d\}}}t tj|||d d S )N)g?g     R@g   0xAgx)>)r   r1   rX  r  )r   r   r*   r+   r,   r,   r-   test_issue_12635   s   
	zTestBeta.test_issue_12635c                 C   sh   t g d}t g d}d}tj||d d| }t|| tj||d d| }t|| d S )N)g@3@?g^?gNC?)rc   rd   r  rr  r   順 )rh   r   r1   rX  r   r   r  )r   inv_R
count_listr   invrC  r,   r,   r-   test_issue_12794,  s   
zTestBeta.test_issue_12794c           	      C   sb   d}t dd}d}d| |d || }}}tj|||}tj|||}t|d|  d S )Nh㈵>r   rq  r  )rh   r   r1   rX  r  rD   r   )	r   alpha_2count_nobsr  r*   r+   r  rC  r,   r,   r-   test_issue_12796>  s   zTestBeta.test_issue_12796c                 C   sD   d\}}t tjd||tj d\}}t tjd||tj d S )Nr  r   )r:  r   r   )r   r1   rX  r:   rh   r   )r   r*   r+   r,   r,   r-   r  J  s   zTestBeta.test_endpointsc                 C   sJ   d\}}}t t tj||| W d    d S 1 sw   Y  d S )N)gףp=
?g   vH7Bg  @0B)r   warnsr   r1   rX  r  )r   r  r*   r+   r,   r,   r-   test_boost_eval_issue_14606U  s   
"z$TestBeta.test_boost_eval_issue_14606N)r   r   r   r+  r	  r  r  r   rK  skipifMACOS_INTELr  r  r  r  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  )rh   r   r1   r   r   r%  r   r   r   r:   r&  r  r,   r,   r-   r+  \  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   r:  r  rp   r  r  c                    s   g | ]
}t j| qS r,   )r1   r   )rI   r   r   rX  gen_cdfr,   r-   rK   p      z*TestBetaPrime.test_cdf.<locals>.<listcomp>g-=rT  )r1   r   rD   r   rh   r   r   r%  r   rN   _cdf_singler   )r   rA   r  cdfs_gr,   r!  r-   r   c  s   
zTestBetaPrime.test_cdfN)r   r   r   r+  r   r,   r,   r,   r-   r   [  r  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  r:  r  g
CTb?r   rc   gBΖ?)r1   r  r:   r   r  r,   r,   r-   r   u  s   
zTestGamma.test_pdfc                 C      t jdd}t|d d S r  )r1   r  r   r   r  r,   r,   r-   r+  }  s   zTestGamma.test_logpdfc                 C   s"   g d}t ttjj|ddd d S )Nr
  r   r  )r   r  )r  r   r1   r  rw   r!  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 )
NFFg<r   gplC@r  r  gJz5rd   g1}t@rS  )rh   iscloser1   r  r   r   r,   r,   r-   r"    s   
zTestGamma.test_isfN)r   r   r   r   r+  r  r"  r,   r,   r,   r-   r&  t  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   rd   g6:֜?r   r1   chi2r:   r   r,   r,   r-   r5    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 )Nr"  gλm:=6g'bd5 <r  rr   rk   gQ8@   gܐ؆0guu[9=ra   g8-*@)r1   r/  r  r   )r   rm  rA   r,   r,   r-   r    s   zTestChi2.test_ppfN)r   r   r   r5  r  r,   r,   r,   r-   r,    s    r,  c                   @   r  )TestGumbelLc                 C   rf  Nrw  r  )rh   r   r1   r  rD   r  r   ri  r,   r,   r-   r    rj  zTestGumbelL.test_cdf_ppfc                 C   sH   t dd}tj|}tj|}t |}t| }t	|| d S r2  )
rh   r   r1   r  r  r  r&  r   expm1r   )r   rA   rX  r  ur  r,   r,   r-   r    s   
zTestGumbelL.test_logcdf_logsfc                 C   rf  )Nr  r   )rh   r   r1   r  r  r   r   ri  r,   r,   r-   rY    rj  zTestGumbelL.test_sf_isfN)r   r   r   r  r  rY  r,   r,   r,   r-   r1    s    r1  c                   @   r  )TestGumbelRc                 C      t tjdddd d S )Nr   g?~T}%m;r  rr   )r   r1   r  r  r   r,   r,   r-   r       
zTestGumbelR.test_sfc                 C   r6  )Nr)  r*  r  rr   )r   r1   r  r   r   r,   r,   r-   r"    r7  zTestGumbelR.test_isfN)r   r   r   r  r"  r,   r,   r,   r-   r5    s    	r5  c                   @   sf   e Zd Zdd Zejjdd Zejjdd Zdd Z	d	d
 Z
ejjejdddgdd ZdS )TestLevyStablec                 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)wgr9  rp   rp   rp   rp   羼 u?r:  r:  r:  r:  67',?r;  r;  r;  r;  tA}˜.?r<  r<  r<  r<  Gz?r   rm   r   )\(̿r8   gۧ1?r  g9]c?)r<  r<  r<  r<  r<  rv  gv?r;  )r1   levy_stablerv  r   r   r   )r   rA   alpha1beta1loc1scale1ru  alpha2beta2loc2scale2r,   r,   r-   r{    s   

zTestLevyStable.test_fitc                    s  t jt jt jtd}t|}tjj	j
|jdd}ttdr&tjntj g dddd fd	d
gddddd
 gddddd
 gddddd
 gddddd
 gddddd
 gddddd
 gg}t|D ]{\}\}}}}|tj_|tj_|dur||| n|}	t T}
|
td |
td tjj|	d |	d |	d ddd}t|	d|}t||	d  }||dd |   kt|B  }t||	d |d!|||f d"d# W d   n1 sw   Y  qedS )$a!   Test pdf values against Nolan's stablec.exe output
            see - http://fs2.american.edu/jpnolan/www/stable/stable.html

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

            Repeat following with beta = -1, -.5, 0, .5 and 1
                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/stable-pdf-sample-data.npyx,p,alpha,betanamesisin)bestNr~  N
quadratureNr~  c                    s   | d dk | d g d@ S )Nr   r   rA   )rR  r}  r   r   rc   r,   r  npisinr,   r-   rV     s   
 z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>	zolotarevc                 S   s   | d dkS Nr   r   r,   rN  r,   r,   r-   rV   !      c                 S   s   | d dk| d dk@ S Nr   r   rX  r   r,   rN  r,   r,   r-   rV   #      r   c                 S      | d dk| d dk@ S rT  r,   rN  r,   r,   r-   rV   %  rU  fftr   r  c                 S      | d dkS rR  r,   rN  r,   r,   r-   rV   )  rS  r   c                 S   s   | d dk | d dk@ S )Nr   r   r   r,   rN  r,   r,   r-   rV   *  rU  c                 S   rV  )Nr   r   rA   r   r,   rN  r,   r,   r-   rV   ,  rU  z6Density calculation unstable for alpha=1 and beta!=0.*z2Density calculations experimental for FFT method.*rA   r   rX  r7   r6   calcr   r+  r  z&pdf test %s failed with method '%s'
%sFverbose)ospathabspathjoindirname__file__rh   loadcorerecords
fromarraysTr)   rK  in1dr  r1   r?  pdf_default_methodpdf_fft_min_points_thresholdr
   recordr   r:   r   rJ  isnanr   r   fnr{   testsixdefault_methodfft_min_pointsdecimal_placesfilter_funcsubdatasupr   subdata2padifffailuresr,   rO  r-   test_pdf_nolan_samples  sj   


z%TestLevyStable.test_pdf_nolan_samplesc              
   C   sL  t jt jt jtd}t|}tjj	j
|jdd}g dddddd	 gg}t|D ]u\}\}}}}|tj_|tj_|d
urH||| n|}	t N}
|
td tjj|	d |	d |	d ddd}t|	d|}t||	d  }||dd|   kt|B  }t||	d |d|||f dd W d
   n1 sw   Y  q.d
S )a!   Test cdf values against Nolan's stablec.exe output
            see - http://fs2.american.edu/jpnolan/www/stable/stable.html

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

            Repeat following with beta = -1, -.5, 0, .5 and 1
                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/stable-cdf-sample-data.npyrH  rI  )rQ  Nr~  NrW  r   r8   c                 S   rX  rR  r,   rN  r,   r,   r-   rV   b  rS  z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>NzXFFT method is considered experimental for cumulative distribution function evaluations.*rA   r   rX  r   rY  rZ  r   r+  r  z&cdf test %s failed with method '%s'
%sFr[  )r]  r^  r_  r`  ra  rb  rh   rc  rd  re  rf  rg  r  r1   r?  ri  rj  r
   rk  r   rD   r   rJ  rl  r   rm  r,   r,   r-   test_cdf_nolan_samplesF  sF   

z%TestLevyStable.test_cdf_nolan_samplesc           
   
   C   s   t g d}t g d}t g d}g dg dg}t jddM t 1}|jtdd	 |D ]\}}}|tj_|tj_	tjj
|d
|d
dd}	t|	||| q1W d   n1 s[w   Y  W d   dS W d   dS 1 ssw   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   r8   r8   r8   r8   r   r   r   r   r  r  r  r  )gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g?gDioɴ?g r?gH?g+?gHPs?gX ?g&?g0*?gv/?ga2U0*?)r   r   rk   r   r   r   rk   r   r   r   rk   r   r   r   rk   r   r   r   rk   r   )rM  Nr  )rQ  Nr   ignorer   zDensity calculation unstable.*)categorymessager   r   rY  N)rh   r   errstater
   rZ   r   r1   r?  ri  rj  r:   r   )
r   xsdensitybetasro  rv  rq  rr  rs  r:   r,   r,   r-   'test_pdf_alpha_equals_one_beta_non_zeroy  s&   Pz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zeroc                 C   s`   ddt jt jt jfgddgg}|D ]\}}tjj|d |d |d |d dd	}t|| qd S )
N)r=  r>  r   r   r   )r8   r8  rc   r+  )rc   r  r   r   r   r8   r   r  r  )rh   r   NaNr1   r?  r   )r   
param_setsr   	exp_stats
calc_statsr,   r,   r-   r    s   zTestLevyStable.test_statsrX  rk   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 )
Nh:r   rk   r+  i  r6   r7   r   r?  rA  rm   )rh   r   r   r1   r?  r   r2  )r   rX  r   r6   r7   rA   statr   r,   r,   r-   test_rvs_alpha1  s   

zTestLevyStable.test_rvs_alpha1N)r   r   r   r{  r   rK  rL  rz  r{  r  r  r,  r  r,   r,   r,   r-   r8    s    
K
2$r8  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  )r1   r  r   rh   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-   r        r  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   r
  )r1   r   r  r   lowerr
  r   r,   r,   r-   test_docstrings  s
   zTestDocstring.test_docstringsc                 C   s   t   t   d S rf   )r1   rN   rM   r   r,   r,   r-   test_no_name_arg  s   zTestDocstring.test_no_name_argN)r   r   r   r  r  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   r8   r   r8   r   r   r   r8   )r   r8   r8   r   r   )r8   r8   r8   r8   r8   r   )r   r   r   r;   r   r*   r+   r  r,   r,   r-   TestArgsreduce  s   
r  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dddgdd Zejdddgdd ZdS )TestFitMethod)ncfr  r  c                 C   r   r   r   r   r,   r,   r-   r     r   zTestFitMethod.setup_method)r  r  r  z	dist,argsc                 C   s~   || 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d	 t	t
|j|ddd	 d
S )r  z"%s fit known to fail or deprecatedr  r  r  r  r  r   r   r  N)fitSkipNonFiniter   skiprh   r   r   r   r   r1   r  r   rw   )r   rJ   r   rA   rX  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|  r}  r   rp         4@rq  r   r8   r   r  r  r  )rh   r   r   r  r1   r   r   rj  r  r   r   r   rw   )r   rA   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   r8   r  rH  )rh   r   r1   r  rw   r   rj  r   r   rA   r6   r7   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   r8   r  )rh   r   r  r   r1   r  rw   r   r   digammar   )r   rA   meanlogr   r*   r6   r7   r@   r   r   r  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 Nr   )r   rh   r  r   r   psi)r*   r+   rA   r   s1ru  psiabr|   r,   r,   r-   mlefunc3  s   z0TestFitMethod.test_fix_fit_beta.<locals>.mlefunc)r  r   rk   r   r   r  r]  r  r8   )r   r   r   r  )r   r   r   rk   r   )r   r   r   )r   r   r   r   )r   r   r   r   )
rh   r   r1   rX  rw   r   r   r   r  r  )r   r  rA   r*   r+   r6   r7   dadbru  a2b2rF  rG  rX  r,   r,   r-   test_fix_fit_beta0  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)r8   r8   r  r  r  r  r  r~  r8   r   rH  r   r  r  )rh   r   r1   r  rw   r   r  r,   r,   r-   test_expon_fitg  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)r+  r   rc   r      ;   r   r  rV  rr   r  r  r8   r   )r   fix_s)rh   r   r  r1   r   rw   r   r   r   r&  r   rj  )r   rA   lnxm1r   r6   r7   r,   r,   r-   test_lognorm_fitv  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   rX  r        "@r   r  rc   rH  ro   r   )rh   r   r1   r  rw   r   r  ptpr  r  r  r  r,   r,   r-   test_uniform_fit  s   


zTestFitMethod.test_uniform_fitmethod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\  rd   r   r-  r  )r   r  )r  r  rV  rT  )r  r  r\  )r   r  )r  r  )r  r  r   r8   )r  r   r  r   r   )r  r   r   r   r  )r  r   r   r  )r  r   r   r   )	r1   rX  r   rw   r   r  r  r   r  )r   r  r*   r+   rA   res_1res_2res_3res_4res_5aabbrL  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 )Nr8   rd   )r  r   i)enikibenikir  )r1   r  r   r   r  r   rw   )r   r  rJ   r{   r   r,   r,   r-   test_extra_params  s   
"zTestFitMethod.test_extra_paramsN)r   r   r   r  r   r  r   rK  r,  r   r  r  r  r  r  r  r  r  r  r  r,   r,   r,   r-   r    s"    

	&7
&r  c                   @   rM  )
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  r5   r  r   r8   )r1   r  r:   r   rD   r  r   r  rI  r   ra  r   rP   r_  r*   r+   )r   rJ   frozenresult_frO  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 )Nro   r  r   r  r8   )r1   r  r:   r   rD   r  r   r  rI  r   ra  r   rP   r_  r*   rJ   r+   )r   r*   rJ   r  r  rO  r,   r,   r-   
test_gamma  sL   






















zTestFrozen.test_gammac                 C   s8   t d}|d}|j dd |d}t|| d S )Nr   r8   r  r  )r1   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 )
Nr  r  rp   r  ra   r   r  r  rk   )r1   r  rJ   r  r   r:   rh   r   r*   r+   r   r  r  r   )r   r  r  r*   r+   rv1r,   r,   r-   r  K  s4   



zTestFrozen.test_abc                 C   s   t ttjd d S )N	rv_frozen)r   r)   r1   r2   r   r,   r,   r-   test_rv_frozen_in_namespacew  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~  r-  )r1   r  r   r)   r.  r   	get_staterh   r   RandomStater   )r   r  rndmr,   r,   r-   test_random_state{  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   r8   r   )ra   r:  r  r@  r  r   r~  r   rk   r   r   )r1   rX  r  rM   r.  r   pickledumpsloadsr   r  rD   )
r   rX  poissr  distfnr@   r0	unpickledr1mediansr,   r,   r-   test_pickling  s&   




zTestFrozen.test_picklingc              	   C   s   dd }t jdddd}|j|dddd	}t jj|d
dddddd}t|| t jddd}||}t jj|ddd}t|| d S )Nc                 S      | S rf   r,   r  r,   r,   r-   r|        z$TestFrozen.test_expect.<locals>.funcr8   r   r  )r*   r6   r7   r   T)lbubconditionalr8   r   r6   r7   r  r  r  r6   )r   r   r6   )r1   r  r  r   r  )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                   @   r  )
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-   rV     rW   z&TestExpect.test_norm.<locals>.<lambda>r   r8   r5   r  r-  r   c                 S   r  rf   r,   r  r,   r,   r-   rV         r/  r  c                 S      dS r  r,   r  r,   r,   r-   rV     r  )r6   r7   r  r  r8  c                 S   r  r  r,   r  r,   r,   r-   rV     r  T)r6   r7   r  r  r  r   )r1   r  r  r   r  )r   r  r  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-   rV     rW   z&TestExpect.test_beta.<locals>.<lambda>r  r   r8   )r   r6   r7   qq?r0  r   c                 S   r  rf   r,   r  r,   r,   r-   rV     r  r   ro   r  r  rc   r5   r/  c                 S   r  )Nr   r,   r  r,   r,   r-   rV     r  )rc   rc   Fr  r8  c                 S   r  r  r,   r  r,   r,   r-   rV     r  Tr   )r1   rX  r  r   r  )r   r  r  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 )Nrq  rc   r~  r   r  c                 S   r  rf   r,   r  r,   r,   r-   rV     r  z+TestExpect.test_hypergeom.<locals>.<lambda>)rq  rc   r~  r  r0  r   c                 S      | d d S Nr  r8   r,   r  r,   r,   r-   rV     rS  r-  c                 S   r  r  r,   r  r,   r,   r-   rV     rS  r   )r   r6   r  r  r   c                 S   r  r  r,   r  r,   r,   r-   rV     r  r  r   c                 S   r  r  r,   r  r,   r,   r-   rV     r  T)r   r6   r  r  r  c                 S   r  r  r,   r  r,   r,   r-   rV     r  r   )r   r  r  )r1   r.  r  r   r   r   )
r   m_truev_truer  r  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-   rV     r  z)TestExpect.test_poisson.<locals>.<lambda>r  r   F)r   r  r  r   r8   r-  r   c                 S   r  r  r,   r  r,   r,   r-   rV     r  T)r1   r  r  rD   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)r+  rA  )rk   r-  r   )r1   genhalflogisticr  r   )r   halflogres1rE  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-   rV     r  z/TestExpect.test_rice_overflow.<locals>.<lambda>)r  rA  c                 S   r  r  r,   r  r,   r,   r-   rV     r  c                 S   r  )Nr   r,   r  r,   r,   r-   rV     r  )r   rh   r%  r1   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  rf   r,   r>   r,   r,   r-   rV     r  z(TestExpect.test_logser.<locals>.<lambda>rA  r   rq   r  c                 S   r  rf   r,   r  r,   r,   r-   rV   $  r  r  )r1   r  r  r   rh   r  )r   r   r6   res_0res_lr,   r,   r-   test_logser  s   zTestExpect.test_logserc                 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[  rs  c                 S   r  rf   r,   r  r,   r,   r-   rV   +  r  z)TestExpect.test_skellam.<locals>.<lambda>rA  c                 S   r  r  r,   r  r,   r,   r-   rV   ,  r  rV  r  r8   )r1   r  r  r   )r   rT  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  rf   r,   r  r,   r,   r-   rV   4  r  z)TestExpect.test_randint.<locals>.<lambda>c                 s   s    | ]}|V  qd S rf   r,   rI   r5  r,   r,   r-   r  6  s    z*TestExpect.test_randint.<locals>.<genexpr>rq   r  )r1   r   r  r   r   rb  )r   lohirC  r,   r,   r-   test_randint0  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-   rV   ;  r  z&TestExpect.test_zipf.<locals>.<lambda>r  )r   r   r1   r  r  r   r,   r,   r-   	test_zipf8  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-   rV   ?  r  z/TestExpect.test_discrete_kwds.<locals>.<lambda>r  rA  c                 S   r  r  r,   r  r,   r,   r-   rV   @  r  r      r  )r   maxcount	chunksize	tolerancer-  r   )r1   r  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   rc   r  r}  r   r   r8   r,   rA  r,   r,   r-   poiss_moment5G  s   0z-TestExpect.test_moment.<locals>.poiss_moment5)r   r  r   r  rr   )r1   r  r_  r   )r   r  rD  m5r,   r,   r-   test_momentD  s
   zTestExpect.test_momentN)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   rk   rv  g K?rc   r   )r1   nctr   rD   r   r  r,   r,   r-   test_nc_parameterP  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   r  r  ra   r   )gMp^j?g6].ftv?gȳ'ς?gu?)g!Y<a?g]d1p?go|?g?)gHdY?g2Ԥg?g}o/u?g .mr?r  rr   )r1   r"  r:   rh   r   r   r   r   )r   rC  r_   r,   r,   r-   test_broadcastingX  s   zTestNct.test_broadcastingc                 C   s   t dd}t| d d S )Nr  r   ro   )r1   r"  r   ra  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 )Nr8  r  r  )rm  ncr  r  rY  )r1   r"  r   rh   r   r   r%  r   r  r,   r,   r-   test_nct_inf_momentsh  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  r8   g@ @g*dn?r   r  rr   r  gqI  @gL) ?r  )r1   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_valuesu  s   
z&TestNct.test_nct_stats_large_df_valuesN)r   r   r   r#  r$  r%  r'  r-  r,   r,   r,   r-   r!  O  s    r!  c                   @   r  )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)r:  r   r   rp   r+   )ra   ra   rk   r8  r   r  r  r  rT  )r   rh   r%  r1   r	  r:   r   r   rD   r  r  r   )r   rA   r  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   )r1   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 )Nrc      )g/Ƹ?g[jǊ\?g 	?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?ra   r   g     @_@r  r  )	g<~@gwd
@gC?@gb
0@g` A@@g'NxP@g33-a@g4pv@g$F@rk      )gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g<
uQ@giff T@g9r[V@g3bXQ Y@gqxJ[@g`*DD ^@g@`@gdAa@)r1   r	  rD   rh   r   r   r  r0   )r   rD   cdf_expprobabilitiesr  ppf_expr,   r,   r-   test_rice_gh9836  s   "

zTestRice.test_rice_gh9836N)r   r   r   r0  r1  r7  r,   r,   r,   r-   r.    s    r.  c                   @   r  )
TestErlangc                 C   r   r   r   r   r,   r,   r-   r     r   zTestErlang.setup_methodc              	   C   s   t  6 t dt tttjjddddd g d}tjj|dd}tj	j|dd}t
||d	d
 W d    d S 1 s=w   Y  d S )Nr   g?r   r   r  r  )rk   r   ro   r\  r2  r  rr   )r   r   r   r   r  r1   erlangr   rw   r  r   )r   r{   result_erlangresult_gammar,   r,   r-   test_erlang_runtimewarning  s   
"z%TestErlang.test_erlang_runtimewarningc                 C   s.   t tjjdddgdtjjdddgd d S )Nrk   r   rv  r!  )r   r1   r9  r:   r  r   r,   r,   r-   test_gh_pr_10949_argcheck  s   z$TestErlang.test_gh_pr_10949_argcheckN)r   r   r   r   r<  r=  r,   r,   r,   r-   r8    s    r8  c                   @   sr   e Zd Zdd Zdd Zdd Zejde	j
dgd	d
 Zejdddge	j
dgdd Zdd ZdS )TestRayleighc                 C   r   )Nr  r   r   r,   r,   r-   r     r   zTestRayleigh.setup_methodc                 C   r  )Nr   g)Zx)r1   r   r   r   r   rX  r,   r,   r-   r+       zTestRayleigh.test_logpdfc                 C   r  )Nr   i)r1   r   r  r   r?  r,   r,   r-   r    r@  zTestRayleigh.test_logsfzrvs_loc,rvs_scaler8   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 )NrQ  rq  c                 S   s"   t | | d dt|   d S )Nr8   rk   )rh   r   r   )r{   r   r,   r,   r-   r5    s   "z(TestRayleigh.test_fit.<locals>.scale_mler  r  rH  )r1   r   r   rw   r   )r   r  r  r{   r5  scale_expectr6   r7   r,   r,   r-   r{    s   



zTestRayleigh.test_fitr  rm   c                 C   r|  )NrQ  rq  r   )r1   r   r   rv  r~  r   )r   r  r  r{   r   r|   r,   r,   r-    test_fit_comparison_super_method  s   z-TestRayleigh.test_fit_comparison_super_methodc                 C   s   t tj d S rf   )r   r1   r   r   r,   r,   r-   r    r  zTestRayleigh.test_fit_warningsN)r   r   r   r   r+  r  r   rK  r,  rh   r   r  r{  rB  r  r,   r,   r,   r-   r>    s    


r>  c                   @   r  )TestExponWeibc                 C   sB   d}d}d}t j|||}t j|||}t||gddg d S )Nra   r   g      Y@g:23W+g~`9k)r1   	exponweibr:   r   r   )r   rA   r*   r  r   r*  r,   r,   r-   test_pdf_logpdf%  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  rv  r  r   rd   )rh   r  r1   rD  r:   weibull_minr   r   r   rA   r*   r  r   r_   r*  r,   r,   r-   test_a_is_10  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 )Nr  r   rc   )rh   r  r1   rD  r:   r  r   r   rG  r,   r,   r-   test_a_is_1_c_is_1@  s   
z TestExponWeib.test_a_is_1_c_is_1N)r   r   r   rE  rH  rI  r,   r,   r,   r-   rC  #  s    rC  c                   @   r  )TestFatigueLifec                 C   rZ  )Nr  r  X9rS  rr   )r1   r   r  r   r  r,   r,   r-   r  Q  s   zTestFatigueLife.test_sf_tailc                 C   s$   d}t j|d}t|ddd d S )NrK  r  r  rS  rr   )r1   r   r   r   )r   r   r  r,   r,   r-   test_isf_tail_  s   zTestFatigueLife.test_isf_tailN)r   r   r   r  rL  r,   r,   r,   r-   rJ  O  s    rJ  c                   @   r  )TestWeibullc                 C   r(  r  )r1   rF  r   r   r?  r,   r,   r-   r+  h     zTestWeibull.test_logpdfc           
      C   sP  d}d}d}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|t	
d  t jj|||d}t|tt	
d  t jj|||d}t|td t jj|||d}	t|	d t jjdddd}t|td	 t jjdddd}	t|	d	 d
}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|td t jj|||d}t|d t jj|||d}t|t	
d  t jj|||d}	t|	tt	
d  t jjdddd}t|t	
d  t jjdddd}	t|	tt	
d  d S )Nr+  ro   r  r  r  r   r   r8   rw  r>  g&.gCe )r1   rF  r:   r   rh   r&  r   r  rD   r   r3  r  r  r  weibull_max)
r   rA   r*   r+   r   r[  r  lcr@   lsr,   r,   r-   test_with_maxima_distribm  sH   


z$TestWeibull.test_with_maxima_distribN)r   r   r   r+  rR  r,   r,   r,   r-   rM  f  s    rM  c                   @   r  )	TestRdistc                 C   s0   t j}g d}t|||dd|dd d S )Nr  g     @r   r   )r1   rdistr   rD   r  )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re  rc   g@rk   r8   r   )rh   r   r   r1   rX  r:   rT  )r   rA   r  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                   @   r  )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  rk   r   r   r   )r   r1   r   r:   triangrD   )r   modesmoderA   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   rc   )rh   r   r   r1   r   r:   r  rD   r!  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   r8   r   rk   r  r  r:  r   ra   g      ?      ?r8  g      ?r  g      ?)r   r1   r   r:   rD   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)r  rv  r8   r   r8   c                    sT   | d  | d     | d   | d        | d  | d  S )Nr8   r   r,   )r   r*   r+   r  dr   r,   r-   r_    s    z6TestTrapezoid.test_moments_and_entropy.<locals>.momentr   rk   r0  r   r   r  r  rv  r   )rh   r  r   r1   r   r   ra  rP   )	r   rT  r  r6   r7   r_  r   ra  rP   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 )N)ra   r:  r  rk   r  )rB  r   r8  )r   rq   r  r  r  r  )rh   r   r1   r   r:   broadcast_arraysemptyr   r   r   r   ravelr   r_  r   r  rg  )r   r  ra  rA   r  ccddr  rC  indr`  rt  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\  )rh   r   r   r1   rQ   r:   r  r!  r,   r,   r-   
test_trapz*  s   "zTestTrapezoid.test_trapzN)	r   r   r   r[  r]  r_  rb  rk  rl  r,   r,   r,   r-   rW    s    	rW  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raiser}  r   ro   rk   r   r   rp   r8   r   r   )rh   r  r   r1   rX  r:   rD   r   r,   r,   r-   test_edge_cases1  s   "zTestTriang.test_edge_casesN)r   r   r   ro  r,   r,   r,   r-   rm  0  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   r1   mielker_  rh   r   r   r%  )r   r>   r@   r,   r,   r-   r  E  s    zTestMielke.test_momentsc                 C   s@   t ddd}d\}}ttj|||| tj||| d S )Nrm   rd   r   )g@gHzG@)rh   r   r   r1   burrr:   rq  )r   rA   r>   r@   r,   r,   r-   test_burr_equivalenceL  s   *z TestMielke.test_burr_equivalenceN)r   r   r   r  rs  r,   r,   r,   r-   rp  D  r  rp  c                   @   r  )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   )rk   r8   )r   r   )r8   rk   r  rk   r   )r   r8   ro   c                 S   r_  r,   r`  ra  r,   r,   r-   rK   _  rd  z0TestBurr.test_endpoints_7491.<locals>.<listcomp>c                 S   re  r,   r,   rf  r,   r,   r-   rK   `  rh  c                 S   r_  r,   )r   r*   ra  r,   r,   r-   rK   c  rd  c                 S   s   g | ]
\}}}t |qS r,   )rh   r  rf  r,   r,   r-   rK   d  r#  )r1   fiskrr  burr12r   )r   r{   rk  rl  r,   r,   r-   test_endpoints_7491S  s   






	
zTestBurr.test_endpoints_7491c                 C   s<   d\}}t ||  \}}d\}}t|| t|| d S )N)r   r   )g4U?g&MI?)r1   rr  r   )r   r  ra  r   variancemean_hcvariance_hcr,   r,   r-   test_burr_stats_9544g  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)rk   r   )r+  r   )r   r8   r   r  )r  r   )r  r   )r  r   )r1   rr  r   rh   rl  r%  _munpr   )	r   r  ra  r   rx  e1e2e3e4r,   r,   r-   test_burr_nan_mean_var_9544r  sL   "z$TestBurr.test_burr_nan_mean_var_9544N)r   r   r   rw  r{  r  r,   r,   r,   r-   rt  R  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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 svw   Y  ej"de!d dd Z#ej"de!d dd Z$ejjej"de!d d d! Z%d"d# Z&ejj'd$d% Z(ej"d&ed'd( Z)ejjd)d* Z*ejj'd+d, Z+dS )-TestStudentizedRange)gQ1@g33333F@g
ףp=*K@gHzM@g/$@g~j!@g33333$@g{Gz&@gh|?5	@gQ8@g&1@g|?5@g@gOn@g!rhm@gB`"@r   gʡEs@g|?5^@g/$@gV-@g/$@gF@g?5^I@)gRV@gffffffl@gp@g     r@gʡ @gHzG/@gQ82@gQ3@g!rh@g     @g+@gʡEs @gjt@gB`"[@g@gnJ@gV-@gFx@gsh|?@g+N@g/$@g @g@gGz@)gfffff"@i  i
  i  gHzG2@g(\A@gQC@gfffffE@g @gNbX9"@gHz$@g(\&@g-@gn@@gw/@g=
ףp @gJ+@g-'@gn@gHz@gV-@gnJ@g$@g/ݤ@)r  re  r  r   r   rc   rq  x   )r8   r~  r-  rq  )ra   r   i)#  gupm1f?)r   rc   r  g?<-=A?gv"?r  gd暕?ga-A?c                 C   s<   | j D ]\}}|\}}}tj|||}t||dd qd S Nr  rr   )r{   r1   studentized_rangerD   r   )r   pvkr  
p_expectedr  r>   res_pr,   r,   r-   test_cdf_against_tables  s
   
z,TestStudentizedRange.test_cdf_against_tablesc                 C   s.   | j D ]\}}tjj| }t||dd qd S r  )r{   r1   r  r  r   )r   r  
q_expected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_resultr  r>   r  expected_atolexpected_rtolrT  r1   r  rD   r   r   r  r  r  qkvrC  r,   r,   r-   test_cdf_against_mp     
z(TestStudentizedRange.test_cdf_against_mppdf_datac                 C   r  r  )r1   r  r:   r   r  r,   r,   r-   test_pdf_against_mp  r  z(TestStudentizedRange.test_pdf_against_mpmoment_datac                 C   r  )	Nr  r  r  r>   r  r  r  rT  )r1   r  r_  r   )r   r  r  r  mkvrC  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   rc   r   rA  r   )r   r1   r  r:   rh   r   r   )r   r>   r  rC  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   rc   rm   )stepr   r  rr   )rh   r   r1   r  rD   r:   r   r   )r   r>   r  rA   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   s*   |\}}}}t j|||}t|| d S rf   r  )r   r  r  r>   r  r_resrC  r,   r,   r-   test_cdf_against_r  s   z'TestStudentizedRange.test_cdf_against_rc                 C   st   t jddgddgddg}t|jd tjtdd	 t jdddgg d
 W d    d S 1 s3w   Y  d S )Nr   r8   r  r   rc   r  r  z...could not be broadcast...r   )rc   r  r   )r1   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|  invalidr   )
r
   rh   r  rZ   r   r1   r  rv  r   	_argcheck)r   rv  r>   rm  r5  r,   r,   r-   test_fitstart_valid"  s   
 z(TestStudentizedRange.test_fitstart_valid),r   r   r   q05q01q001rh   r  qspsr   vsksr   r"   r{   r_datar  r   rK  rL  r  r]  r^  ra  rb  path_prefixrelative_pathopenr`  filejsonrc  pregenerated_datar,  r  r  r  r  xslowr  r  r  r  r,   r,   r,   r-   r    sN    








	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?rc   test_540_567)r   err_msgg2gk?g;B.?gͣh?gHŎ*?r5   g.y?)r   r1   r  rD   r,   r,   r,   r-   r  +  s   
r  c                   C   s   t jjdd d S )Nr  r  )r1   _continuous_distns	gamma_genr,   r,   r,   r-   test_regression_ticket_13167  s   r  c                   C   s   t tjdddd d S )Nrp   r8   rk   r-  r.  r,   r,   r,   r-   test_regression_ticket_1326=  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   rb   r|  dividerp   r  r  ro   r   r   r8   )rh   r   r  r   r1   r%   r:   r   r   rl  any)rA   r  r   r,   r,   r-   test_regression_tukey_lambdaB  s   "	r  zdocstrings strippedr  c                   C   s$   t dtjjv t dtjjv  d S )Nzpdf(x, mu, loc=0, scale=1)zpmf(x,)r   r1   r  r  r,   r,   r,   r-   test_regression_ticket_1421W  s   r  c                   C   s  t jdd tt tjdt j tt tjdt j tt tj	dt j tt tj
dt j tt tjdt j tt tjdt j tt tjdt j tt tjdt j tt tjt jd tt tjt jd tt tj	t jd tt tj
t jd tt tjt jd tt tjt jd tt tjt jd tt tjt jd W d    d S 1 sw   Y  d S )Nr|  r  r   rk   )rh   r  r   rl  r1   rl  r  r   rD   r  r  r:   r   r  r   r
  r   r'  r,   r,   r,   r-    test_nan_arguments_gh_issue_1362]  s$   "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   rp   rk   r   r   r8   rd   r   r|  r  rp   r  r   rk   )r   r6   r   )r   r6   r  r8  ro   r  )rh   r   r   r   r1   r   r   r  rw   r   r  rj  r   )truerA   paramsr6   r   r_   r,   r,   r-   test_frozen_fit_ticket_1536r  s(     r  c                  C   s<   t jd tjjdd} tj| }d}t||dd d S )Ni	 rd   r   )g
ףp=
?gʡE?r   r   )rh   r   r   r1   ro  r   rw   r   )r   r  r_   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  )rh   r   r   randnr1   ro  rw   r   )rA   offsetr6   r7   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  r8   r   r  rc   r   g
ףp=
	@)r   gz5v?r   gRTgQ?)r   gNg @r   gJFٻ)r1   r%   rh   r<   r   )r  r_   r,   r,   r-   "test_tukeylambda_stats_ticket_1545  s   r  c                   C   s   t ttjdd d S )Nr,  r  )r   rh   r%  r1   r  r'  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   )rk   r  rp   r  )ro   )gUUUUUU?r  g^cQg333333r  r  N)r1   powerlawr   )casesr*   
exact_mvskr  r,   r,   r-   test_powerlaw_stats  s   r  c                  C   s   t jdd} t| d d S )Nr   r   rp   )r1   r  r   r   r   r,   r,   r-   test_powerlaw_edge  rN  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   rp   )r   r   r+  r   )r1   r  r   r   r:   rh   r   r  r,   r,   r-   test_exponpow_edge  s   
r  c                  C   sR   t jddd} t| d t jddd} t| d t jddd} t| d d S )	Nr   r   r   r  r  g>rc   gqq?)r1   gengammar:   r   r|  r   r  r,   r,   r-   test_gengamma_edge  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)
rh   r   r  r
   rZ   r   r   r1   r  rw   )ra  rv  r,   r,   r-   test_ksone_fit_freeze  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  r  )gDB.g8_$g%`OAgjhwHRgWMB@v`g7VY}igۦx\Arg	xg#g/dg3$gegd)gNq{3gيGǓgr4g37'
gfFg?dJgضg2,
gm%gӅJgz;pgɿ{gk2gij<%giVSͶgBR4g
Q/Mr  r  y        +=y        |=r  )rh   r  listrb  r   r1   r  r  realimagr&  r   )rA   r_   derivderiv_expectedr,   r,   r-   test_norm_logcdf  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   rk   ra   rm   r  )g~V1?g|N?gba"?g܄4ťY?r  g$%+Ir  rr   rS  )rh   r   r1   r   rD   r   r  )rA   r_   rX  r  r,   r,   r-   test_levy_cdf_ppf/  s   r  c                  C   :   t g d} t g d}tj| }t||dd d S )N)g  4&kCg(,* EgMraB3Ggd~QJ)gep[>g}XEQ=gѭEG<g?_%~:r  rr   )rh   r   r1   r   r  r   rA   r_   rX  r,   r,   r-   test_levy_sfG     r  c                  C   r  )N)gMbg{Gzg{Gztg~jtX)g#]<gOul2;gޢا6g̅7=!rS  rr   )rh   r   r1   r   r  r   r  r,   r,   r-   test_levy_l_sfS  r  r  c                  C   s8   t g d} tj| }tj|}t|| dd d S )N)g [n<r   re  gvIh%,=rr   )rh   r   r1   r   r   r  r   )r   rA   r  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 )Nr  i i  i  )g      c@g     h@g=
ףp=?Gz?)g      c@g     h@{Gz?rd   r~  r   )r   r1   r.  r  r  r,   r,   r,   r-   test_hypergeom_interval_1802g  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   ra   gffffff?r   )numr8   r   r   r  r  rk   r5   ro   r  r  r   r  r  )rh   r   r   r   r  r   r1   r  r:   r   rD   r  rP   rw   r  r   r  rD  r  r  r,   r,   r-   test_distribution_too_many_argsv  s8   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 )	Nrq  r}  r:  r8   gYZ@r  r   r   )r1   ncx2rD   rh   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^  r8   r   r  r   r   gsq6)r   r   r   r   r   r1   r  r:   rh   r   r   r   r  r   r   )logvalr,   r,   r-   test_ncx2_tails_pdf  s   

"r  zmethod, expectedrD   gu%>g	;Q=r:   g<x>gRz\R>r   gʎK$/gԆX1r  gfHu@ge:@c                 C   s,   t tj| dddgdd}t||dd d S )Nra   r   r  rc   )r&  rm  rq   r  )r   r1   r  r   )r  r_   rO  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 )Nrc   r   r   )rm  r&  r.  )rm  r.  rq   r  )r1   r  r   r/  r   )rO  r_   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 )Nrc   r   r:  r   rm  r&  r   )rh   r   r   r1   r  rD   )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@)rq  gh ?8@r  )r   r   r   r   r   g?gy[qD?rp   rp   rp   rp   rp   rp   rV  r  )rh   r   r1   r  r  r   )rA   nur  r  sf_expectedr,   r,   r-   test_ncx2_gh8665  s
   
r  c                  C   s"   t jddd} t| dd d S )Nr   r   r  )r1   foldnormr   rD   r  r,   r,   r-   test_foldnorm_zero  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)rp   rk   r   r   rk   r   c                 s   s     | ]}t jt j|f V  qd S rf   rh   r   r   r  r,   r,   r-   r    r  z-test_stats_shapes_argcheck.<locals>.<genexpr>)r8   r]  rv  r8   r]  c                 s   s     | ]}t j|t jf V  qd S rf   r  r  r,   r,   r-   r    r  )r1   r   tupler   r   )mv3mv2mv2_augmentedr,   r,   r-   test_stats_shapes_argcheck  s   
r  c                   @   r  )
_distr_genc                 C   r  Nr  r,   r   rA   r*   r,   r,   r-   _pdf  r  z_distr_gen._pdfNr   r   r   r  r,   r,   r,   r-   r    r  r  c                   @   r  )_distr2_genc                 C      d| | S r  r,   r  r,   r,   r-   _cdf     z_distr2_gen._cdfN)r   r   r   r  r,   r,   r,   r-   r	    r  r	  c                   @   r  )_distr3_genc                 C   s   || S rf   r,   r   rA   r*   r+   r,   r,   r-   r    s   z_distr3_gen._pdfc                 C   r
  r  r,   r  r,   r,   r-   r    s   z_distr3_gen._cdfNr   r   r   r  r  r,   r,   r,   r-   r    r  r  c                   @   r  )_distr6_genc                 C   s   || | S rf   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$   t ddd}t|jdddd d S )Ndummyr*   r  r   r   r!  r  r  r   r:   r   dummy_distrr,   r,   r-   test_correct_shapes/  s   z1TestSubclassingExplicitShapes.test_correct_shapesc                 C   s,   t ddd}tt|jdfi tdd d S )Nr  Ar  r   r!  )r  r  r   r:   r   r  r,   r,   r-   test_wrong_shapes_13  s    z1TestSubclassingExplicitShapes.test_wrong_shapes_1c                 C   s4   t ddd}tdddd}tt|jdfi | d S )Nr  za, b, cr  r   r8   r   r  )r  r   r  r   r:   )r   r  r   r,   r,   r-   test_wrong_shapes_27  s   z1TestSubclassingExplicitShapes.test_wrong_shapes_2c                 C   "   t ddd}tttfi | d S )Nr  r  r  )r   r  r   r  r   r   r,   r,   r-   test_shapes_string<     z0TestSubclassingExplicitShapes.test_shapes_stringc                 C   r  )Nr  z(!)r  r   r  SyntaxErrorr  r  r,   r,   r-   test_shapes_identifiers_1A  r  z7TestSubclassingExplicitShapes.test_shapes_identifiers_1c                 C   r  )Nr  4chanr  r  r  r,   r,   r-   test_shapes_identifiers_2F     z7TestSubclassingExplicitShapes.test_shapes_identifiers_2c                 C   r  )Nr  zm(fti)r  r  r  r,   r,   r-   test_shapes_identifiers_3J  r$  z7TestSubclassingExplicitShapes.test_shapes_identifiers_3c                 C   r  )Nr  za=2r  r  r  r,   r,   r-   "test_shapes_identifiers_nodefaultsN  r$  z@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaultsc                 C   r  )Nr  z*argsr  r  r  r,   r,   r-   test_shapes_argsR  r$  z.TestSubclassingExplicitShapes.test_shapes_argsc                 C   r  )Nr  z**kwargsr  r  r  r,   r,   r-   test_shapes_kwargsV  r$  z0TestSubclassingExplicitShapes.test_shapes_kwargsc                 C   r  )Nr  za, b, c, lambdar  r  r  r,   r,   r-   test_shapes_keywordsZ  r  z2TestSubclassingExplicitShapes.test_shapes_keywordsc                 C   s@   G dd dt j}|dd}t|jdddt jdd  d S )Nc                   @   r  )zFTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_genc                 S      t j|| S rf   r1   r  r  r  r,   r,   r-   r  b  r   zKTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_gen._pdfNr  r,   r,   r,   r-   	_dist_gena  r  r,  r*   r   rk   r8   r!  r1   rN   r   r:   r  r   r,  rJ   r,   r,   r-   test_shapes_signature_  s   
$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   r*  rf   r+  r  r,   r,   r-   r  k  r   zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_gen._pdfNr  r,   r,   r,   r-   r,  j  r  r,  a, br-  rk   r   r8   r  )r1   rN   r  r   r:   r   r/  r,   r,   r-   "test_shapes_signature_inconsistenth  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   r+  )r   rA   r   extra_kwargr,   r,   r-   r  u  s   zDTestSubclassingExplicitShapes.test_star_args.<locals>._dist_gen._pdfNr  r,   r,   r,   r-   r,  t  r  r,  r4  r-  rk   !   r4  )xxx)r1   rN   r   r:   r  r  r   r   r/  r,   r,   r-   test_star_argsq  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 r3  r+  )r   rA   r  r   r4  r,   r,   r-   r    s   zFTestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_gen._pdfNr  r,   r,   r,   r-   r,    r  r,  zoffset, extra_kwargr-  rk   o   r5  )r  r4  r.  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 )Nr4  r   )popr1   r  r  )r   rA   r   kwargsr4  r,   r,   r-   r    s   zGTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_gen._pdfNr  r,   r,   r,   r-   r    r  r  r4  r-  r   r   r6  r.  )r   r  rJ   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 rf   )r1   r  r:   r!  r,   r,   r-   r    r  zITestSubclassingExplicitShapes.shapes_empty_string.<locals>._dist_gen._pdfNr  r,   r,   r,   r-   r,    r  r,   r-  rk   r.  r/  r,   r,   r-   shapes_empty_string  s   
z1TestSubclassingExplicitShapes.shapes_empty_stringN)r   r   r   r  r  r  r  r!  r#  r%  r&  r'  r(  r)  r0  r2  r8  r:  r=  r?  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findallr  r   r   r   r  rC  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  r8   r1  z!logpdf\(x, a, b, loc=0, scale=1\)r   )	r  r   rD  r   rE  rF  r  r   r   rG  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  r4   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-   r,    s    r,  r  r  r1   rN   r  r   r   r   r,  r,   r,   r-   test_defaults_raise     z+TestSubclassingNoShapes.test_defaults_raisec                 C   rK  )Nc                   @   r  )z>TestSubclassingNoShapes.test_starargs_raise.<locals>._dist_genc                 W   r  r  r,   )r   rA   r*   r   r,   r,   r-   r    r  zCTestSubclassingNoShapes.test_starargs_raise.<locals>._dist_gen._pdfNr  r,   r,   r,   r-   r,    r  r,  r  r  rL  rM  r,   r,   r-   test_starargs_raise  rO  z+TestSubclassingNoShapes.test_starargs_raisec                 C   rK  )Nc                   @   r  )z<TestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_genc                 [   r  r  r,   )r   rA   r*   r<  r,   r,   r-   r    r  zATestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_gen._pdfNr  r,   r,   r,   r-   r,    r  r,  r  r  rL  rM  r,   r,   r-   test_kwargs_raise  rO  z)TestSubclassingNoShapes.test_kwargs_raiseN)r   r   r   rA  rB  r   rK  r  DOCSTRINGS_STRIPPEDrH  rI  rJ  rN  rP  rQ  r,   r,   r,   r-   r@    s    


	r@  rC  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*:)
r1   rY   r   r   rM   rN   r   rE  searchr  )badonesdistnamerJ   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 )Nrc   r  r   r~  ra   r   )r   r1   r  r  rh   r   r  r  r,   r,   r,   r-   test_infinite_input  s   rW  c                  C   &   t jt jddd} t| d d S Ng0.++r   )r1   lomaxr  rD   r   r  r,   r,   r-   test_lomax_accuracy     r[  c                  C   rX  rY  )r1   gompertzr  rD   r   r  r,   r,   r-   test_gompertz_accuracy  r\  r^  c                  C   rX  rY  )r1   
truncexponr  rD   r   r  r,   r,   r-   test_truncexpon_accuracy  r\  r`  c                  C   s*   t jt jddd} t| ddd d S )N	   r   r  r   r   )r1   r   r   r  r   r  r,   r,   r-   test_rayleigh_accuracy   s   rb  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)rk  alwaysrk   r   rp   N)r   r   r   r1   r  rD   r:   r  r   rh   r   r   r   )r  number_of_warnings_thrownr,   r,   r-    test_genextreme_give_no_warnings  s   
"re  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  r8   r   r  rr   r   r   r  rc   r  r   r  rR  r  )r1   r  rP   r   r   rh   r  )euler_gammar   r,   r,   r-   test_genextreme_entropy  s   
 rg  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?)r1   r  r  r   r   )rA   r@   ru  r,   r,   r-   test_genextreme_sf_isf+  s   




rh  c                  C   s"   d} t j| dd}t|d d S )NgؗҜ<r8   r   gH&8>)r1   rv  r  r   )probr@  r,   r,   r-   test_burr12_ppf_small_argW  s   	rj  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      Nrv  r   ro   )rX  r  )gC,d	Ɣ?gH㸘?g5?gM"M#w?gɫs^?g @?gƴ?g@w?ɫs^?|?q ?g C?rm  rl  gJó?g,BV\ۤ?g;?g#ek?g%ǓE?g(Ȍx?g>J>r  rr   r  )g#{`?gdf?g Jq?gSS){?g'	w?uL? T)?cAJ?GTn?R1#?gA]P?rr  rq  rp  ro  gvӢ?gKq?gL?g
	N<!?gAw>rk   )rX  r  r6   r7   )g=aO}?gI8?g#T?aW)?ǓI?
J?E?d۳?GTn?8?R1#?kP?g(*T?rz  ry  rx  rw  rv  ru  rt  rs  )gD
)?g:3P?g9?g?S[?rl  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?rn  ğ@ _?y}D?焂Rr/?N?YjhG?a0L?4f?<@?@CH?g	ސF?g5+-#?g?g?q ?r{  )g}'v?rn  g*V?r|  gr/0+?r}  g[8	?r~  gΥ?r  gY?r  g#)a?r  g?̔?r  g]ؚ?r  g|c ?r  )rh   r   r1   crystalballr:   r   r   rD   )r  
calculatedr_   r,   r,   r-   test_crystalball_functione  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
    )ro   r   r  ro   r  )r  r  ro   r\  r  )r   r   r   r   r   r   r  rr   )gԚh@g[&@gͪ@g2dQ@gn6-@g?ޫV&̿g BgQCRgQF\ jr   g
@gn(@r8   g?Җ)r   gMg'#@r  g('UHr   N)rh   r   r1   r  r|  r   r   )rX  r  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 )Nr8   r   )ir   i@ Hz>rr   )	r1   r  rP   rh   r   r   r   r:   r   )cbr  r  r  r1  rA   rE  r,   r,   r-   test_crystalball_entropy  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 )NrV  )r   dispxtolftol)r!   )r|   x0r   r  r,   r,   r-   	optimizer  s   z"test_invweibull.<locals>.optimizer)r   r^  r8   r  r   r   r8  r  r   r~  rc   r   @   c   )r   r  g`?r  rr   g [@N)r,   r   )rh   r   r1   r   rw   r   )r  rA   r  r6   r7   r,   r,   r-   test_invweibull  s   
r  z	df1,df2,xr8   )r@  r:  r   r*  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  rr   r]  )r1   ri  rD   r  r   r:   )df1df2rA   r&  expected_cdfcalculated_cdfru   calculated_pdfr,   r,   r-   test_ncf_edge_case  s   
r  c                  C   s"   t jddd} t| ddd d S )Nr8   r  r  g     `E@r  rr   )r1   r  ra  r   )r  r,   r,   r-   test_ncf_variance     r  c                   @   r  )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   r8   r8   r   r   r   r  r  r  r  r   r   r   r   r   r  r  r  r  r  r  r  r~  r~  ra  r~  binsr   r  r  {   )r6   r7   r   r.  r   )
rh   r   r   	histogramr1   rO   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rp   rk   r   r+  ro   r  r  r  r\  r  r         @r  rm        @      @rQ        !@r  g      #@)rp   rp   r   r   {Gz?r  Q?r  {Gz?r  r:  r:  r  r  r  r  r  r  rp   rp   rQ  r  r  r  rp   r  r  r8   rc   r   r  r5   ra   rr   )rh   r   r  r   r  r:   r   r   r  r1   r  )r   r  
pdf_valuesrA   r,   r,   r-   r   8  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  )rp   rp   rp   r  r   r  r  
ףp=
?Q?{Gz?r@  rk   r  (\?RQ?=
ףp=?)\(?r  r   r   r8   rv  r   r  rd   rp   r  rc   r  r5   ra   rr   )rh   r   r  r   r  rD   r  r   r  r1   r  )r   r  
cdf_valuesrA   r,   r,   r-   r  R  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$kd%| dd	 tt|d&kd| dd	 tt|d&kd| dd	 tt|d&kd d S )'Nr  r  r-  r   rp   ro   r   r:  rr   r  r  r  r  ra   r  r  r\  r  r  r  r   r@  r/  r  rk   r  r  rm  r  r  r  r  r  rQ  r  r  r  r  )r  r   r   rh   r   r   )r   r1  r  r,   r,   r-   r   h  s(   zTestHistogram.test_rvsc                 C   s6   t dD ]}t| j|tdd|dd qd S )Nr  r   r  r/  rr   )rb  r   r  r|  r1   r  r_  )r   r   r,   r,   r-   	test_munp~  s
   zTestHistogram.test_munpc                 C   s$   t | j tjjddddd d S )Nr   r  r5   r/  rr   )r   r  rP   r1   r  r   r,   r,   r-   r     s   

zTestHistogram.test_entropyN)	r   r   r   r   r   r  r   r  r   r,   r,   r,   r-   r  '  s    r  c                  C   s   t dd} | jddd}tjt|dd\}}d|   kr-|   kr-d	ks0J  J tt	|d
 dks>J d S )Nr  r   r  r  r-  rc   r  r  iL  r  )
r1   
loguniformr   rh   r  log10r  r  rJ  rI  )r  r   r   r5  r,   r,   r-   test_loguniform  s
   . r  c                   @   s   e Zd Zdd Z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   r/  iE  r-  r  r   )r1   argusr   r   r   r!  r,   r,   r-   test_argus_rvs_large_chi  s    z"TestArgus.test_argus_rvs_large_chic                 C   sN   t jjdddd}tt d | dd tt d | dd d S )Nr  r,  i  r-  r   r   )r1   r  r   r   r   r   r!  r,   r,   r-   test_argus_rvs_ratio_uniforms  s    z'TestArgus.test_argus_rvs_ratio_uniformszchi, expected_mean))r   g щi?)rc   g.憃?)r  g\paP?)<   g	?)r  g,6?c                 C   s"   t jj|dd}t||dd d S )Nr   r  rS  rr   )r1   r  r   r   )r   r  expected_meanr  r,   r,   r-   	test_mean  r  zTestArgus.test_meanzchi, expected_var, rtol))r   gLH'B?rS  )rc   go$?rr  )r  g
=>r  )r  g2W>r  )r  gb~P>r  c                 C   s"   t jj|dd}t|||d d S )Nr   r  rr   )r1   r  ra  r   )r   r  expected_varrs   r  r,   r,   r-   r    r  zTestArgus.test_varzchi, expected, rtol))r8  gwM?r  )rk   gj?r  )ra   gHEA`!?r  )rm   gcف>rq   )r  gF=r  )r  g߹Q#B=r  )r]  g0ޟ<r  )r  g*W%:rq   c                 C   s   t t|||d d S )Nrr   )r   r   )r   r  r_   rs   r,   r,   r-   test_argus_phi_small_chi  s   
z"TestArgus.test_argus_phi_small_chizchi, expected))rk   )g-\/?g+p7c?g5Ϧ\?)r:  )g
f?gi{?ٸ?gZ@7?)ra   )gB	?g]?gR{?)rm   )glͅw?g,?g[Z=?)r  )gz,?g]?gѪ1?)r  )g8<?gE-?gI?)r]  )g~7?g7B.?g9?)r  )g;?g9B.?g}5?c                 C   *   t g d}ttj|||dd d S )Nra   rk   r8  rS  rr   )rh   r   r   r1   r  r:   r   r  r_   rA   r,   r,   r-   test_pdf_small_chi     zTestArgus.test_pdf_small_chi))rk   )gQ߹?e?grJ,?g򺗄?)r:  )gΎd?g?gh?)ra   )g|
o?gvb?g+@?)rm   )g̈́On?ge?gC|[3?)r  )g!?m?g{jiH?gu53?)r  )g~m?g0-.?g3?)r]  )g~m?g7;B.?gŗ3?)r  )g~m?g9B.?gŗ3?c                 C   r  )Nr  r  rr   )rh   r   r   r1   r  r  r  r,   r,   r-   test_sf_small_chi  r  zTestArgus.test_sf_small_chi))rk   )g+&?gk?gμm/?)r:  )g?CL\f?g^N?g]AͭR?)ra   )ga>$?g;Lf?gaW?)rm   )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  rV  rr   )rh   r   r   r1   r  rD   r  r,   r,   r-   test_cdf_small_chi  r  zTestArgus.test_cdf_small_chi))rk   )gQ)?g6{?rV  )gB`"۹?)g?g8%?rr  )ra   )g388?gV%?rS  )rm   )g*j?gRS%?rS  )r  )g!|?gZ%?rS  )r  )gy[|?gG%?rS  )r]  )g"3|?gW%?rS  )r  )g!3|?gW%?rS  c                 C   s"   t jj |dd}t|||d d S )Nr  r  rr   )r1   r  r   )r   r  r_   rs   r   r,   r,   r-   test_stats_small_chi  s   zTestArgus.test_stats_small_chiN)r   r   r   r  r  r   rK  r,  r  r  r  r  r  r  r  r,   r,   r,   r-   r    sF    


	






r  c                   @   s   e Zd Zdd Zdd Z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+)r1   nakagamir   r   )r   r  rA   r*  r,   r,   r-   r+    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+:rS  rr   )r1   r  r  r   r   )r   r  r  r  rt  r,   r,   r-   rY    s   zTestNakagami.test_sf_isfr  )g?r  r9  r6   )rn   rc   #   r7   )r0  r   rq  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 )Nrd   9  r   r  r6   r7   r.  r:  rr   c                    s<   d|  d t d |   d|  |d  t  |   S )Nr  r   r8   rh   r   r  r6   r7   )r  r,   r-   	dlogl_dnu1  s   z(TestNakagami.test_fit.<locals>.dlogl_dnuc                    sN    dt |  td|   dt t | |   t | | d  S )Nr   r   r8   )rh   r  r   r   r  r1  r  r,   r-   
dlogl_dloc5  s
   z)TestNakagami.test_fit.<locals>.dlogl_dlocc                    s2   d  |  | d|  |d  t | d   S )Nr  r8   r   r  r  r  r,   r-   dlogl_dscale:  s    z+TestNakagami.test_fit.<locals>.dlogl_dscaler   r  r  )r1   r  r   rw   r   )
r   r  r6   r7   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 )	Nrk   rd   r  r  r2  r8   r  rr   )	r1   r  r   rw   rh   r  rj  r   r   )r   r6   r7   r  r   r  r  r  r  loc_theo
scale_theor,   r,   r-   test_fit_nuB  s   
zTestNakagami.test_fit_nuN)
r   r   r   r+  rY  r   rK  r,  r{  r  r,   r,   r,   r-   r    s    r  c                   @   r  )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   rk   r   r   r\  r  c                 S   s   g | ]\}}t j||qS r,   )r1   
wrapcauchyrD   )rI   rt  ri  r,   r,   r-   rK   `  s    z>TestWrapCauchy.test_cdf_shape_broadcasting.<locals>.<listcomp>rS  rr   )	rh   r   r1   r  rD   r   nditerr   re  )r   r  rA   r   scalar_valuesr,   r,   r-   test_cdf_shape_broadcastingX  s   z*TestWrapCauchy.test_cdf_shape_broadcastingc                 C   s"   t jtjd}t|ddd d S )Nr  rk   r  rr   )r1   r  rD   rh   r<   r   r  r,   r,   r-   test_cdf_centerd  r#  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   r8   )r1   r  rD   r   rh   arctantanr<   )r   rt  ru  r  r   crr,   r,   r-   r   h  s   (6zTestWrapCauchy.test_cdfN)r   r   r   r  r  r   r,   r,   r,   r-   r  V  s    r  c                  C   sT   G dd dt j} | dd}ttj |  W d    d S 1 s#w   Y  d S )Nc                   @   r  )z1test_rvs_no_size_warning.<locals>.rvs_no_size_genc                 S   r  r  r,   r   r,   r,   r-   _rvst  r  z6test_rvs_no_size_warning.<locals>.rvs_no_size_gen._rvsN)r   r   r   r  r,   r,   r,   r-   rvs_no_size_gens  r  r  rvs_no_sizer  )r1   rN   r   rh   VisibleDeprecationWarningr   )r  r  r,   r,   r-   test_rvs_no_size_warningr  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   r  r   r1   r   rN   r   supportr   rh   r   )rU  r   rJ   a0b0rB  rC  a1b1r*   r+   r,   r,   r-   test_support_gh13294_regression}  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   rv  rv  r  )	r1   r  r  rh   r   r   r   r   r   )r  r  ex_a0ex_b0r  r  ex_a1ex_b1r  r  ex_a2ex_b2r,   r,   r-   ,test_support_broadcasting_gh13294_regression  s(    





r  r(  )gn!	g:I"<)gQ	@gE?c                 C   s*   t tj| | t tj|  | d S rf   )r   r1   cosinerD   r  )rA   r_   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 rf   )r   r1   r  r  r   )r   r_   r,   r,   r-   test_cosine_ppf_isf  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   rS   rI   r  r5  r,   r,   r-   	<setcomp>  s    
z*test_distr_params_lists.<locals>.<setcomp>c                 S      h | ]\}}|qS r,   r,   r	  r,   r,   r-   r
    rL   c                 S   r  r,   r,   r	  r,   r,   r-   r
    rL   c                 S   r  r,   r,   r	  r,   r,   r-   r
    rL   )r   r   r   r   )discrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamesr,   r,   r-   test_distr_params_lists  s   r  rf   )r  r   rE  r\  r  r]  r  platformnumpy.testingr   r   r   r   r   r   r   r	   r
   r   r   r  r;   rh   r   r   numpy.lib.recfunctionsr   r0   r   scipy._lib._utilr   r  r   r   r   r   scipy.statsr1   !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optimizerR  machiner  r  r.   r3   rC   rE   r`   re   ri   rl   rK  r,  rv   r   r   r   r   r   r  r	  r  r  r$  r(  rN  rz  r  r  r  r  r  r  r'  r-  rT  re  r  r  r  r  r  r  r  r  r  r&  r.  rG  rW  r^  rz  r|  r~  r  r  r  r  r  r  r  r  r  r  r  r  r   r&  r,  r1  r5  r8  r  r  r  r  r  r  r!  r.  r8  r>  rC  rJ  rM  rS  rW  rm  rp  rt  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rN   r  r	  r  r  r  r@  r  rW  r[  r^  r`  rb  re  rg  rh  rj  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r,   r,   r,   r-   <module>   s   ,

.	
H $&5# \ 'E( w:?* $ l)+ !-:v,U* V
 o h =E6,\^K 
	
&(
	x;	,G.!a	lY

