o
    5Bi                    @   s@  d Z ddlZddlZddlZddlZddlmZ ddlZddlZddl	Z	ddl
mZmZmZmZmZmZmZmZmZ 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/m0Z0m1Z1 ddl2m3Z3m4Z4 ddl5m6Z6m7Z7 ddl8m9Z9m:Z:m;Z; ddl<m=Z= ej>j?dkZ@ej	dkoe	A dkZBddgZCdddZDdd ZEdd ZFG dd dZGdd d!ZHd"d# ZIejJKd$g d%d&d' ZLG d(d) d)ZMG d*d+ d+ZNG d,d- d-ZOG d.d/ d/ZPG d0d1 d1ZQG d2d3 d3ZRG d4d5 d5ZSG d6d7 d7ZTG d8d9 d9ZUG d:d; d;ZVG d<d= d=ZWG d>d? d?ZXG d@dA dAZYG dBdC dCZZG dDdE dEZ[G dFdG dGZ\G dHdI dIZ]G dJdK dKZ^G dLdM dMZ_G dNdO dOZ`G dPdQ dQZaG dRdS dSZbG dTdU dUZcG dVdW dWZdG dXdY dYZeG dZd[ d[ZfG d\d] d]ZgG d^d_ d_ZhG d`da daZiG dbdc dcZjG ddde deZkG dfdg dgZlG dhdi diZmG djdk dkZnG dldm dmZoG dndo doZpG dpdq dqZqG drds dsZrG dtdu duZsG dvdw dwZtG dxdy dyZuG dzd{ d{ZvG d|d} d}ZwG d~d dZxG dd dZyG dd dZzG dd dZ{G dd dZ|G dd dZ}G dd dZ~G dd dZddeddej   ddeddej   ddeddej   ddeddej   ddeddej   g	fdeddej  ddeddej   ddeddej   d ddeddej   d ddeddej   d g	fddedej  dddedej   dddedej   dddedej   dddedej   dddedej   dddedej   dgfgZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG ddÄ dÃZG ddń dŃZG ddǄ dǃZG ddɄ dɃZdd˄ ZG dd̈́ d̓ZG ddτ dσZG ddф dуZG ddӄ dӃZG ddՄ dՃZG ddׄ d׃ZG ddل dكZddۄ ZG dd݄ d݃ZG dd߄ d߃ZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG d d dZG dd dZG dd dZdd Zdd	 Zd
d ZejJje@dddd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# ZejJKd$g d%d&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 ZejJKd4g d5d6d7 ZĐd8d9 ZŐd:d; ZƐd<d= Zǐd>d? ZȐd@dA ZɐdBdC ZejJKdDdEedFdGgfdHedIdJgfdKedLdMgfdNedOdPgfgdQdR ZːdSdT Z̐dUdV Z͐dWdX ZΐdYdZ ZejJKd[g d\d]d^ ZejJKd_g d`dadb ZejJKdcg dddedf ZҐdgdh ZejJKd[g didjdk ZԐdldm ZG dndo doe'jփZG dpdq dqe'jփZG drds dse'jփZG dtdu due'jփZG dvdw dwZG dxdy dyZejJje@dzdd{d| Zݐd}d~ Zސdd Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZejJKd[g ddd ZejJKdddgdd ZejJKdddg dfddg dfddg dfgdd Zdd Zdd ZejJjejdkdddd ZG dd dZdd ZG dd dZG dd dZG dd dZG dd dZdd ZejJKde4e1 dd Zdd Zdd ZejJKd_dÐdgdŐdƄ ZejJKdcg dǢdȐdɄ Zdʐd˄ Zd̐d̈́ Zdΐdτ ZG dАdф dуZ G dҐdӄ dӃZG dԐdՄ dՃZG d֐dׄ d׃ZejJKdg d٢dڐdۄ ZdS (  z!
Test functions for stats module
    N)Path)	assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_assert_warnsassert_array_lesssuppress_warnings)raises)	typecodesarray)rec_append_fields)special)check_random_state)IntegrationWarningquad	trapezoidcumulative_trapezoid)
argsreduce)xlogy	polygammaentr)distcontinvdistcont   )distdiscreteinvdistdiscrete)FitDataError
_argus_phi)rootfmindifferential_evolution)productdarwinx86_64tukeylambdapearson3c                 C   s,   |d u r|  d| }t t| ||d d S )Nz does not have attribute msg)r   hasattr)abr*    r.   d/var/www/html/Trade-python/venv/lib/python3.10/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattr4   s   r0   c                   C   s   t tjjd d S )Nf_gen)r0   scipystatsdistributionsr.   r.   r.   r/   test_api_regression:      r5   c                  C   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>A       z0test_distributions_submodule.<locals>.<listcomp>c                 S   r7   r8   r.   r9   r.   r.   r/   r<   B   r=   )rv_discreterv_continuousrv_histogramentropytrapzc                 S   s   t | d S )N<)str
startswithsr.   r.   r/   <lambda>I       z.test_distributions_submodule.<locals>.<lambda>)setr2   r3   r4   __all__r   r   filter)actual
continuousdiscreteotherexpectedr.   r.   r/   test_distributions_submodule?   s   rR   c                	   @   s@  e Zd Zejdg dejdddejddgdd	 Zd
d Z	dd Z
ejdg ddd Zejdg ddd Zdd Zejdg ddd Zdd Zejjejdddgejd g d!ejd"d#d$gejd%d#d$gd&d' Zd(d) Zejd*d+dgd,d- Zd.d/ Zd0d1 Zd2d3 Zd4S )5TestVonMisesk)皙?r   e   xr   r   
   d   c                 C   sh   dd }dd }||dd| ||dd| ||dd| ||dd| ||dd| ||dd| d S )Nc                 S   s8   t j| ||d}t||||dtj |   d S )Nlocscale   )r3   vonmisesr   pdfnppirT   LrG   rW   vmr.   r.   r/   check_vonmises_pdf_periodicR   s   (zHTestVonMises.test_vonmises_periodic.<locals>.check_vonmises_pdf_periodicc                 S   s@   t j| ||d}t||d ||dtj |  d  d S )NrZ   r   r]   )r3   r^   r   cdfr`   ra   rb   r.   r.   r/   check_vonmises_cdf_periodicV   s   zHTestVonMises.test_vonmises_periodic.<locals>.check_vonmises_cdf_periodicr   r   rX   r.   )selfrT   rW   re   rg   r.   r.   r/   test_vonmises_periodicO   s   z#TestVonMises.test_vonmises_periodicc                 C   s&   t tjjtj  t tjjtj d S N)r   r3   vonmises_liner,   r`   ra   r-   rh   r.   r.   r/   test_vonmises_line_supportc   s   z'TestVonMises.test_vonmises_line_supportc                 C   s   t d}t|dd d S )N   r         ?)r3   r^   r   rf   )rh   rd   r.   r.   r/   test_vonmises_numericalg   s   
z$TestVonMises.test_vonmises_numericalzx, kappa, expected_pdf))rU   {Gz?g|65?)rU         9@g?U?)rU   rn   g"?)       @rq   gDfI?)rs   rr   g1<)rs   rn           c                 C       t j||}t||dd d S NV瞯<rtol)r3   r^   r_   r   )rh   rW   kappaexpected_pdfr_   r.   r.   r/   test_vonmises_pdfu      zTestVonMises.test_vonmises_pdfzkappa, expected_entropy))r   gA	?)   g,eޞ?)rY   gBb9d22)  g
G )  gc                 C      t j|}t||dd d S NvIh%<=rx   )r3   r^   rA   r   )rh   rz   expected_entropyrA   r.   r.   r/   test_vonmises_entropy   s   z"TestVonMises.test_vonmises_entropyc                 C   s   d}t j|}t j|}t j|}tjddddj|d}tjddt j ddj|d}tjdddt j t| d dj|d}t||dd t||dd d S )	Ni@}r   r   rZ   random_stater]   rw   atol)	r`   randomdefault_rngr3   r^   rvsra   absr   )rh   seedrng1rng2rng3rvs1rvs2rvs3r.   r.   r/   test_vonmises_rvs_gh4598   s   z%TestVonMises.test_vonmises_rvs_gh4598zx, kappa, expected_logpdf))rU   rq   gEJ?)rU   rr   goι?)rU   rn   g0,)rs   rq   gdty)rs   rr   gʹw[A)rs   rn   gc                 C   ru   rv   )r3   r^   logpdfr   )rh   rW   rz   expected_logpdfr   r.   r.   r/   test_vonmises_logpdf   r}   z!TestVonMises.test_vonmises_logpdfc                 C   s  t jd}|dd \}}}tj||ddd }t|d t |jt j	s+J ||dt j
  f}tj||djd	d g|R  }t|d t |jt j	sSJ ||dt j
  f}tj||djd
d g|R ddi}tt ||dt j
   t |jt jsJ dS )a   
        Test that the vonmises expectation values are
        computed correctly.  This test checks that the
        numeric integration estimates the correct normalization
        (1) and mean angle (loc).  These expectations are
        independent of the chosen 2pi interval.
           kD +xNn    rX   r[   rz   c                 S      dS Nr   r.   rW   r.   r.   r/   rH          z3TestVonMises.test_vonmises_expect.<locals>.<lambda>r   r]   c                 S   r   r   r.   r   r.   r.   r/   rH      r   c                 S   s   t d|  S )Ny              ?)r`   expr   r.   r.   r/   rH      s    complex_funcN)r`   r   r   r3   r^   expectr   
issubdtypedtypefloatingra   anglecomplexfloating)rh   rngr[   rz   lbresboundsr.   r.   r/   test_vonmises_expect   s"   
 
z!TestVonMises.test_vonmises_expectrvs_locr]   	rvs_shape)r   rY       חAfix_locTF	fix_shapec                 C   sp   |r	|r	t d tjd}tjj|d||d}ddi}|r#||d< |r)||d< ttj|tjj	fi | d S )	NzNothing to fit.r   r   )sizer[   r   fscaler   flocf0)
pytestskipr`   r   r   r3   r^   r   _assert_less_or_close_loglikennlf)rh   r   r   r   r   r   datakwdsr.   r.   r/   test_fit_MLE_comp_optimizer   s    

z(TestVonMises.test_fit_MLE_comp_optimizerc                 C   sb   g d}t |}dt j }tjj||d\}}}|t tjks#J t	tj|tjj
d|d d S )N)g!*Kg4,%OԿgZ۵?g
ge_@g-8gPghn?g<t?g.6@gjb?g0]o@g݅ZgSsgx7W?g%H?g65Jg:m2?g@g;,gM^lsF      ࿩r   r   )r   r   )r`   asarrayra   r3   r^   fitfinfofloattinyr   r   )rh   r   r[   	kappa_fitloc_fit	scale_fitr.   r.   r/   test_vonmises_fit_bad_floc   s   



z'TestVonMises.test_vonmises_fit_bad_flocsignc                 C   s   t jd}tj|d t j ddjd|d}|dt j  }tj|\}}}tj|\}}	}
t||	 t|| |dks@J t j |  k rNt jk sQJ  J d S )	Nr   ro   rX   r   順 r      r   )	r`   r   r   r3   r^   ra   r   r   r   )rh   r   r   r   shifted_datar   r   r   kappa_fit_shiftedloc_fit_shifted_r.   r.   r/    test_vonmises_fit_unwrapped_data   s   

&z-TestVonMises.test_vonmises_fit_unwrapped_datac                 C   s   t d}t|dddtj  dd t|tjd ddd t|tj d ddd t|dtjd dd t|	 ddd	 t|
 ddd	 tt|jd
ddtjks`J d S )Nr   r   r]   rw   rx         ??皙?r   rX     r   r   )r3   r^   r   r_   r`   ra   rf   sfppfmeanr   allr   r   )rh   r;   r.   r.   r/   test_vonmises_kappa_0_gh18166   s   
(z*TestVonMises.test_vonmises_kappa_0_gh18166c                 C   s4   t jdg\}}}|dkr|dkr|dksJ d S )Nr   g 7yACr   )r3   r^   r   )rh   rz   r[   r\   r.   r.   r/   test_vonmises_fit_equal_data  s    z)TestVonMises.test_vonmises_fit_equal_datac                 C   s8   t jjjddgdd t jjjtjd d gdd d S )Nr   gl=c>r   r]   gd?)r2   r3   r^   r   r`   ra   rl   r.   r.   r/   test_vonmises_fit_bounds	  s   "z%TestVonMises.test_vonmises_fit_boundsN)__name__
__module____qualname__r   markparametrizer`   ra   ri   rm   rp   r|   r   r   r   r   xslowr   r   r   r   r   r   r.   r.   r.   r/   rS   N   s@    



rS   Fc           	      K   s   |du r| j }| j|fi |}tt| | j|fi |}|s)t||ks)J |||}|||}||ksAtj||ddsAJ d|v rO|d |d ksOJ d|v r]|d |d ks_J dS dS )a^  
    This utility function checks that the negative log-likelihood function
    (or `func`) of the result computed using dist.fit() is less than or equal
    to the result computed using the generic fit method.  Because of
    normal numerical imprecision, the "equality" check is made using
    `np.allclose` with a relative tolerance of 1e-15.
    Nrw   rx   r   r   r   )r   r   supertyper`   anyallclose)	r;   r   funcmaybe_identicalr   mle_analyticalnumerical_optll_mle_analyticalll_numerical_optr.   r.   r/   r     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 )Nr   r   ,)r   f1f2r   r]   r   3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:r]   )extra_keywordzToo many positional arguments.r   )shapeslensplitdictzipr`   aranger   r   RuntimeErrorr   
ValueErrornaninf	TypeError)r;   paramnshapes	all_fixedr   r.   r.   r/   assert_fit_warnings9  s6   ""r  r;   )alpha	betaprimefatiguelifeinvgammainvgauss
invweibull	johnsonsblevylevy_llognormgibratpowerlognormrayleighwaldc                 C   s   t t}||  }tt| } t| j| jg|R  d t| j| jg|R  t	j
  t| j| jg|R  d t| j| jg|R  t	j
  dS )zgh-6235r   N)r   r   getattrr3   r   r_   r,   r   r   r`   r   r-   )r;   dctargsr.   r.   r/   test_supportP  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 Nr   r`   r   r   rl   r.   r.   r/   setup_methodc     zTestRandInt.setup_methodc                 C   s   t jjdddd}tt|dk t|dk@  tt|dk t jjdddd}tt|dk t|jj	t
d v  t jdd}t|dk|dk @  tt|tjtt|d	 t ddd
}t|jj	t
d v  d S )Nr~      rY   r   r]   2   
AllInteger   .   r)   r   )r3   randintr   r   numpyr   r   shaper   charr   
isinstance
ScalarTypereprr   rh   valsvalr.   r.   r/   test_rvsf  s    zTestRandInt.test_rvsc                 C   sF   t jdd }t |dk|dk @ dd}tj|dd}t|| d S )Nr   $   r~   r  {Gz?)r&  r_wherer3   r%  pmfr   )rh   rT   outr-  r.   r.   r/   test_pdfs  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   r0  rY   r  r~         ?      @r   rr      decimal)	r`   linspacer&  floorselectr3   r%  rf   r   )rh   rW   rT   r5  r-  r.   r.   r/   test_cdfy  s
   
*zTestRandInt.test_cdfN)r   r   r   r  r/  r6  r?  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 )	TestBinomc                 C   r  r  r  rl   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 NrX   r   r   r  r   r"  r   )r3   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 )NrY   r   r   r7  rw   ry   r   r3   rC  r4  r   )rh   vals1vals2r.   r.   r/   test_pmf  s   zTestBinom.test_pmfc                 C   s|   t dd}tg d}tt|| }| }t|| t dd}| }t|d t dd}| }t|d d S )Nr]   ro   )      ?ro   rK  rt   r7  )	r3   rC  r`   r   sumr   rA   r   r   )rh   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errorr]   r   np)	warningscatch_warningssimplefilterRuntimeWarningr   r3   rC  r   stdrl   r.   r.   r/   test_warns_p0  s
   
"zTestBinom.test_warns_p0c                 C   s"   d}t jjd|dd|ksJ d S )Nr   333333?r7  )qrS  rT  )r3   rC  r   rh   rS  r.   r.   r/   test_ppf_p1  s   zTestBinom.test_ppf_p1c                 C   sH   d}d}t d}tjj|||d}tj||| }t||dd d S )NglyCgq]\	T3<r   rR  缉ؗҜ<r   )r`   r   r3   rC  r4  poissonr   )rh   rS  rT  rW   r   refr.   r.   r/   test_pmf_poisson  s   
zTestBinom.test_pmf_poissonc                 C   s>   d}d}d}t j|||}t j|||}t||dd d S )NgJ-DgO
;r   r_  r   )r3   rC  r4  rf   r   )rh   rS  rT  rr   ra  r.   r.   r/   test_pmf_cdf  s   zTestBinom.test_pmf_cdfc                 C   s"   t jddd}t|ddd d S )Nr   r   +?r   r_  r   rG  )rh   r   r.   r.   r/   test_pmf_gh15101  s   zTestBinom.test_pmf_gh15101N)r   r   r   r  r/  rJ  rP  rZ  r^  rb  rd  rf  r.   r.   r.   r/   rA    s    		rA  c                   @      e Zd Zdd ZdS )TestArcsinec                 C   s&   t jddg}t|tjtjg d S Nr   r   )r3   arcsiner_   r   r`   r   rh   rT  r.   r.   r/   test_endpoints  s   zTestArcsine.test_endpointsN)r   r   r   rl  r.   r.   r.   r/   rh        rh  c                   @   $   e Zd Zdd Zdd Zdd ZdS )TestBernoullic                 C   r  r  r  rl   r.   r.   r/   r    r  zTestBernoulli.setup_methodc                 C   s   t jjddd}tt|dkt|dk@  tt|dk t|jjt	d v  t jd}tt
|t t dd}tt
|tj t|jjt	d v  d S )Nr   r   r  r   r   r"  r   )r3   	bernoullir   r   r&  r   r'  r   r(  r   r)  rD  rE  r,  r.   r.   r/   r/    s    zTestBernoulli.test_rvsc                 C   st   t d}dtd dtd  }| }t|| t d}| }t|d t d}| }t|d d S )NrK        пr   rt   r7  )r3   rp  r`   logrA   r   r   )rh   r-   rN  rO  r.   r.   r/   rP    s   




zTestBernoulli.test_entropyN)r   r   r   r  r/  rP  r.   r.   r.   r/   ro        ro  c                   @   rg  )TestBradfordc                 C   s:   d}t dd}tj||}tj||}t|| d S )NrU   )r`   logspacer3   bradfordrf   r   r   )rh   crW   r\  xxr.   r.   r/   test_cdf_ppf  s
   zTestBradford.test_cdf_ppfN)r   r   r   r{  r.   r.   r.   r/   rt    rm  rt  c                   @   s\   e Zd ZdZdZdd Zdd Zej	ddefd	gd
d Z
ej	dg ddd ZdS )TestChignT9;g2 >h?@c                 C   s"   t jdd}t|| jdd d S )NrX   r   rw   rx   )r3   chir   r   CHI_SF_10_4rh   rG   r.   r.   r/   test_sf     zTestChi.test_sfc                 C   s"   t j| jd}t|ddd d S )Nr   rX   rw   rx   )r3   r}  isfr~  r   rh   rW   r.   r.   r/   test_isf
     zTestChi.test_isfdf, ref     @@)g  ļBgcAc                 C      t tj||dd d S N-q=rx   )r   r3   r}  r   rh   dfra  r.   r.   r/   	test_mean     zTestChi.test_mean))-C6?gQ(݂)r   ńjɮ9?)r  gWr4'?)    _Bgr$h(?)}Ô%ITgs$h(?c                 C      t t| |dd d S rv   )r   r3   r}  rA   r  r.   r.   r/   rP  %     zTestChi.test_entropyN)r   r   r   r~  CHI_MEAN_1000r  r  r   r   r   r  rP  r.   r.   r.   r/   r|    s    

r|  c                   @   r  )

TestNBinomc                 C   r  r  r  rl   r.   r.   r/   r  0  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 rB  )r3   nbinomr   r   r&  r   r'  r   r(  r   r)  rD  rE  r,  r.   r.   r/   r/  3  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   r`   r   r3   r  logpmfr4  r2   r   )rh   r.  r.   r.   r/   rJ  >  s
   zTestNBinom.test_pmfc                 C   s@   t jjg dddd}tt jjg dddd}t|| d S )N)r   r~   r   r~   333333@?rR  )r3   r  logcdfr`   rr  rf   r   )rh   r-  ra  r.   r.   r/   test_logcdf_gh16159F  s   zTestNBinom.test_logcdf_gh16159N)r   r   r   r  r/  rJ  r  r.   r.   r.   r/   r  /  s
    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  rl   r.   r.   r/   r  N  r  zTestGenInvGauss.setup_methodc                 C   :   t dd}t |jddd|j\}}t|dkd d S )Nffffff@      ?  r   r   皙?Tr3   geninvgausskstestr   rf   r   rh   gigr   rT  r.   r.   r/   test_rvs_with_mode_shiftQ     z(TestGenInvGauss.test_rvs_with_mode_shiftc                 C   r  )Nr   r   r  r   r   r  Tr  r  r.   r.   r/   test_rvs_without_mode_shiftX  r  z+TestGenInvGauss.test_rvs_without_mode_shiftc                 C   r  )NrU   皙?r  r   r   r  Tr  r  r.   r.   r/   test_rvs_new_method_  r  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  )r3   r  r   r  rf   )rT  r-   r  r   r.   r.   r/   my_ks_checkh  s   z4TestGenInvGauss.test_rvs_p_zero.<locals>.my_ks_checkr   r  Tr   r  )r   )rh   r  r.   r.   r/   test_rvs_p_zerof  s   zTestGenInvGauss.test_rvs_p_zeroc                 C   s6   t tddjddddtddjddd  d S )N      r]   rX   r   r   r   r  )r   r3   r  r   rl   r.   r.   r/   test_rvs_negative_pq  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   rT  r-   r   r	  r  333333?TrY   rq   rX   )rT  r-   r\   )r3   r  r   r   r  r`   r<  r_   r   r	  rf   )rh   igmurW   pdf_igcdf_igr.   r.   r/   test_invgaussw  s    zTestGenInvGauss.test_invgaussc                 C   s6   t g d}t ddd}t|tj|dd d S )N)
g;g8y8?g\}Z?ghܲ<?g&Khdd?g7!L?g	Cf?g_诱?g>0|?gRq?rq   r~   rX   ro   r   )r`   r   r<  r   r3   r  r_   )rh   vals_RrW   r.   r.   r/   
test_pdf_R  s   zTestGenInvGauss.test_pdf_Rc                 C   s0   t tjdddd t tjdddd d S )Nr   ro   g    >Ar!  r]   )r   r3   r  r_   rl   r.   r.   r/   test_pdf_zero  s   zTestGenInvGauss.test_pdf_zeroN)r   r   r   r  r   r   slowr  r  r  r  r  r  r  r  r.   r.   r.   r/   r  M  s    




r  c                   @   s   e Zd Zdd Zdd Zdd Zejdg dd	d
 Z	ejdg d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  rl   r.   r.   r/   r    r  zTestGenHyperbolic.setup_methodc           
      C   l   t g d}d\}}}d\}}||| || f}tj|||d}t ddd}	t||	|ddd	 d S )
N)
gF^T=g{X'=gNunƢsy>g7!t?gɫzI?g̸?g?gq6.?gmPZz?g:PgN?r]   r]   r   ro   r  rZ   rX   r   r   r   ry   )r`   r   r3   genhyperbolicr<  r   r_   
rh   r  lmbdar  betar  deltar  ghrW   r.   r.   r/   
test_pdf_r     
zTestGenHyperbolic.test_pdf_rc           
      C   r  )
N)
g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?r  r  rZ   r  rX   r   ư>r  )r`   r   r3   r  r<  r   rf   r  r.   r.   r/   
test_cdf_r  r  zTestGenHyperbolic.test_cdf_rzx, p, a, b, loc, scale, ref)
)r]   r   r  ro   r  g8ɹvF(;)r  rX   r  rK  r   r~   g[Ϡ?)r  rX   r  g      ?r   r   g ✝`D;)r        ?r  ):?r   r   gdL;)r   r  r  r  r   r   gzK^7?)r~         r  r  r   r   gj?)r~   r  r     r   r   ga=vG:)   r  r   r  r   r   g?)(   r  r   r  r   r   g1bV?)<   r  r   r  r   r   g?c           	      C   *   t jj||||||d}t||dd d S NrZ   dy=rx   )r3   r  rf   r   )	rh   rW   rT  r,   r-   r[   r\   ra  rf   r.   r.   r/   test_cdf_mpmath  s   z!TestGenHyperbolic.test_cdf_mpmath))r   r  r9  r   r   r   gC!,?)r   r         @      @r   r   g,Ћf?)ru  r   r  r  r   r   r7  )   r]   r   r  ro   r  gm"چ>),  rX   r  rK  r   r~   g:;)r  r  r   r  r   r   gw=)K   r  r   r  r   r   g3Z0&K<c           	      C   r  r  )r3   r  r   r   )	rh   rW   rT  r,   r-   r[   r\   ra  r   r.   r.   r/   test_sf_mpmath  s   z TestGenHyperbolic.test_sf_mpmathc                    s\   g d}d\}}}d\|| | f  fddt ddD }t||dd	d
 d S )N)g@쐧@g@쐧 @g܊B@gvGăi@r  r  c                    s$   g | ]}t j d |qS )rZ   )r3   r  moment)r:   ir  r  r  r.   r/   r<     s    z4TestGenHyperbolic.test_moments_r.<locals>.<listcomp>r   r~   r   r   r  )ranger   )rh   r  r  r  r  vals_usr.   r  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 )	Nr  r  rZ   r  r   r   r  T)r3   r  r  r   rf   r   )
rh   r  r  r  r  r  r  r  r   rT  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  rX   r]   r   rZ   rq   Gz?r!  r  r  )r`   r<  float_powerr   float32epssqrtr3   r  r   newaxisr   r_   t)	rh   r  r  r  r  r  r  r  rW   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   rZ   rq   r  r!  r  r  )r`   r   r  r  r3   r  r<  r   r  r   r_   cauchy)	rh   r  r  r  r  r  r  r  rW   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 )Nr  rX   )r   r   r   rZ   ru  r  r!  r   r   dy=r  )r`   r<  r   r  r  r3   r  r  r   r_   laplace)	rh   r[   r  r  r  r  r  r  rW   r.   r.   r/   test_pdf_laplace3  s   

z"TestGenHyperbolic.test_pdf_laplacec           	   	   C   s   t dddt dddt dtd t dddt dddf\}}}}d	}||| || f}tj|||d
}t |d|ddd d t jf }t|	|tj
j	|||||dddd d S )Nr   r  rX   r      r   rY   r   rZ   rq   r  r!  )r,   r-   r[   r\   r   r  )r`   r<  r  r  r3   r  r   r  r   r_   norminvgauss)	rh   r  r  r  r  r  r  r  rW   r.   r.   r/   test_pdf_norminvgaussH  s   (

z'TestGenHyperbolic.test_pdf_norminvgaussN)r   r   r   r  r  r  r   r   r   r  r  r  r/  r  r  r  r  r.   r.   r.   r/   r    s(    


r  c                   @   s@   e Zd Zejdddgdd Zejdddgd	d
 ZdS )TestHypSecantzx, reference)r  gA0=)r!  g!b;c                 C   r   N+<rx   )r3   	hypsecantr   r   )rh   rW   	referencer   r.   r.   r/   r  d     zTestHypSecant.test_sfzp, reference)r  g9bT*@)r  gTW-;@c                 C   r   r  )r3   r  r  r   )rh   rT  r  rW   r.   r.   r/   r  n  r  zTestHypSecant.test_isfNr   r   r   r   r   r   r  r  r.   r.   r.   r/   r  _  s    
r  c                   @   s^   e Zd Zdd Zdd Zdd Zejdg dd	d
 Z	dd Z
dd Zdd Zdd ZdS )TestNormInvGaussc                 C   r  r  r  rl   r.   r.   r/   r  w  r  zTestNormInvGauss.setup_methodc                 C   @   t g d}t g d}tjj|ddd}t||dd d S )N)gp~٧>g @X>g}e?g{)߳?gwH?ir      r#  r   ro   r,   r-   &.>r   )r`   r   r3   r  rf   r   )rh   r_cdfx_testvals_cdfr.   r.   r/   
test_cdf_Rz  s   zTestNormInvGauss.test_cdf_Rc                 C   r  )N)gp϶>g\H55$?geСt&?go NiH?g]u>r  r   ro   r  r  r   )r`   r   r3   r  r_   r   )rh   r_pdfr  vals_pdfr.   r.   r/   r    s   zTestNormInvGauss.test_pdf_Rzx, a, b, sf, rtol))r   r   r   !7?r   )r  r   r   ?=r  )r   r~   r  gy5`?r  )rX   r~   r  gMLC9r  c                 C   s@   t j|||}t|||d t j|||}t|||d d S Nrx   r3   r  r   r   r  )rh   rW   r,   r-   r   ry   rG   r  r.   r.   r/   test_sf_isf_mpmath  s   z#TestNormInvGauss.test_sf_isf_mpmathc                 C   s^   ddg}ddg}d}ddg}t j|||}t||ddd	 t j|||}t||d
d d S )Nr   r  r   r   r	  r
  r   r_  rF  r  rx   r  )rh   rW   r,   r-   r   rG   r  r.   r.   r/   test_sf_isf_mpmath_vectorized  s   z.TestNormInvGauss.test_sf_isf_mpmath_vectorizedc                 C   s<   t dd}tddd}||}||}t|| d S )Nr   r   r  r]   )r3   r  r`   r   r   r  r   )rh   dstrW   r   r  r.   r.   r/   test_gh8718  s
   

zTestNormInvGauss.test_gh8718c                 C   s   d\}}t |d |d  }|| |d |d  d| |t |  ddd|d  |d    | f}t|tjj||dd d S )	Nr   ro   r]   r         @r   r   mvskmoments)r`   r  r   r3   r  )rh   r,   r-   gammav_statsr.   r.   r/   
test_stats  s   (zTestNormInvGauss.test_statsc                 C   s@   d\}}t g d}tj|||}t|tj||| d S )Nr  MbP?ro   re  )r`   r   r3   r  r   r   rf   )rh   r,   r-   r  r-  r.   r.   r/   test_ppf  s   zTestNormInvGauss.test_ppfN)r   r   r   r  r  r  r   r   r   r  r  r  r  r  r.   r.   r.   r/   r  v  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S )TestGeomc                 C   r  r  r  rl   r.   r.   r/   r    r  zTestGeom.setup_methodc                 C      t jjddd}tt|dk tt|dk t|jjt	d v  t jd}tt
|t t dd}tt
|tj t|jjt	d v  d S )Nr   r   r  r   r"  r   )r3   geomr   r   r&  r   r'  r   r(  r   r)  rD  rE  r,  r.   r.   r/   r/       zTestGeom.test_rvsc                 C   sT   t jd}tjjt dd|d}|jt jksJ t 	|t 
t jjks(J d S )Nl   A: ir~   r   )r`   r   r   r3   r  r   r   r   int64r   iinfoint32max)rh   r   r   r.   r.   r/   test_rvs_9313  s    zTestGeom.test_rvs_9313c                 C   s$   t jg dd}t|g d d S )Nr   ro   )ro   rK  r  )r3   r  r4  r   rh   r-  r.   r.   r/   rJ    s   zTestGeom.test_pmfc                 C   sV   t tjg dd}tjg dd}t||ddd tjdd}t|d d S )Nr   ro   rw   r   rF  r   rt   )r`   rr  r3   r  r4  r  r   r   )rh   rH  rI  r.  r.   r.   r/   test_logpmf  s
   zTestGeom.test_logpmfc                 C   sL   t jg dd}t jg dd}tg d}t|| t|d|  d S )Nr   ro   ro   r         ?r   )r3   r  rf   r   r   r   rh   r-  vals_sfrQ   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   ro   r'  )	r3   r  r  logsfr   r   r`   rr  log1pr)  r.   r.   r/   test_logcdf_logsf  s
   zTestGeom.test_logcdf_logsfc                 C   ,   t jg dd}tg d}t|| d S )Nr'  ro   )r7  rs   r  )r3   r  r   r   r   rh   r-  rQ   r.   r.   r/   r       zTestGeom.test_ppfc                 C   s   t tjddddd d S )N#B;r7  +=r   )r   r3   r  r   rl   r.   r.   r/   test_ppf_underflow  s   zTestGeom.test_ppf_underflowc                 C   s    t d }t|ddd d S )Ng<,Ԛ?g۩@rw   rx   )r3   r  rA   r   )rh   rO  r.   r.   r/   test_entropy_gh18226  s   zTestGeom.test_entropy_gh18226N)r   r   r   r  r/  r$  rJ  r&  r+  r.  r  r4  r5  r.   r.   r.   r/   r    s    	
r  c                   @   rn  )
TestPlanckc                 C   r  r  r  rl   r.   r.   r/   r    r  zTestPlanck.setup_methodc                 C   r/  )Nr   r8  )g|dy?g8'\>ggrU!>)r3   planckr   r   r   r0  r.   r.   r/   r    s   zTestPlanck.test_sfc                 C   r/  )N)r       @@     p@r  )g    P.g    h>g    TF)r3   r7  r,  r   r   r0  r.   r.   r/   
test_logsf  r1  zTestPlanck.test_logsfN)r   r   r   r  r  r:  r.   r.   r.   r/   r6     s    r6  c                   @   r  )
TestGennormc                 C   0   g d}t j|d}t j|}t|| d S Nr   r   )r3   gennormr_   r  r   rh   pointspdf1pdf2r.   r.   r/   test_laplace     zTestGennorm.test_laplacec                 C   4   g d}t j|d}t jj|dd}t|| d S Nr   r]   g;f?r\   )r3   r>  r_   normr   r?  r.   r.   r/   	test_norm     zTestGennorm.test_normc                 C   s   t jd td}|jdd}t||jjdksJ td}|jdd}tj	jdd}t
||jdks:J td}|jdd}tjjddd	}t
||jdksXJ d S )
Nr   ro   r   r  rU   r   r]   g;f?r\   r   )r`   r   r   r3   r>  r   r  rf   pvaluer  ks_2samprH  )rh   r;   r   rvs_laplacervs_normr.   r.   r/   r/     s   


zTestGennorm.test_rvsc                 C   s   t jd tddgddgg}|jg dd}t|d d ddf tdjd d	ks0J t|d d ddf tdjd d	ksGJ t|d d ddf tdjd d	ks^J t|d d ddf tdjd d	ksuJ d S )
Nr   ro   r7  rs   r8  )r   r]   r]   r  r   rU   )r`   r   r   r3   r>  r   r  rf   )rh   r;   r   r.   r.   r/   test_rvs_broadcasting1  s   ...2z!TestGennorm.test_rvs_broadcastingN)r   r   r   rC  rI  r/  rP  r.   r.   r.   r/   r;    s
    r;  c                   @   &   e Zd Zejdddgdd ZdS )
TestGibratx, sfx)r  gD.?)  gJ]b<c                 C   0   t tj||dd t tj||dd d S N+=rx   )r   r3   r  r   r  rh   rW   sfxr.   r.   r/   test_sf_isfI     zTestGibrat.test_sf_isfN)r   r   r   r   r   r   rZ  r.   r.   r.   r/   rR  ;  s
    
rR  c                   @   sH   e Zd Zdd Zejdg ddd Zejdg dd	d
 ZdS )TestGompertzc                 C   s&   t jt jddd}t|d d S N0.++r   )r3   gompertzr   rf   r   rk  r.   r.   r/   test_gompertz_accuracyR     z#TestGompertz.test_gompertz_accuracyz	x, c, sfx))r   r  g|t?)r   r  g(fMr;)r  r~   g[?)g      @r~   gg[<c                 C   4   t tj|||dd t tj|||dd d S Nr3  rx   )r   r3   r_  r   r  )rh   rW   ry  rY  r.   r.   r/   rZ  c  s   zTestGompertz.test_sf_isfc, ref))r  geUT8?)r   gtqq?)r   gs{)r  gN*6c                 C   r  rc  )r   r3   r_  rA   rh   ry  ra  r.   r.   r/   rP  r  r  zTestGompertz.test_entropyN)	r   r   r   r`  r   r   r   rZ  rP  r.   r.   r.   r/   r\  P  s    
r\  c                   @   rQ  )TestFoldNorm	x, c, ref)r  :0yE>g:0N<?)r  r  g:?c                 C      t tj|||dd d S rv   )r   r3   foldnormrf   rh   rW   ry  ra  r.   r.   r/   r?       zTestFoldNorm.test_cdfN)r   r   r   r   r   r   r?  r.   r.   r.   r/   rf  z  s
    
rf  c                   @      e Zd Zejdddgdd Zejdg ddd	 Zejd
ddgejdg dejdddgejdddgdd Zdd Z	dS )TestHalfNormrS  )r   |N?)rX   Oul2;c                 C   rU  rc  )r   r3   halfnormr   r  rX  r.   r.   r/   rZ    r[  zTestHalfNorm.test_sf_isfx, ref))Ww'&l7g;G<^͛7)C]r2<gE~o-<)r   g?c                 C   r  rv   )r   r3   rq  rf   rh   rW   ra  r.   r.   r/   r?       zTestHalfNorm.test_cdfr   h㈵>r  	rvs_scalerq   rY   r   r   TF	fix_scalec           	      C   s   t jd}tjj||d|d}|r9|r9d}tjt|d tj	j
|||d W d    d S 1 s2w   Y  d S i }|rA||d< |rG||d< ttj|fi |d	d
i d S Nr   r   r[   r\   r   r   r   r   r   r   r   r   r   T)r`   r   r   r3   rq  r   r   r   r   halflogisticr   r   	rh   r   rx  r   rz  r   r   	error_msgr   r.   r.   r/   r     s(   
z(TestHalfNorm.test_fit_MLE_comp_optimizerc                 C   D   t t tjjg ddd W d    d S 1 sw   Y  d S Nr   r]   r   )r   r   r   r3   rq  r   rl   r.   r.   r/   test_fit_error     "zTestHalfNorm.test_fit_errorN)
r   r   r   r   r   r   rZ  r?  r   r  r.   r.   r.   r/   rn    s    


rn  c                   @   sd   e Zd Zejdddgejdddgejddd	gejd
dd	gdd Zdd ZdS )TestHalfCauchyr   rw  r  rx  rq   r   r   TFrz  c           	      C   s   t jd}tjj||d|d}|r9|r9d}tjt|d tj	j
|||d W d    d S 1 s2w   Y  d S i }|rA||d< |rG||d< ttj	|fi | d S )	Nr   r   r|  r   r   r}  r   r   )r`   r   r   r3   rq  r   r   r   r   
halfcauchyr   r   r  r.   r.   r/   r     s$   
z*TestHalfCauchy.test_fit_MLE_comp_optimizerc                 C   r  r  )r   r   r   r3   r  r   rl   r.   r.   r/   r    r  zTestHalfCauchy.test_fit_errorN)r   r   r   r   r   r   r   r  r.   r.   r.   r/   r    s    r  c                   @   rm  )TestHalfLogisticrr  )rY   ]6)   L-c                 C   r  rv   )r   r3   r~  r   ru  r.   r.   r/   r    s   zTestHalfLogistic.test_sfq, ref))r  rY   )r  r  )gv?g   .!>)g?g      <c                 C   r  rv   )r   r3   r~  r  rh   r\  ra  r.   r.   r/   r    r  zTestHalfLogistic.test_isfr   rw  r  rx  ry  r   TFrz  c           	      C   s   t jd}tjj||d|d}i }|r;|r;d}tjt|d tjj	|||d W d    d S 1 s4w   Y  d S |rA||d< |rG||d< t
tj|fi |d	d
i d S r{  )r`   r   r   r3   r~  r   r   r   r   r   r   )	rh   r   rx  r   rz  r   r   r   r  r.   r.   r/   r     s(   
z,TestHalfLogistic.test_fit_MLE_comp_optimizerc                 C   sJ   d}t t|d tjjg ddd W d    d S 1 sw   Y  d S )Nz; Maximum likelihood estimation with 'halflogistic' requiresr   )r   r]   r   r   r   )assert_raisesr   r3   r~  r   rh   r*   r.   r.   r/   test_fit_bad_floc%  s   "z"TestHalfLogistic.test_fit_bad_flocN)
r   r   r   r   r   r   r  r  r   r  r.   r.   r.   r/   r    s    



r  c                   @   rn  )TestHalfgennormc                 C   r<  r=  )r3   halfgennormr_   exponr   r?  r.   r.   r/   
test_expon,  rD  zTestHalfgennorm.test_exponc                 C   rE  rF  )r3   r  r_   rq  r   r?  r.   r.   r/   test_halfnorm3  rJ  zTestHalfgennorm.test_halfnormc                 C   s6   g d}t j|d}t j|d}t|d|  d S )Nr   g
(?r]   )r3   r  r_   r>  r   r?  r.   r.   r/   test_gennorm:  s   zTestHalfgennorm.test_gennormN)r   r   r   r  r  r  r.   r.   r.   r/   r  +  s    r  c                   @   rn  )TestLaplaceasymmetricc                 C   s6   t g d}tj|d}tj|}t|| d S r=  )r`   r   r3   laplace_asymmetricr_   r  r   r?  r.   r.   r/   rC  C  s   z"TestLaplaceasymmetric.test_laplacec                 C   sL   t g d}d}d| }tj||}tj||d  |}t|| d S )Nr   r]   r   )r`   r   r3   r  r_   r   )rh   r@  rz   kapinvrA  rB  r.   r.   r/   test_asymmetric_laplace_pdfJ  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   rX   r]   rU   gMbp?r  gV-?r   gMb`?)r`   r   rr  r3   r  r_   rf   r   r   r  r   concatenate)rh   r@  rz   rA  cdf1sf1rB  cdf2sf2ppf1ppf2isf1isf2r.   r.   r/   !test_asymmetric_laplace_log_10_16S  s   z7TestLaplaceasymmetric.test_asymmetric_laplace_log_10_16N)r   r   r   rC  r  r  r.   r.   r.   r/   r  B  s    	r  c                   @   s   e Zd Zdd Zejdg ddd Zejdg ddd	 Zd
d Z	dd Z
dd Zdd Zdd Zdd Zdd Zg dg dg dg ddejdddd gej dd!dd"d gg d#g d$g d%g	ZeeZejd&ed'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5S )6TestTruncnormc                 C   r  r  r  rl   r.   r.   r/   r  f  r  zTestTruncnorm.setup_method	a, b, ref))r   rY   r  )333333?ffffff?gܲl)r  g>g+c                 C   ri  N绽|=rx   r   r3   	truncnormrA   rh   r,   r-   ra  r.   r.   r/   rP  i  s   zTestTruncnorm.test_entropy))r  r  ghiɮ9?)r^  r  r  )g0.+r  r  )}Ô%Ir  Z_2?c                 C   ri  rc  r  r  r.   r.   r/   test_extreme_entropy}  s   z"TestTruncnorm.test_extreme_entropyc              	   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   r  ro   H.?r   r]         r7  r      r]   rZ   r   fO?l@r~   )r3   r  r   r`   r   r   r   r0  r.   r.   r/   test_ppf_ticket1131  
   
z!TestTruncnorm.test_ppf_ticket1131c              	   C   r  )Nr  r  r7  r   r  r]   rZ   r~   r  r  r   )r3   r  r  r`   r   r   r   r0  r.   r.   r/   test_isf_ticket1131  r  z!TestTruncnorm.test_isf_ticket1131c                 C   s   d\}}t jj||dddd}t||   k o"|   k o"|k n   d\}}t jj||dddd}t||   k oK|   k oK|k  d S    d S )N)ir  r   r   rX   r  )rX      r3   r  r   r   minr#  rh   lowhighrW   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)rY   rV   r   r   rX   r  )r     )'  i'  )i)r3   r  r   r   r  r#  rD   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   rv  rs   r   r   r   r   r7  r7  rt   rt   )r   d._MT
@BKg?r   r   )r   r  r  r   r   r]   ro   r   ro   r7  gĖy	@gdv*?g,mj%V?rK  )r`   r   r   r3   r  rf   r   r_   r   rr  r   r   )rh   r  r  xvalsxmidcdfssfspdfsexpected_cdfsexpected_sfsexpected_pdfspvalsppfsexpected_ppfsr_   r.   r.   r/   test_gh_9403_nontail_values  sJ   



"z)TestTruncnorm.test_gh_9403_nontail_valuesc                 C   s  ddgddgfD ];\}}t t j ||t jg}|| d }tj|||}tj|||}tj|||}t g d}t g d}	t g d}
|d	k rWt g d
}
t|| t||	 t||
 tt 	|
d |
d  |d  t g d}tj
|||}t |t |d |g}t|| tj|||}t|| |d	k rttj|||d ttj|||d nttj|||d ttj|||d tj|||}tt 	||
d  |d d  t ||d}|d d d  }ttj|||tj|| | d d d  ttj|||tj|| | d d d  ttj|||tj|| | d d d  qd S )N'   r  irs   r  r  )r   pGC@Ff<r   r   )r   r  r  r   r   r]   ro   r  gEC@g i?gspXio)>rK  r  r   )r`   r   r   r3   r  rf   r   r_   r   rr  r   r   r<  )rh   r  r  r  r  r  r  r  r  r  r  r  r  r  r_   xvals2r.   r.   r/   test_gh_9403_medium_tail_values  sd   




 z-TestTruncnorm.test_gh_9403_medium_tail_valuesc                 C   s6   t tdddd t tdtjdd d S )Ng      *@g      .@      ,@g T?r   g @gR?)r   r3   r  rf   r`   r   rl   r.   r.   r/   test_cdf_tail_15110_14753
  s   z'TestTruncnorm.test_cdf_tail_15110_14753)r  rt   r7  rt   rt   )r  rX   rt   r7  rt   gLFu)r  r   rt   gMFmz%?rt   gſ)r   r]   rt   ghI}?rt   gHNMr   gQ63E?gnl$A?gr1"D?gK8L?gQ63Egr1"D)r   r   gU*? bn?gnA??c3TXʿ)r  r   gU*ҿr  gnAr  )r  g"$7"gOxr?gp7`g'>K@casec                 C   sL   |\}}}}}}t jj ||dd\}}	}
}t||	|
|g||||gdd d S )Nr  r  FFg<r   )r3   r  r   )rh   r  r,   r-   m0v0s0k0mvrG   rT   r.   r.   r/   test_moments=  s   "zTestTruncnorm.test_momentsc                 C   s0   t jj dtjdd\}}t|d t|d d S )Nr   mvr  g e3E?g:&A?)r3   r  r`   r   r   )rh   r  r  r.   r.   r/   test_9902_momentsC  s   
zTestTruncnorm.test_9902_momentsc                 C   sV   d\}}t jj||dddd}t||   k o%|   k o%|k  d S    d S )N)rX   r#  r   r   rX   r  r  r  r.   r.   r/   test_gh_1489_trac_962_rvsH  s   8z'TestTruncnorm.test_gh_1489_trac_962_rvsc                 C   s   ddt j dt j t j dddddg}dddt jddddd	t jt jg}tjj||dt|fd
}t |dt|fks=J tt ||j	ddk tt |j
dd|k d S )Nr  rX   r  ir  r  r~   r  -   r  r   )axis)r`   r   r3   r  r   r   r'  r   r   r  r#  r  r.   r.   r/   test_gh_11299_rvsN  s   & zTestTruncnorm.test_gh_11299_rvsc                 C   s.   t tjdrtjjdddtj d d S d S )Nr   r  r  r~   r   )r+   r`   r   r3   r  r   r   rl   r.   r.   r/   test_rvs_GeneratorX  s
   
z TestTruncnorm.test_rvs_Generatorc                 C   s   t t j t j dt j dg}t t jt jddt jg}t g d}g d}tt|||| tt| | | | d S )NrX   r   )rX         @r  	   r  )gOul"gځ=!gL!g>EG	f g^K[X)r`   r   r   r   r3   r  r  r,  )rh   r,   r-   rW   rQ   r.   r.   r/   test_logcdf_gh17064^  s    "z!TestTruncnorm.test_logcdf_gh17064c                 C   s$   t ddd}d}t|| d S )Nr   r   r~   gl).0S?)r3   r  r  r   )rh   r   ra  r.   r.   r/   test_moments_gh18634i  s   z"TestTruncnorm.test_moments_gh18634N)r   r   r   r  r   r   r   rP  r  r  r  r  r  r  r  r  r`   r   _truncnorm_stats_datar   r  r  r  r  r  r  r  r.   r.   r.   r/   r  e  s\    


#/
#

r  c                   @   s   e Zd Zejdg ddd Zejdg ddd Zejd	d
dgdd Zejdddgdd Z	ejdddgdd Z
ejd	ddgdd ZdS )TestGenLogisticx, expected))ig4`n)ig4	ncg)r   gX
=)rY   gh@X)r   gh<c                 C   s$   d}t j||}t||dd d S )Nr  r   rx   )r3   genlogisticr   r   )rh   rW   rQ   ry  logpr.   r.   r/   test_logpdfv  s   zTestGenLogistic.test_logpdfrd  ))r^  gTKEl@)r  gJk$@)r   gsF<?)r  7~F<?c                 C   r  r  )r   r3   r  rA   re  r.   r.   r/   rP    r  zTestGenLogistic.test_entropyrg  )r  rX   g8.)  r  gpT	oc                 C   ri  rc  )r   r3   r  r   rk  r.   r.   r/   r    rl  zTestGenLogistic.test_sf	q, c, ref)rq   r  g^ #@)r  r]   gGFf@c                 C   ri  NV瞯<rx   )r   r3   r  r  rh   r\  ry  ra  r.   r.   r/   r    rl  zTestGenLogistic.test_isf)ro   r  gİ@)r  r  g1a@c                 C   ri  r  )r   r3   r  r   r  r.   r.   r/   r    rl  zTestGenLogistic.test_ppf)rY   {Gz?g(?)r!  r  g'Tn7c                 C   ri  rv   )r   r3   r  r  rk  r.   r.   r/   test_logcdf  rl  zTestGenLogistic.test_logcdfN)r   r   r   r   r   r   r  rP  r  r  r  r  r.   r.   r.   r/   r  s  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d Z
dd Zdd Zdd ZdS )TestHypergeomc                 C   r  r  r  rl   r.   r.   r/   r    r  zTestHypergeom.setup_methodc                 C   s   t jjddddd}tt|dkt|dk@  tt|dk t|jjt	d v  t jddd}tt
|t t dddd}tt
|tj t|jjt	d v  d S )Nr  rX   r   r   r  r   r"  )r3   	hypergeomr   r   r&  r   r'  r   r(  r   r)  rD  rE  r,  r.   r.   r/   r/    s   zTestHypergeom.test_rvsc                 C   s6   d}d}d}|}|}t jd|||}t|dd d S )Ni	  r!  r   r]   gkㅒP?r  )r3   r  r4  r   )rh   MrS  Ntotgoodhgpmfr.   r.   r/   test_precision  s   zTestHypergeom.test_precisionc                 C   sl   t tjdddddd t tjdddddd t tjdddddd t tjdddddd d S )Nr   r]   r   r7  r  rt   )r   r3   r  r4  rl   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  r7  )r   r3   r  rf   rl   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@@r~        @     @c                    s"   g | ]}t j   |qS r.   )r3   r  r   )r:   eatenorangespearsquantiler.   r/   r<     s    z1TestHypergeom.test_precision2.<locals>.<listcomp>)r   gpR(g㘍R2gJޱ p9g?Mf=
G?r   r   gƠ>r  )g     @r  g     @g     @g     @)r   r  g)9g"1)r`   r   r   r3   r  r   )rh   fruits_eatenr   rQ   	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   rK  rt   )	r3   r  rA   r`   r   rL  r   r   r   )rh   hgrO  rM  rN  r.   r.   r/   rP    s   
zTestHypergeom.test_entropyc                 C   sl   d}d}d}d}t j||||}d}t||dd d}d	}d
}d}t j||||}d}t||dd d S )Nr      cA    .A     j@gor   r:  r   @  X  r  g_7	j$r#  )r3   r  r,  r   rh   rT   r	  rS  r
  resultrQ   r.   r.   r/   r:    s   zTestHypergeom.test_logsfc                 C   s   d}d}d}d}t j||||}d}t||dd d}d	}d
}d}t j||||}d}t||dd d}d	}d}d}t j||||}d}t||dd tg d}d	}d
}d}t j||||}tdd}t||dd d S )Nr   r"  r#  r$  g)\Ur   r:  r  r%  r!  r  g*@Vr#  }      r   gר)r  r  r  )r3   r  r  r   r`   r   fullr'  r.   r.   r/   r    s8   zTestHypergeom.test_logcdfc                 C   s6   d}d}d}t j|||}|| | }t|| d S )Nip iP i.  )r3   r  r   r   )rh   r	  rS  r
  hmrmr.   r.   r/   test_mean_gh18511?  s   zTestHypergeom.test_mean_gh18511c                 C   s`   d}d}t dd}d| }tj|d |||}t |dks"J t t |dk s.J d S )NrX   r   r~   r#        $@r   r   )r`   r   r3   r  r   r   diff)rh   rS  r
  r  population_sizerT  r.   r.   r/   test_sf_gh18506J  s   zTestHypergeom.test_sf_gh18506N)r   r   r   r  r/  r  r  r  r   rP  r:  r  r.  r2  r.   r.   r.   r/   r    s    
	.r  c                   @   s   e Zd Zejdg ddd Zejdg ddd Zd	d
 Zdd Z	ejdddgdd Z
ejdg ddd ZdS )TestLoggammaz	x, c, cdf))r   r]   g;Y%?)r      gRٲa6_<)gHr  gi|e?)r  g6l?)i+rU   g֬CCf9)ir   g ֺlc                 C   <   t j||}t||dd t j||}t||dd d S r   )r3   loggammarf   r   r   )rh   rW   ry  rf   rT  yr.   r.   r/   r{  ]  s   zTestLoggamma.test_cdf_ppfzx, c, sf))r   r  gQOu3;)   rY   g\Z{0)r5  r  geɐ?)ig{Gzd?gr0T?c                 C   r6  r   )r3   r7  r   r   r  )rh   rW   ry  r   rG   r8  r.   r.   r/   rZ  o  s   zTestLoggamma.test_sf_isfc                 C       t jdd}t|ddd d S )Nr]   g     @r3  rx   )r3   r7  r   r   )rh   lpr.   r.   r/   r  z  s   zTestLoggamma.test_logpdfc                 C   sT   t g ddd}|D ]\}}}}}tjj|dd}t|||||gdd qd S )N)ro   g"~jg46<@g oŏ      @r7  g	h"lxgQ?gZd;333333@g      (@g{/L@g??gгYҿgh|?5?r   r~   msvkr  r   r:  )r`   r   reshaper3   r7  r   )rh   tablery  r   varskewkurtcomputedr.   r.   r/   r    s   zTestLoggamma.test_statsry  rU   r  c                 C   sx   t jj|dd}t| sJ t j|}t t||k t	|}|j
dd}|jd  k r7|jk s:J  J d S )Nr   r  re  )confidence_levelro   )r3   r7  r   r`   isfiniter   median	binomtestcount_nonzeror   proportion_cir  r  )rh   ry  rW   medbtestcir.   r.   r/   r/    s   $zTestLoggamma.test_rvsrd  ))rh  g3H໱k3@)r   r  )r  g8,[H^}	)r  g90$)r  gtum\c                 C   r  rc  )r   r3   r7  rA   re  r.   r.   r/   rP       zTestLoggamma.test_entropyN)r   r   r   r   r   r   r{  rZ  r  r  r/  rP  r.   r.   r.   r/   r3  V  s"    


r3  c                   @   *   e Zd Zg dZejdedd ZdS )TestJohnsonsu))r;  r   r   g?rh  )r   r   r   gH';vIh%,=)r   r   r   g?x7rR  r  c                 C   sF   |\}}}}}t tj||||dd t tj|||||d d S NrR  rx   )r   r3   	johnsonsur   r  rh   r  rW   r,   r-   r   tolr.   r.   r/   rZ       zTestJohnsonsu.test_sf_isfNr   r   r   casesr   r   r   rZ  r.   r.   r.   r/   rQ        rQ  c                   @   rP  )TestJohnsonb))r  r   r   g?Hz>)r  r   r   g0jA:rR  )g!?r   r   gQbF5rR  r  c                 C   sF   |\}}}}}t tj||||dd t tj|||||d d S )NrR  rx   r   )r   r3   r  r   r  rU  r.   r.   r/   rZ    rW  zTestJohnsonb.test_sf_isfNrX  r.   r.   r.   r/   r[    rZ  r[  c                   @   sx   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zej	
dddgdd Zdd Zej	
dddgdd Zdd ZdS )TestLogisticc                 C   2   t dd}tj|}tj|}t|| d S Nru  r  )r`   r<  r3   logisticrf   r   r   rh   rW   r8  rz  r.   r.   r/   r{       zTestLogistic.test_cdf_ppfc                 C   r^  r_  )r`   r<  r3   r`  r   r  r   ra  r.   r.   r/   rZ    rb  zTestLogistic.test_sf_isfc                 C   s4   d}d}t tjd| | t tj|| d S )Ng      <gg|EA@r   )r   r3   r`  r   r  )rh   rT  desiredr.   r.   r/   test_extreme_values  s   z TestLogistic.test_extreme_valuesc                 C   s*   t jg d}g d}t||dd d S )N)r  r   rX   )gm\  .g9B.gO& $r   rx   )r3   r`  r   r   )rh   r  rQ   r.   r.   r/   test_logpdf_basic  s   zTestLogistic.test_logpdf_basicc                 C   s"   t jddg}t|ddg d S )Nrn   r5  )r3   r`  r   r   rh   r  r.   r.   r/   test_logpdf_extreme_values  s   z'TestLogistic.test_logpdf_extreme_valueszloc_rvs,scale_rvs)g9x&?gi '?)gB"?gs^&?c                 C   sR   t jjd||d}dd }t|t j||fdj}t j|}t||dd d S )NrY   r   r[   r\   c                 S   s   | \}}t |}tt|| | dt|| |   |d  }t|| | t|| | d t|| | d   | }||fS Nr   r]   )r   r`   rL  r   )inputr   r,   r-   rS  x1x2r.   r.   r/   r     s   z#TestLogistic.test_fit.<locals>.funcr  gKH9r   )r3   r`  r   r!   	_fitstartrW   r   r   )rh   loc_rvs	scale_rvsr   r   expected_solution
fit_methodr.   r.   r/   test_fit   s   
zTestLogistic.test_fitc                 C   sB   t jjdddd}tt j| tt j|dd tt j|dd d S )NrY   ro   r]   rh  r   r   r   )r3   r`  r   r   rh   r   r.   r.   r/   test_fit_comp_optimizer  s   z$TestLogistic.test_fit_comp_optimizer
testlogcdfTFc                 C   sH   t g d}|rtj|}ntj| }g d}t||dd d S )N)r  r5     r!  r   )     g      g%h9fg?~T}%mgCx^&ْV瞯<rx   )r`   r   r3   r`  r  r,  r   )rh   rv  rW   r8  rQ   r.   r.   r/   test_logcdfsf_tails  s   z TestLogistic.test_logcdfsf_tailsc                 C   s2   t g ddgd  dgd  }ttj| d S )N)	i5%   +   r  r  0   6   7   :   ;   r   =   r  )r`   r   r   r3   r`  rt  r.   r.   r/   test_fit_gh_18176,  s   
zTestLogistic.test_fit_gh_18176N)r   r   r   r{  rZ  rd  re  rg  r   r   r   rr  ru  rz  r  r.   r.   r.   r/   r]    s    


r]  c                   @   r  )

TestLogserc                 C   r  r  r  rl   r.   r.   r/   r  6  r  zTestLogser.setup_methodc                 C   r  )Nr   r   r  r   r"  r   )r3   logserr   r   r&  r   r'  r   r(  r   r)  rD  rE  r,  r.   r.   r/   r/  9  r  zTestLogser.test_rvsc                 C   s   t jdd}t|d d S )Nr   r2  g&Y3)r3   r  r4  r   rh   r  r.   r.   r/   test_pmf_small_pD  s   zTestLogser.test_pmf_small_pc                 C      t jd}t|d d S )Nrh  gW  ?)r3   r  r   r   r  r.   r.   r/   test_mean_small_pR  s   zTestLogser.test_mean_small_pN)r   r   r   r  r/  r  r  r.   r.   r.   r/   r  5  s
    r  c                	   @   s   e Zd Zejdddd Zejdej	ej
gejdg dejdg d	ejd
ddgddgfdd Zejdej	dfej
dfgdd ZdS )TestGumbel_r_lfunctionscopec                 C      t jdS r  r`   r   r   rl   r.   r.   r/   r   ^     zTestGumbel_r_l.rngr;   rn  r   r   r   ro  rU   r   r~   zfix_loc, fix_scaleTFc           	      C   sN   |j d|||d}t }|r|d |d< |r|d |d< t||fi | d S )NrY   r   r[   r\   r   r]   r   r   )r   r   r   )	rh   r;   rn  ro  r   rz  r   r   r   r.   r.   r/   ru  b  s   
z&TestGumbel_r_l.test_fit_comp_optimizerz	dist, sgnr   r   c                 C   s@   |t g d }||\}}t||d  t|ddd d S )N)r   r   r   r   r   r   r   gW  @g   @g3qtw>r  rx   )r`   r   r   r   )rh   r;   sgnzr[   r\   r.   r.   r/   rr  w  s   zTestGumbel_r_l.test_fitN)r   r   r   r   fixturer   r   r   r3   gumbel_rgumbel_lru  rr  r.   r.   r.   r/   r  ]  s    

r  c                   @   s  e Zd Zdd Zdd Zejdddd Zej	d	ej
d
ddgej
dddgej
dddgdd Zej
d
ddgej
dddgej
dddgej
ddd eddgddD ejdddd Zejdddd  Zd!d" Zd#d$ Zd%S )&
TestParetoc                 C   s  t  R t dt tjjddd\}}}}t|tj t|tj t|tj	 t|tj	 tjjddd\}}}}t|tj t|tj t|tj	 t|tj	 tjjddd\}}}}t|d t|tj t|tj	 t|tj	 tjjddd\}}}}t|d t|tj t|tj	 t|tj	 tjjd	dd\}}}}t
|d
 t
|d t|tj	 t|tj	 tjjddd\}}}}t
|d t
|d t|tj	 t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t
|d W d    d S 1 s[w   Y  d S )NrQ  ro   r  r  r7  r  r  rs   r  g?grq@r         @gffffff?gK~?g      2@g۶m۶m?r=  UUUUUU?gqq?r/        @g%I$I?gQ?gUUUUUU@grq?g88Nb@)rU  rV  rW  rX  r3   paretor   r`   r   r   r   r  rh   r  r  rG   rT   r.   r.   r/   r    s`   











$zTestPareto.test_statsc                 C   s:   d}d}d}t jj||d|d}|| | }t|| d S )Ng    eAr]   r  r   rZ   )r3   r  r   r   )rh   rW   r-   r\   rT  rQ   r.   r.   r/   r    s   zTestPareto.test_sfr  r  c                 C   r  r  r  rl   r.   r.   r/   r     r  zTestPareto.rngz2ignore:invalid value encountered in double_scalarsr   r   r]   r   r   rx  r~   c              
   C   s  t jjd||||d}t jj|dddd }t jj|dddd }t jj|dddd }||  kr<|  kr<dks?J  J t jjd|||d |d}t jj|dd	\}	}
}t|d |  |d }|jd }t|	|tt	||    t|
d d S )
NrY   r   r-   r\   r[   r   r   p=
ף?)r   r   )r   fix_b)r   fbr]   r   )
r3   r  r   r   r   r  r'  r`   rL  rr  )rh   r   r   rx  r   r   shape_mle_analytical1shape_mle_analytical2shape_mle_analytical3shape_mle_a	loc_mle_ascale_mle_a
data_shiftndatar.   r.   r/   rr    s,   
zTestPareto.test_fitrU   fix_shape, fix_loc, fix_scalec                 C      g | ]}d |v r|qS Fr.   r:   rT  r.   r.   r/   r<         zTestPareto.<listcomp>TFr   repeatignoreinvalidc           
      C   sV   t jjd||||d}i }	|r||	d< |r||	d< |r||	d< tt j|fi |	 d S )NrY   r  r   r   r   )r3   r  r   r   
rh   r   r   rx  r   r   rz  r   r   r   r.   r.   r/   r     s   	z&TestPareto.test_fit_MLE_comp_optimizerc                 C   s8   d\}}}t jj|||dtjdd}tt j| d S )N)r   r   r   rY   ið& r   )r3   r  r   r`   r   r   r   )rh   r'  locationr\   r   r.   r.   r/   test_fit_known_bad_seed  s
   

z"TestPareto.test_fit_known_bad_seedc                 C   s@   t tj tttjjg ddd tttjjg dddd d S )Nr   r]   r   )r~   r]   r   r   r   r}  )r  r3   r  r  r   r   rl   r.   r.   r/   test_fit_warnings	  s
   

zTestPareto.test_fit_warningsc                 C   s.   t jjddd|d}t|d t j|}d S )Ni~r   rY   )r[   r-   r   r   r   )r3   r  r   r
   r   )rh   r   r   r   r.   r.   r/   test_negative_data	  s   
zTestPareto.test_negative_dataN)r   r   r   r  r  r   r  r   r   filterwarningsr   rr  r$   r`   errstater   r  r  r  r.   r.   r.   r/   r    s,    <





	r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zejddg dfdddded ejgfdddded d gfd!g d"fgd#d$ Zd%d& Zd'S )(TestGenparetoc                 C   sl   dD ]}t |}tj|\}}t|d tt | qt d}tj|\}}t||gddg d S )Nr7  rt   rt          ro   )	r`   r   r3   	genpareto_get_supportr   r   isposinfr   )rh   ry  r,   r-   r.   r.   r/   test_ab	  s   


zTestGenpareto.test_abc                 C   s   t jdd}tddd}t||t j| t||t j| t||t j| tddd}t|	|t j	| d S )Nrt   ry  r   r/  r  r7  rX   )
r3   r  r`   r<  r   r_   r  rf   r   r   rh   rvrW   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  rt   r7  rX   r   )r3   r  r`   r<  r   r_   uniformrf   r   r   r   r  r.   r.   r/   test_cm13	  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 )NrU   r  rt   r7  r  )
r3   r  r   r_   r`   r   rf   r   isneginfr   rh   r  r.   r.   r/   
test_x_infA	  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   rX   r  r   r   r3  g+r  r   )r3  r3  )r`   r<  r3   r  r_   r   rf   )rh   rW   ry  pdf0dcpdfccdf0cdfcr.   r.   r/   test_c_continuityO	  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 Nr  rq   rU   baser   r  Fendpointr7  )rt   r  r  r   )r`   r2  rw  r<  r3   r  r   r   )rh   r\  ry  ppf0r  ppfcr.   r.   r/   test_c_continuity_ppf]	     z#TestGenpareto.test_c_continuity_ppfc              	   C   r  r  )r`   r2  rw  r<  r3   r  r  r   )rh   r\  ry  isf0r  isfcr.   r.   r/   test_c_continuity_isfg	  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 )Nr  rq   rU   r  r   r  Fr  r7  )rh  gC]r2rw   gV瞯Ҽrw   r   )	r`   r2  rw  r<  r   r3   r  rf   r   )rh   r\  ry  r.   r.   r/   test_cdf_ppf_roundtripq	  s   z$TestGenpareto.test_cdf_ppf_roundtripc                 C   s    t jdddd}t|d d S )Nr  rq   r   r   gpEȜ)r3   r  r,  r   rf  r.   r.   r/   r:  z	  s   zTestGenpareto.test_logsfzc, expected_statsr   )r   r   r]   r9  rK  r  gqq@rX   r]   gqq?g      ?g$I$	?rq?r  gll0@r   )ro   UUUUUU?r   333333c                 C   s$   t jj |dd}t||ddd d S )Nr  r  r   rw   rF  )r3   r  r   )rh   ry  expected_statsr(  r.   r.   r/   r  	  s   zTestGenpareto.test_statsc                 C   s   t jd}t|ddd d S )Nrh  gvǼ
  ?r   rx   )r3   r  rB  r   )rh   r  r.   r.   r/   test_var	  s   zTestGenpareto.test_varN)r   r   r   r  r  r  r  r  r  r  r  r:  r   r   r   r`   r  r   r  r  r.   r.   r.   r/   r  	  s(    

	


r  c                   @   sL   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dS )TestPearson3c                 C   r  r  r  rl   r.   r.   r/   r  	  r  zTestPearson3.setup_methodc                 C   s   t jjddd}tt|dk t|jjtd v  t jd}tt	|t
 t dd}tt	|tj t|jjtd v  tt|dk d S )NrU   r   r  AllFloatro   r   )r3   r(   r   r   r&  r'  r   r(  r   r)  r   rE  r   r,  r.   r.   r/   r/  	  s   zTestPearson3.test_rvsc                 C   s|   t jdg d}t|tg ddd t jdd}t|tdgdd t jg d	d}t|tg d
dd d S )Nr]   rt   rU   r  )gtT?g+q?g?r  r   r  rU   ND}i?r  r   r   r   r   )r  gj?gdC?gs?g'M?)r3   r(   r_   r   r`   r   r%  r.   r.   r/   r6  	  s   
zTestPearson3.test_pdfc                 C   sp   t jdg d}t|tg ddd t jdd}t|dgdd t jg d	d}t|g d
dd d S )Nr]   r  )grE?gTp]0?g~?r  r   r  rU   g E&"J?r  )giZ*J?gh+8w?gcK?g|<x6?gG?)r3   r(   rf   r   r`   r   r%  r.   r.   r/   r?  	  s   

zTestPearson3.test_cdfc                    s@   g d}dd t j|} fdd|D }t|| d S )Nr  r   r   ro   ro   r  c                    s$   g | ]}t t|j d  qS r8   )r   r3   r(   r_   )r:   rC  neg_infx_evalr.   r/   r<   	  s    z<TestPearson3.test_negative_cdf_bug_11186.<locals>.<listcomp>)r3   r(   rf   r   )rh   skewsr  int_pdfsr.   r  r/   test_negative_cdf_bug_11186	  s   z(TestPearson3.test_negative_cdf_bug_11186c                 C   sT   t jdd}t|d t|tjsJ t jdd}t|d t|tjs(J d S )Nr   r]   r   r  )r3   r(   r  r   r)  r`   number)rh   r  r.   r.   r/   test_return_array_bug_11746	  s   

z(TestPearson3.test_return_array_bug_11746c                 C   s   g d}d}t jt j|||}t|| tdgdgg}tdd}tt j||t j| |  tt j||t j	| |  tt j||t j
||   d S )Nr  ro   r   r  r   r]   )r3   r(   r   rf   r   r`   r   r<  r_   r   r  )rh   r  r  r   rC  rW   r.   r.   r/   test_ppf_bug_17050	  s   
zTestPearson3.test_ppf_bug_17050c                 C   sT   g d}g d}g d}t tj|||dd t tj|dtj|dd d S )N)rU   ro   r7  皙)r8  r/  g      I@       @)g7>g~׼=gp'+7g;rW  rx   r   )r   r3   r(   r   rH  )rh   rC  rW   ra  r.   r.   r/   r  	  s
   $zTestPearson3.test_sfN)r   r   r   r  r/  r6  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)rt   rU   r  ro   r7  )
gffffffr  r   皙ɿr  rU   r  ro   r7  ffffff?)r3   kappa4rf   r  r   rh   rW   rO  rT   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~   rX   rt   r  r   )r`   r<  r3   r  rf   
genextremer   r  r.   r.   r/   test_cdf_genextreme	  s   zTestKappa4.test_cdf_genextremec                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr   rX   r7  rt   )r`   r<  r3   r  rf   r  r   r  r.   r.   r/   test_cdf_expon	     zTestKappa4.test_cdf_exponc                 C   @   t ddd}d}d}tj|||}tj|}t|| d S )Nr  r~   rX   rt   )r`   r<  r3   r  rf   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~   rX   r  rt   )r`   r<  r3   r  rf   r`  r   r  r.   r.   r/   test_cdf_logistic
  r  zTestKappa4.test_cdf_logisticc                 C   r  )Nr  r~   rX   r7  )r`   r<  r3   r  rf   r  r   r  r.   r.   r/   test_cdf_uniform
  r  zTestKappa4.test_cdf_uniformc                 C   s   t dd d S ri  )r3   r  rl   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                   @   s4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )TestPoissonc                 C   r  r  r  rl   r.   r.   r/   r  (
  r  zTestPoisson.setup_methodc                 C   s@   t d}tjg d|}d|d |d d g}t|| d S )Nr]   r   r   r]   ro   r   )r`   rr  r3   r`  r4  r   )rh   ln2r-  rQ   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   )r3   r`  r4  r   intervalr   )rh   r-  rQ   r  r.   r.   r/   test_mu02
  s
   
zTestPoisson.test_mu0c                 C   r  )Nro   r   r  r   r"  r   )r3   r`  r   r   r&  r   r'  r   r(  r   r)  rD  rE  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  r7  )rt   r7  rs   r   r]   ro   )r3   r`  r   r`   r  r   r   )rh   r  r(  rQ   r.   r.   r/   r  F
  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  rl   r.   r.   r/   r  R
  r  zTestKSTwo.setup_methodc                 C   s   dD ]W}t dd| d| ddd|  dg}d| | }tj|d }|dkr.t |nd}t dd|| ddtjd|  t	dd|  ddg}tj
||}t|| qd S )Nr   r]   r   rX   rY   r   r   ro   r   r7  r]   rt   )r`   r   r2   r   gammalnr   r3   ksoner   r#  kstworf   r   )rh   rS  rW   v1lgelgrQ   r  r.   r.   r/   r?  U
  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  ro   r7  r]   )r`   r<  r   r2   r   r  r   r3   r  r   r  r  r   )rh   rW   rS  r  r  r  rQ   r*  r.   r.   r/   r  i
  s   &
zTestKSTwo.test_sfc                 C   s\   t ddddd  }g d}|D ]}|t | }tj||}t |}t|d qd S )Nr   r]   r  r   )r!  rY   r  i  r   r   rh  )r`   r<  r  r3   r  rf   r0  r
   )rh   rW   ns_xxnprobsdiffsr.   r.   r/   test_cdf_sqrtnx
  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  )r`   r<  r3   r  rf   r   r   )rh   rW   rS  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  )r`   r<  r  r3   r  rf   r   r   )rh   rW   rS  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  ro   r  r  rx   )r`   r<  r3   r  rf   r   r   rh   rW   rS  r  r  condr-  r.   r.   r/   test_ppf_of_cdf
  s   zTestKSTwo.test_ppf_of_cdfc                 C   r!  )	Nr   r   r  r  ro   r7  r  rx   )r`   r<  r3   r  r  r   r   )rh   rW   rS  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  ro   r7  )r`   r<  r  r3   r  rf   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  ro   r  )r`   r<  r  r3   r  r   r  r   )rh   rW   rS  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  )r`   r<  r3   r  r   rf   r   )rh   r  rS  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)rX   r!  rY   r  r   r   )rK  gUUUUUU?ro   r   r]   r   )gRT>gr	?gK5
?gn
"5?gU
?gk?)g&6#>gb
E>gI5?g\?g;?g%1?)g6>gL>g<?g䓀^?gO|6$?g qO?)g}+: >gwQ9>gH{?g]qv(?g)~/v?gmJ?)gV27J=gGk(>gWX?gY?g{0`?gZ
H?)g_R=g4>g̪?gT_@?g<e?g2?r]   rw  rx   )
r`   r   	enumeraterr  r  ra   r3   r  rf   r   )rh   r  ratiosrQ   idxrS  rW   r  r.   r.   r/   test_simard_lecuyer_table1
  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  Q
  s    
		
r  c                   @   rn  )TestZipfc                 C   r  r  r  rl   r.   r.   r/   r  
  r  zTestZipf.setup_methodc                 C   r  )Nr  r   r  r   r"  r   )r3   zipfr   r   r&  r   r'  r   r(  r   r)  rD  rE  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,   r  skr,   r  )r3   r/  r   r`   rG  r   r   r   r  r.   r.   r/   r  
  s
   zTestZipf.test_momentsN)r   r   r   r  r/  r  r.   r.   r.   r/   r.  
  rs  r.  c                   @   r  )
TestDLaplacec                 C   r  r  r  rl   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   )r3   dlaplacer   r   r&  r'  r   r(  r   r)  rD  rE  r,  r.   r.   r/   r/     s   zTestDLaplace.test_rvsc                 C   s   d}t |}| d\}}}}d}t| |d }||}	t|	|d  t|	|d  }
}t||fd t||f|
||
d  d fd	d
d d S )Nr7  r  r{  r   r]   r   r  r  r3  rh  r  )r3   r5  r`   r   r4  rL  r   r   )rh   r,   dlr  r  rG   rT   r
  rz  ppm2m4r.   r.   r/   r    s   

&(zTestDLaplace.test_statsc                 C   sF   t d}t|}|d\}}}}t||fd t||fd d S )Nrs   r  )rt   rt   )r=        
@)r`   rr  r3   r5  r   r   )rh   r,   r6  r  r  rG   rT   r.   r.   r/   test_stats2  s
   

zTestDLaplace.test_stats2N)r   r   r   r  r/  r  r;  r.   r.   r.   r/   r4  
  s
    r4  c                       s   e Zd Zdd Zejdddgdd Zejdddg fd	d
Zdd Z	dd Z
dd Zejdg ddd Z  ZS )TestInvgaussc                 C   r  r  r  rl   r.   r.   r/   r  !  r  zTestInvgauss.setup_methodzrvs_mu,rvs_loc,rvs_scale)r]   r   r   )g
ףp=@g r@gʡE6@c                 C   sB  t jjd|||d}t jj||d\}}}|| }t|}t|t|d |d   }	||	 }
t|
|ddd t|	|ddd t	|| t jjd|||d}t jj||d |d d\}}}t	|d | t	|d | t jj|d	d
d }t jj|d	dd }t jj|d	dd }||  kr|  krd	ksJ  J d S )NrY   )r   r  r[   r\   r   r   rw   r  r   r}  r  )fmur   )fix_mur   )
r3   r	  r   r   r`   r   r   rL  r   r   )rh   rvs_mur   rx  r   r  r[   r\   mu_temp	scale_mlemu_mle
shape_mle1
shape_mle2
shape_mle3r.   r.   r/   rr  $  s.   



*zTestInvgauss.test_fit)gX9v>@g	@gGz@c           	         s   t jd}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
tj||d t ||d  dksTJ t
tj||d d t
tj|dd t
tj||t jdd d	 d S )
Nr   rY   )r   r  r[   r\   r   r   r]   )r   r=  r   r   r}  )r`   r   RandomStater3   r	  r   r   r   r   r   r   r   rand)	rh   r@  r   rx  r   r   	super_fitsuper_fittedinvgauss_fit	__class__r.   r/   r   C  s$   




z(TestInvgauss.test_fit_MLE_comp_optimizerc                 C   sN   t tj tt tjjg ddd W d    d S 1 s w   Y  d S r  )r  r3   r	  r   r   r   r   rl   r.   r.   r/   test_fit_raise_errorsg  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?r  r  ?gfFn   gr^:g9̗?r  gx_;:g!?gٷ
??)r3   r	  rf   r   r   r   )rh   r  rQ   rM   
cdf_actual	sf_actualr.   r.   r/   r+  m  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  rQ  rP  giJ.rR  gr^ߺr  gpgFgpQ^L)r3   r	  r  r   r,  )rh   r  r,  r.   r.   r/   r.    s   	


zTestInvgauss.test_logcdf_logsfzmu, ref))g:0yU>g,9)r  g%!)rq   g40)r   gK'
@)r  g`p
@c                 C   r  rS  )r   r3   r	  rA   )rh   r  ra  r.   r.   r/   rP       zTestInvgauss.test_entropy)r   r   r   r  r   r   r   rr  r   rN  r+  r.  rP  __classcell__r.   r.   rL  r/   r<     s    
"#r<  c                       sz   e Zd Zejdg dejdg ddd Zejdg d fd	d
Zdd Zdd Z	dd Z
dd Z  ZS )TestLaplacer   )r  r   r   r]   rx  )r   r]   r   rX   c           	      C   sZ  t jd}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 )
Nr   rY   r  rw   r  r   rs  r]   r}  )r`   r   rG  r3   r  r   rH  rL  r   r   r   r   r   r  r   r   r   r   )	rh   r   rx  r   r   loc_mlerB  r[   r\   r.   r.   r/   rr    s0   



zTestLaplace.test_fitrvs_loc,rvs_scale))r  rX   rX   r~   )ro   r  c                    s   t jd}tjjd|||d}dd }tj|\}}tttjtj|\}}	||||}
|||	|}|
|k sEt j	|
|dddsGJ d S d S )Nr   r   r  c              	   S   s8   dt | td|  d| tt||     S )Nr   r]   r   )r   r`   rr  rL  r   )r[   r\   r   r.   r.   r/   ll  s   z3TestLaplace.test_fit_MLE_comp_optimizer.<locals>.llrw   r  )
r`   r   rG  r3   r  r   r   r   r   r   )rh   r   rx  r   r   r[  r[   r\   loc_opt	scale_optll_mlell_optrL  r.   r/   r     s    
z'TestLaplace.test_fit_MLE_comp_optimizerc                 C   sZ   t g d}tjj|dd\}}t|dddd tjj|dd\}}t|dddd d S )N)r7  r7  r  r8  r  r  r9  r   r   rw   r  rs  )r`   r   r3   r  r   r   )rh   r   r[   r\   r.   r.   r/   test_fit_simple_non_random_data  s
   z+TestLaplace.test_fit_simple_non_random_datac                 C   sl   d}t j| }|dksJ t j|}|dksJ t j|}|dks'J t j| }|dks4J d S )Nr   rt   r7  )r3   r  rf   r   )rh   rW   p0p1r.   r.   r/   test_sf_cdf_extremes   s   z TestLaplace.test_sf_cdf_extremesc                 C   s.   d}t j|}t|t| d dd d S )Nr  r]   r   rx   )r3   r  r   r   r`   r   )rh   rW   rT  r.   r.   r/   r       zTestLaplace.test_sfc                 C   s.   d}t j|}t|td|  dd d S )Ng}:r]   r   rx   )r3   r  r  r   r`   rr  )rh   rT  rW   r.   r.   r/   r    rd  zTestLaplace.test_isf)r   r   r   r   r   r   rr  r   r`  rc  r  r  rV  r.   r.   rL  r/   rW    s    -	rW  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
ejddgejdddgejdddgdd Z	dS )TestLogLaplacec                 C   s@   t g d}t g d}g d}ttj|||dd d S )N)rs   r  r8  )rw  r    4&kC)g ?gKH9gXrL0rw   rx   )r`   r   r   r3   
loglaplacer   )rh   ry  rW   ra  r.   r.   r/   r  "  s   zTestLogLaplace.test_sfc                 C   0   d}g d}g d}t tj|||dd d S )Nr:  )r   rU   r  r2  rs  )gHhlh#?gH]9@?g"fj#@g11Ags!8wBr3  rx   )r   r3   rg  r  )rh   ry  r\  ra  r.   r.   r/   r  *  s   zTestLogLaplace.test_isfrc  r   r]   r   r   c                 C   sX   d|d  }t d|d d}ttj||t j t t tjj||dr*J d S )Nr  r   ro   r  )	r`   r   r   r3   rg  r  r   r   rG  )rh   rc  momry  r.   r.   r/   test_moments_stats3  s   $z!TestLogLaplace.test_moments_statsry  )ro   r7  rs   z
loc, scale)r  g@fix_cTFrz  c                 C   s   t jd}tjj|||d|d}d|i}|r||d< |r!||d< dt| }	|	dkrSd	}
tjt	t
f|
d
 tjj|fi | W d    d S 1 sLw   Y  d S ttj|fi | d S )Nr   rY   r|  r   fcr   r   r   r   r   )r`   r   r   r3   rg  r   r   r   r   r   r   r   r   )rh   ry  r[   r\   rl  rz  r   r   r   nfreer  r.   r.   r/   test_fit_analytic_mle>  s&   
z$TestLogLaplace.test_fit_analytic_mleN)
r   r   r   r  r  r   r   r   rk  ro  r.   r.   r.   r/   re     s    	

re  c                   @   s   e Zd Zejdddgdd Zejdddd	 Zejd
g dejdg dejdg dejddd e	ddgddD dd Z
dd Zdd Zdd ZdS ) TestPowerlawzx, a, sf)rK  rs   g      ?)g     ?g      p?gSQ>c                 C   ri  rv   )r   r3   powerlawr   )rh   rW   r,   r   r.   r.   r/   r  \  s   zTestPowerlaw.test_sfr  r  c                 C   r  r  r  rl   r.   r.   r/   r   b  r  zTestPowerlaw.rngr   )rU   ro   r   r   r]   r   r  rx  r  r  c                 C   r  r  r.   r  r.   r.   r/   r<   j  r  zTestPowerlaw.<listcomp>TFr   r  c           
      C   sp   t jjd||||d}t }	|r||	d< |r"t| tj |	d< |r(||	d< tt j|fi |	ddi d S )Nr*  )r   r,   r[   r\   r   r   r   r   r   T)	r3   rq  r   r   r`   	nextafterr  r   r   r  r.   r.   r/   r   f  s   z(TestPowerlaw.test_fit_MLE_comp_optimizerc                 C   sT   d}d}d}t jj|||dtjdd}dt|d i}tt j|fi | d S )	Ng`- @rt   grߟA@rY   r~   )r,   r[   r\   r   r   r   r]   )r3   rq  r   r`   r   r   ptpr   )rh   r,   r  r\   r   r   r.   r.   r/   test_problem_case~  s   
zTestPowerlaw.test_problem_casec                 C   sf  t tj d}tt|d tjjg dddd W d    n1 s#w   Y  d}tt|d tjjg ddd W d    n1 sEw   Y  d}tt|d tjjg dd	d W d    n1 sgw   Y  d
}tt|d tjjg ddd W d    n1 sw   Y  d}tt|d tjjg ddd W d    d S 1 sw   Y  d S )Nz7 Maximum likelihood estimation with 'powerlaw' requiresr   r   r]   r   r   r   r}  r]   r   r   z$Negative or zero `fscale` is outsider  rs  z0`fscale` must be greater than the range of data.)r  r3   rq  r  r   r   r   r  r.   r.   r/   r    s*   
"zTestPowerlaw.test_fit_warningsc                 C   sJ   g d}t j}tjdd t|| W d    d S 1 sw   Y  d S )N)r   r   r]   r]   r   r   r   r   r   r   r~   r9  r  over)r3   rq  r`   r  r   )rh   r   r;   r.   r.   r/   test_minimum_data_zero_gh17801  s
   "z+TestPowerlaw.test_minimum_data_zero_gh17801N)r   r   r   r   r   r   r  r  r   r$   r   rt  r  rx  r.   r.   r.   r/   rp  Y  s&    


rp  c                   @   st   e Zd Zejdg ddd Zejdddgdd	 Zejdg d
dd Zejdg ddd Z	dS )TestPowerLogNormzx, c, s, ref))rY   r  r   ga!R()r  r  r   g;?)r  r  r   gE?)MDr  r   g=c                 C      t tj||||dd d S r   )r   r3   r  r   rh   rW   ry  rG   ra  r.   r.   r/   r       zTestPowerLogNorm.test_sfzq, c, s, ref)g?r  r   rq   )gR4-r  r   r   c                 C   r{  )Ng|=rx   )r   r3   r  r  )rh   r\  ry  rG   ra  r.   r.   r/   r    s   zTestPowerLogNorm.test_isf))(,* Er  r   g?)r  r  r   gv6)r  r  r   g+	94|7)r[  r  r   g?c                 C   r{  )Ngt =rx   )r   r3   r  rf   r|  r.   r.   r/   r?    r}  zTestPowerLogNorm.test_cdf))rz  r  r   gS^Ռe9)@xDr  r   g0g;)g\)c=Hr  r   g7H7c                 C   r{  )NgAfc=rx   )r   r3   r  r_   r|  r.   r.   r/   r6    s   zTestPowerLogNorm.test_pdfN)
r   r   r   r   r   r   r  r  r?  r6  r.   r.   r.   r/   ry    s&    


ry  c                   @   sZ   e Z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 )TestPowerNormrg  ))r  r   g| <)r  r]   ge()rY   r  g%!@6)r  rq   gT;-c                 C   ri  r   )r   r3   	powernormr   rk  r.   r.   r/   r    s   zTestPowerNorm.test_sfr  ))rw  r  gĿ)gwJ?rY   g!X)r  r  g缂U)r  r  gͫ1@)rt  r]   gD@)Jz5r~   gU!zYr@c                 C   ri  Nr  rx   )r   r3   r  r  r  r.   r.   r/   r       zTestPowerNorm.test_isf))ir  g.u	T9)r]   r  ?)ru  r  gsK-)r  r  gk8>)ru  r  g^u1-c                 C   ri  rS  )r   r3   r  rf   rk  r.   r.   r/   r?    r  zTestPowerNorm.test_cdfN)	r   r   r   r   r   r   r  r  r?  r.   r.   r.   r/   r    s    


r  c                   @   >   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	dS )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 )NrQ  g(\O3@r  r3  )g~?gCX&?g*7gS?gBqFq @)皙?@gffffff@)r/  gEy?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@)rU  rV  rW  rX  r3   r  r   r`   r   r   r   r   )rh   r  rQ   r,   rW   r8  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   )r`   rw  r3   r  rf   r   r   ra  r.   r.   r/   r{  3  s   zTestInvGamma.test_cdf_ppfc                 C   sR   t jdkrtdd}ntdd}tj|d}tj|d}t||dd d S )N        r]   rY      r   r7  rx   )	sysmaxsizer`   rw  r3   r  r   r  r   ra  r.   r.   r/   rZ  :  s   
zTestInvGamma.test_sf_isfa, ref)r   g70K6:)r  gVMOuc                 C   r  rv   )r   r3   r  rA   rh   r,   ra  r.   r.   r/   test_large_entropyG  s   zTestInvGamma.test_large_entropyN)
r   r   r   r  r{  rZ  r   r   r   r  r.   r.   r.   r/   r    s    r  c                   @   r  )
TestFc                 C   s\   t jddgg}|D ]\}}}|j|jg|R  }q	dd |D }dd |D }t|| d S )N)r]   r   r7  c                 S   &   g | ]\}}}|j |jg|R  qS r.   r_   r,   r:   _f_argsr   r.   r.   r/   r<   ]     & z(TestF.test_endpoints.<locals>.<listcomp>c                 S      g | ]\}}}|qS r.   r.   r:   r  r  	_correct_r.   r.   r/   r<   ^      )r3   fr_   r,   r   )rh   r   r  r  _correctanscorrectr.   r.   r/   rl  W  s   zTestF.test_endpointsc                 C   sX   t jj dddd\}}}}tt| tt| tt| tt|  d S )Nr        @r  r  )r3   r  r   r`   rG  r  r.   r.   r/   test_f_momentsa  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 )NrQ  r  r   )r]   r   r9  r   r  dfndfdr  )rU  rV  rW  rX  r3   r  rl   r.   r.   r/   test_moments_warningsi  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  r9  r  r  r]   r   r   r9  r~      )r`   r   r3   r  r   r  )rh   r  r  r  r  rG   rT   r8  v2s2k2numk2denk2r.   r.   r/   test_stats_broadcasto  s"   
0
 
 zTestF.test_stats_broadcastN)r   r   r   rl  r  r  r  r.   r.   r.   r/   r  V  s
    
r  c                   @   s   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	ejdg dejdddgddgddgg dg dgddgddggdgdgggdd Z
ejdddgddgddgg dg dgddgddggdgdgggdd Zdd ZdS )TestStudentTc                 C   s   t tjddgddg d S )Nr~   r9  g?g?)r   r3   r  rY  rl   r.   r.   r/   test_rvgeneric_std     zTestStudentT.test_rvgeneric_stdc                 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  )r  r  )\(?rt   r]   gGz @g     i@r   r2  gGz@r   g
ףp=
@)rt   gq    @)r   r3   r  r`   r   r   rl   r.   r.   r/   test_moments_t  s    zTestStudentT.test_moments_tc                 C   s*   g d}g d}t tj||dd d S )N)r   r]   r  rY   )g?@gTM]?ggY?U?r   rx   r   r3   r  rA   )rh   r  rQ   r.   r.   r/   test_t_entropy  s   zTestStudentT.test_t_entropyzv, ref)rY   r  )r  r  c                 C   r  rc  r  )rh   r  ra  r.   r.   r/   test_t_extreme_entropy  rO  z#TestStudentT.test_t_extreme_entropymethname)r_   r   rf   r   r   r  
df_infmaskr   r   )r   r   r   )r   r   r   c                 C   s   t jd t j|td}t jjdd|jd}t jj|j }t j||< t	j
|ddd}t	j
||  ddd}t	jddd}t||}t||}	t||}
||}t|| |
||  t||  |	||   d S )	Nr   r   rX   r  r   r   r  r[   r\   rZ   )r`   r   r   r   boolr  r'  randnr   r3   r  rH  r  r   )rh   r  r  r  rW   t_dist
t_dist_ref	norm_distt_meth
t_meth_ref	norm_methr   r.   r.   r/   test_t_inf_df  s   



zTestStudentT.test_t_inf_dfc                 C   s  t jd t j|td}t jjdd|jd}t j||< tj	j|dddd}tj
jdddd	}tj	j||  dddd}td
D ]}t|| | ||  t|| |  ||  q@tj	j|ddd}tj
jddd}tj	j||  ddd}t|| | t||  | d S )Nr   r  rX   r  r   r   r  )r  r[   r\   r  r[   r\   r  r   r  rZ   )r`   r   r   r   r  r  r'  r   r3   r  rH  r  r   rA   )rh   r  r  r   
res_ex_infres_ex_noinfr  r.   r.   r/   test_t_inf_df_stats_entropy  s"   
z(TestStudentT.test_t_inf_df_stats_entropyc                 C   sT   g d}g d}g d}g d}t tj|||dd t tj|||dd d S )N)r   r  rX   r   )r  d~QJr  r   )gZ_2g9g!ǟuIgdg)g73?r   gմFhAW;gm0_?r3  rx   )r   r3   r  r   r_   )rh   rW   r  
logpdf_refpdf_refr.   r.   r/   test_logpdf_pdf  s   zTestStudentT.test_logpdf_pdfN)r   r   r   r  r  r  r   r   r   r  r  r  r  r.   r.   r.   r/   r    s0    



r  c                   @   r  )TestRvDiscretec                 C   r  r  r  rl   r.   r.   r/   r    r  zTestRvDiscrete.setup_methodc                 C   s   g d}g d}d}t jd||fd}|j|d}tt|tj t||D ]\}}ttt	||kt
| | dk  q&| }tt|tjsLJ d S )N)r   r   r   r]   r   r   )rt   r[  rO  rt   r[  rt   r   sample)namevaluesr  r  )r3   r>   r   r   r)  r&  rE  r   r   rL  r   r`   r   r   integer)rh   statesprobabilitysamplesrc  rW   rG   rT  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)rK  r  r[  r	  r  )r7  r   r   rt   )	r`   r   r3   r>   rL  r   rA   r   r   )rh   r  rT  rN  rO  r.   r.   r/   rP    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 )Nru  ro   r[  r  r  r7  r=  r  r]   ro   r  rt   r[  r3  r   )r3   r>   r   r4  )rh   xkpkr  rW   r.   r.   r/   rJ    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 )
Nru  r  r  )r   r7  r  r  rs   r  r   r~   )r   ro   ro   ro   r   r   r   r   r3  r   c                       g | ]}  |qS r.   )rf   )r:   rz  r  r.   r/   r<     r  z+TestRvDiscrete.test_cdf.<locals>.<listcomp>)r3   r>   r   rf   )rh   r  r  x_valuesrQ   r.   r  r/   r?       
zTestRvDiscrete.test_cdfc                    r  )
Nru  r  r  )rU   ro   r  r   r   r7  )r   r   r]   r]   r   r   r3  r   c                    r  r.   )r   )r:   r\  r  r.   r/   r<   '  r  z+TestRvDiscrete.test_ppf.<locals>.<listcomp>)r3   r>   r   r   )rh   r  r  q_valuesrQ   r.   r  r/   r    r  zTestRvDiscrete.test_ppfc                 C   sN   g dg df}t j|d}t|||jd d d |jdd   d S )N)r   r]   r   r  r   )rU   r  r[  r[  rU   r  r   rh  r   )r3   r>   r   r   rf   r  )rh   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 )Nr9  )r   r   )rU   rU   r  r  )rU   rU   r  r  r  r3  r   )r`   r   r@  r   r3   r>   r   r   rL  r  r  rh   r  r  r  r.   r.   r/   test_multidimension2  s   
$z"TestRvDiscrete.test_multidimensionc                 C   s   g d}ddg}t ttjfi t||fd g d}t ttjfi t||fd g d}g d}t ttjfi t||fd g d}g d}t ttjfi t||fd ddg}ddg}t ttjfi t||fd d S )Nr   ro   r  )ro   333333?gffffff濩r   r]   r   r   r~   )r[  r[  r[  r[  r  r   )r  r   r3   r>   r   rh   r  r  r.   r.   r/   test_bad_input;  s   "zTestRvDiscrete.test_bad_inputc                 C   s   t ddt dd}}tttjfi t||fd t ddt dd}}tttjfi t||fd t ddt dd}}t	tj||fd
dd d S )	Nr   r]   r]   r]   r   gUUUUUU?r  r9  r   r]   r   )r`   r   r@  r+  r  r   r3   r>   r   r   r4  r  r.   r.   r/   test_shape_rv_sampleO  s    z#TestRvDiscrete.test_shape_rv_samplec                 C   sD   g d}g d}t j||fd}t| t|j|j dd d S )N)r   r]   r   r9  r  r  )rU   r  r  r  r  rU   r  r3  r   )r3   r>   r   r   r`   rL  r  r  r  r.   r.   r/   test_expect1^  s   $zTestRvDiscrete.test_expect1c                 C   s   g d}g d}t j||fd}t| | dd t| tdd t||D dd t|dd	 td
d t||D dd d S )N)/g      i@g     r@g      y@g     @@g     @g     @      @g      @r  g     0@g     @g     P@g     @g     p@g      @g     @g      @g     @r8  g     h@g     0@g     @g     @g     @g     P@g     @g     @g     @r9  g     8@g      @g     ȩ@g     @g     X@g      @g     @g     @g     x@g     @@g     @g     h@g     ̰@g     0@g     @g     @g     \@g     @)/g-C6:?rt   gF%uk?g:vz?rt   rt   g.nr?g|гY?rt   rt   rt   g @6*? 4U0*C?g@+?gC6z?g nr?g ?gOjM?g n?g1w-!?g:pΈ?gףp=
?g _Le?rt   g^)p?g~jtx?gJ4q?gGzt?g J4q?g Mb@?g@Psׂ?g@^)ˀ?rt   rt   g N@s?g 1w-!_?r  gൄ|г?rt   gH}}?rt   g
F%u?rt   rt   g ^)ˀ?g v?rt   r  r3  r   c                 s   s    | ]	\}}|| V  qd S rj   r.   r:   r  wr.   r.   r/   	<genexpr>  s    z.TestRvDiscrete.test_expect2.<locals>.<genexpr>c                 S      | d S Nr]   r.   r   r.   r.   r/   rH         z-TestRvDiscrete.test_expect2.<locals>.<lambda>c                 s   s     | ]\}}|d  | V  qdS )r]   Nr.   r  r.   r.   r/   r        )r3   r>   r   r   r   rL  r   )rh   r8  pyr  r.   r.   r/   test_expect2e  s   
zTestRvDiscrete.test_expect2N)r   r   r   r  r/  rP  rJ  r?  r  r  r  r  r  r  r  r.   r.   r.   r/   r    s    	r  c                   @      e Zd Zdd Zdd ZdS )TestSkewCauchyc                 C   sl   t ddd}ttjj|ddtj| ttjj|ddtj| ttjj|ddtj| d S Nr  r~   rY   r   r1  )	r`   r<  r   r3   
skewcauchyr_   r  rf   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   rX   r]   r   r~   )
g& 45?gQʶ?g-4<??gJ?gw@v?gJ%?g>[u?g
a2?g	Rn?gѦ}cي?)
gN@Q?gPPz@	?g?g;
7?glg?g!?%?gQҙ?gC"?go?g@Sg?)
r`   r   r   rH  r   r3   r  r_   rf   r   )rh   r,   rW   r_   rf   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                   @   s<   e Zd Zdd Zejdd Zejdg ddd Z	d	S )
TestJFSkewTc                 C   s   d }}|d }g d}g d}t ||}t |}t|||| t|||| t|||| t| d| d d S )Nr~   r]   )r  rt   r7  rs   )rt   rU   rK  r   r   r7  r  )r3   	jf_skew_tr  r   r_   rf   r   )rh   r,   r-   r  rW   r\  jfr  r.   r.   r/   test_compare_t  s   
zTestJFSkewT.test_compare_tc                 C   s$   t ttjd }t jj|ddS )a  Sample data points computed using the `ST5` distribution from the
        GAMLSS package in R. The pdf has been calculated for (a,b)=(2,3),
        (a,b)=(8,4), and (a,b)=(12,13) for x in `np.linspace(-10, 10, 41)`.

        N.B. the `ST5` distribution in R uses an alternative parameterization
        in terms of nu and tau, where:
            - nu = (a - b) / (a * b * (a + b)) ** 0.5
            - tau = 2 / (a + b)
        z"data/jf_skew_t_gamlss_pdf_data.npyz	x,pdf,a,bnames)r`   loadr   __file__parentrec
fromarraysrt  r.   r.   r/   gamlss_pdf_data  s   zTestJFSkewT.gamlss_pdf_dataza,b)r  )r   r   )r9     c                 C   sN   ||d |k|d |k@  }|d |d }}t |t|||dd dS )zCompare the pdf with a table of reference values. The table of
        reference values was produced using R, where the Jones and Faddy skew
        t distribution is available in the GAMLSS package as `ST5`.
        r,   r-   rW   r_   r  rx   N)r   r3   r  r_   )rh   r  r,   r-   r   rW   r_   r.   r.   r/   test_compare_with_gamlss_r  s
    z&TestJFSkewT.test_compare_with_gamlss_rN)
r   r   r   r  r   r  r  r   r   r  r.   r.   r.   r/   r    s    
r  r]   r~   g@r   gףp=
1@r#  gRZ@i   gS㥛Ԋ@rU   rV   g&@iQ i'  i0ybi l   HO1Z i3r  irX   irY   ikr  i1r   i  i4i N  i(  lEI. @ i c                   @   sj   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	e
jdedd Zdd Zdd ZdS )TestSkewNormc                 C   s   t d| _d S r  )r   r   rl   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  )r`   r<  r   r3   skewnormr_   rH  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  )r3   r  r   r   r   r'  )rh   r'  rW   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   r#  r~   r]   )r,   r   r[   r\   r   r  )r,   r[   r\   r  r:  rv  )r3   r  r   rD  r   r`   r   rB  rC  kurtosisr   )rh   XrQ   rE  r.   r.   r/   r  "  s   $$zTestSkewNorm.test_momentsc                 C   s^   g dg dg dg dg dg dg dg}|D ]\}}}t j||}t||dd	 qd S )
N)r  r   gEAV)r  r   gV|@$a)r  r   g0rY)r  ro   Zk)r  r   r  )r   r"  ļ)r]   g    cr  rh  rx   )r3   r  r   r   )rh   
logpdfvalsrW   r,   	logpdfvalr  r.   r.   r/   test_pdf_large_x/  s   	zTestSkewNorm.test_pdf_large_xc                 C   sF   t jg dd}t|tddd t jdd}t|ddd d S )	N)rX   r  r  r   r   r3  rx   r  r  r7  )r3   r  rf   r   r`   onesrk  r.   r.   r/   test_cdf_large_x?  s   zTestSkewNorm.test_cdf_large_xc                 C   sr   g dg dg dg dg dg}|D ]#\}}}t j||}t||dd t j| | }t||dd qd S )N)r  r   gzbLe9)rv  r]   gn'/2;)r   r~   g::)r  r   g|<)r  rv  rp  rh  rx   )r3   r  rf   r   r   )rh   cdfvalsrW   r,   cdfvalrT  r.   r.   r/   test_cdf_sf_small_valuesH  s   z%TestSkewNorm.test_cdf_sf_small_valuesz
a, momentsc                 C   s6   t |ddD ]\}}tj||}t||dd qd S )Nr   )startr3  rx   )r*  r3   r  r  r   )rh   r,   r  orderrQ   rj  r.   r.   r/   test_noncentral_momentsY  s   z$TestSkewNorm.test_noncentral_momentsc           %      C   s"  t jd}d\}}}t|||}|jd|d}tjj|ddd\}}}	tjj|ddd\}
}}||  kr<dks?J  J ||
ksEJ tjj|ddd	d
\}}}|dksXJ t|||}|jdd}t |t|f}t	|| tj
jdd|d}tj|}t t |sJ tjj|d	d\}}}t |sJ t |t |}}t	|||t dt j    t	||d ddt j    tjj|dd\}}}tjj| dd\}}}t	|||g| | |g tjj|d	d\}} }!tjj| d	d\}"}#}$t	|"|#|$g| |  |!g d S )Nl   #ke )r   r  ro   rY   r   r  r   r   gmmr   methodmsr  r   r   r]   mle)r`   r   r   r3   r  r   r   r   rC  r   r  r   rG  isinfrB  r  ra   )%rh   r   r,   r[   r\   r;   r   a2loc2scale2a3loc3scale3a4loc4scale4dist4r   ra  r   a5loc5scale5r  r  a6ploc6pscale6pa6mloc6mscale6ma7ploc7pscale7pa7mloc7mscale7mr.   r.   r/   rr  _  s8   

zTestSkewNorm.test_fitc           	         s   t g dddg  dg }tj|}tj||}tjj|dd}tj||}||d k s3J t jd d	d
dd} fdd}tjtj|||d}t jj	||j
dd d S )N)r  r   rw  r9  r   r~   T)superfitro   l   y
ND )r  r~   )r  rX   )r_  rX   r,   r[   r\   c                    s   t | | dS )N)r   )r#   )funr   r   r.   r/   	optimizer  r  z0TestSkewNorm.test_fit_gh19332.<locals>.optimizer)rB  r  rx   )r`   r   r3   r  r   r   r   r   testingr   params)	rh   rW   rD  r   params_superra  r   rB  
fit_resultr.   rA  r/   test_fit_gh19332  s   zTestSkewNorm.test_fit_gh19332N)r   r   r   r  r  r/  r  r  r  r  r   r   r   _skewnorm_noncentral_momentsr  rr  rG  r.   r.   r.   r/   r    s    	
0r  c                   @   r  )
	TestExponc                 C   s   t tjdd d S ri  )r   r3   r  r_   rl   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 )Nrt  r  )r   r3   r  rf   r  r   rl   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@)r`   r   r   r  r   r3   r  r   r  r.   r.   r/   test_nan_raises_error     zTestExpon.test_nan_raises_errorc                 C   rL  rM  )r`   r   r   r  r   r3   r  r   r  r.   r.   r/   test_inf_raises_error  rT  zTestExpon.test_inf_raises_errorN)r   r   r   rJ  rK  rS  rU  r.   r.   r.   r/   rI    s
    rI  c                   @   r  )TestNormc                 C   rL  rM  )r`   r   r   r  r   r3   rH  r   r  r.   r.   r/   rS    rT  zTestNorm.test_nan_raises_errorc                 C   rL  rM  )r`   r   r   r  r   r3   rH  r   r  r.   r.   r/   rU    rT  zTestNorm.test_inf_raises_errorc                 C   s    g d}t ttjj|dd d S )Nr   shrimp)plate)r  r   r3   rH  r   r  r.   r.   r/   test_bad_keyword_arg  s   zTestNorm.test_bad_keyword_argr[   r   r   c                 C   s^   d}t jjd| d| |d}t||dd t jjd|  d|  | d}t||dd d S )Ngg	{F.:r  r9  r[   r   rx   )r3   rH  
_delta_cdfr   )rh   r[   rQ   r  r.   r.   r/   test_delta_cdf  s
    zTestNorm.test_delta_cdfN)
r   r   r   rS  rU  rY  r   r   r   r\  r.   r.   r.   r/   rV    s    rV  c                   @   s    e Zd ZdZdd Zdd ZdS )TestUniformgh-10300c                 C   rL  rM  )r`   r   r   r  r   r3   r  r   r  r.   r.   r/   rS    rT  z!TestUniform.test_nan_raises_errorc                 C   rL  rM  )r`   r   r   r  r   r3   r  r   r  r.   r.   r/   rU    rT  z!TestUniform.test_inf_raises_errorN)r   r   r   __doc__rS  rU  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 )Nr7  r   r]   r   r        @r   r.   )lamsigr  opK2exp_skewexp_kurtr.   r.   r/   get_moms  s   $z,TestExponNorm.test_moments.<locals>.get_moms)r   r   r   r7  r  r  )r  r]   rU   )r   r   r   )r  r  r  )r3   	exponnormr   )rh   rg  r  rc  rb  Kstsr.   r.   r/   r    s"   



zTestExponNorm.test_momentsc                 C   2   t dddddt jg}tttjj|ddd d S 	NrN  rO  rP  rQ  rR  r   r   r}  )r`   r   r   r  r   r3   rh  r   r  r.   r.   r/   rS       z#TestExponNorm.test_nan_raises_errorc                 C   rk  rl  )r`   r   r   r  r   r3   rh  r   r  r.   r.   r/   rU    rm  z#TestExponNorm.test_inf_raises_errorc                 C   sT   t tjddd t tjddd t tjddd t tjddd d S )Ni|r   rt     rq   )r   r3   rh  r_   rl   r.   r.   r/   test_extremes_x  s   zTestExponNorm.test_extremes_xzx, K, expected))r  rq   g6
N-)r   rq   g՜n+H?)r   rq   gi?)ru  rq   gbJI-)rX   r   gI8?)rX   r  gQ3|-0?c                 C   ri  r  )r   r3   rh  r_   )rh   rW   ri  rQ   r.   r.   r/   test_std_pdf  r  zTestExponNorm.test_std_pdfzx, K, scale, expected)r   rq   r   gVAҤ?)r  {Gzt?r   g'^>)rx  rq   rY   rt   )rx  rq   r   gbr ;)r~   r  r   gVMe?c                 C   <   t jj|||d}|dkr|dksJ d S t||dd d S )NrG  rt   r   rx   )r3   rh  rf   r   rh   rW   ri  r\   rQ   rT  r.   r.   r/   test_cdf_small_K5  s   zTestExponNorm.test_cdf_small_K)rX   rq   r   ghG}$;)r]   rq  r   g]fJ?)r~   rq  ro   g31"g#;)rX   rq  ro   gf
+-)r  rq  ro   rt   )r  r  r   ga9S?c                 C   rr  )NrG  rt   -a=rx   )r3   rh  r   r   rs  r.   r.   r/   test_sf_small_KN  s   zTestExponNorm.test_sf_small_KN)r   r   r   r  rS  rU  ro  r   r   r   rp  rt  rv  r.   r.   r.   r/   r`    s8    

r`  c                   @   sP   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	dS )TestGenExponc                 C   s@   ddl m} tjtdddddd}t||dddd d S )	Nr   )simpsonrX   rq   ro   rs   )dxr   )scipy.integraterx  r3   genexponr_   r&  r   r   )rh   rx  rT  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   rX   rq   ro   rs   r   )r3   r{  rf   r&  r   r   r   )rh   rf   r.   r.   r/   test_cdf_boundsd  s   zTestGenExpon.test_cdf_boundszx, p, a, b, c))r#  gM <r   r]   r  )rK  g%DYY?ro   r]   r   )rK  gS4z?      #@r]   ro   )rq   ga^5?r  rK  ro   )r:  gs%)?r  rK  ro   )r  gdm?rK  r~   ro   c                 C   D   t j||||}t||dd t j||||}t||dd d S rV  )r3   r{  r   r   r  )rh   rW   rT  r,   r-   ry  r   r  r.   r.   r/   rZ  t  s   zTestGenExpon.test_sf_isf))rK  g;\i?ro   r]   r   )rK  gu0?r~  r]   ro   )rq   g-%I?r  rK  ro   )r:  g]d?r  rK  ro   )r  g泩'?rK  r~   ro   c                 C   r  rV  )r3   r{  rf   r   r   )rh   rW   rT  r,   r-   ry  rf   r   r.   r.   r/   r{    s   zTestGenExpon.test_cdf_ppfN)
r   r   r   r|  r}  r   r   r   rZ  r{  r.   r.   r.   r/   rw  ]  s    
rw  c                   @   rg  )TestTruncexponc                 C   sL   ddg}ddg}ddg}t tj|||dd t tj|||d	d d S )
Nr  rY   g_93@gBX@g,M<gǃ@֫5gLa㧝=rx   r  )r   r3   
truncexponr   r  )rh   r-   rW   ra  r.   r.   r/   rZ    s
   zTestTruncexpon.test_sf_isfN)r   r   r   rZ  r.   r.   r.   r/   r    rm  r  c                   @   rg  )TestExponpowc                 C   s6   t tjddd t tjtjdddd d S )Nr  rs   r2  r~   r   )r   r3   exponpowrf   r  r   rl   r.   r.   r/   rK    s   zTestExponpow.test_tailN)r   r   r   rK  r.   r.   r.   r/   r        r  c                   @   rn  )TestSkellamc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )Nr  r#  rZ  )gYjP'?g$S?gQ`s2?gC/qF?gD<]Y?g/Xj?g86y?g]a¨?g:?g?gQ>?g?g:?g]a¨?g96?g0X?gA<]?gB/q?gQ`s?g$S?gYjP'?gX_?g+rx?gfSr?gJXx~?r:  )r&  r   r   r   r3   skellamr4  )rh   rT   mu1mu2skpmfRr.   r.   r/   rJ       zTestSkellam.test_pmfc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )Nr  r#  rZ  )gƃQ?gS`X'?gVy)>?g:	 S?gei.f?gȼJ]x?g)?g{^'+i?gLIg>?gnZ?g?rvͪ?gA?g0?g#J?gqSm
.?g~B?gd?gFBD?gQ9?gmF^?gcMy?gGJq?gC^c?g.){?gñݸ?r~   r:  )r&  r   r   r   r3   r  rf   )rh   rT   r  r  skcdfRr.   r.   r/   r?    r  zTestSkellam.test_cdfc                 C   sB   d\}}}t tj|||ddd t tj|||ddd d S )N)r   r   gs1Cr   r_  r   r   )r   r3   r  r4  rf   )rh   rW   r  r  r.   r.   r/   test_extreme_mu2  s   
zTestSkellam.test_extreme_mu2N)r   r   r   rJ  r?  r  r.   r.   r.   r/   r    s    r  c                   @   s   e Zd Zdd Zdd Zejdddd Zej	d	d
dgej	dg dej	dg dej	ddd e
dddD ejdddd Zdd ZdS )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 )NrQ  r   ro   r   r   )rt   g~r?g e3E?)rU  rV  rW  rX  r3   r  r_   r   rh   r_   r.   r.   r/   r6    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?rF   )r   r3   r  r   rH  r`   rr  r,  )rh   rl  r  sigmar.   r.   r/   r    s   
zTestLognorm.test_logcdfr  r  c                 C   r  r  r  rl   r.   r.   r/   r     r  zTestLognorm.rngr   rU   r]   r   )r   r   r]   rx  )r  r   r~   r  c                 C   r  r  r.   )r:   er.   r.   r/   r<     r  zTestLognorm.<listcomp>)FTr   r  r  r  c           
      C   s^   t jjd||||d}i }	|r||	d< |r||	d< |r||	d< tt j|fi |	ddi d S )NrY   )r   rG   r\   r[   r   r   r   r   r   T)r3   r  r   r   r  r.   r.   r/   r     s   	z'TestLognorm.test_fit_MLE_comp_optimizerc                 C   rh  )NgI+?)rU   g|=gҶOɃ;gk3;9"7)g?y+@g~K8ax@gƶ@g9]Ar3  rx   )r   r3   r  r  )rh   rG   r\  ra  r.   r.   r/   r    s   zTestLognorm.test_isfN)r   r   r   r6  r  r   r  r   r   r   r$   r`   r  r   r  r.   r.   r.   r/   r    s    


r  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zejj	e
d	d
dd Zejj	e
d	d
dd Zejj	e
d	d
dd Zdd Zejjdd
dd Zejdejjejjgejdddgdd Zejdg ddd Zejd g d!d"d# Zd$S )%TestBetac                 C   s:   t jddd}t|d t jddd}t|tj d S )Nr   r   ro   g;B.)r3   r  r   r   r`   r   rh   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  ro   r  gƒ)	r`   r   r3   r  r   r   rL  r_   r   rh   r  r  rW   r-   r.   r.   r/   test_logpdf_ticket_1866  s
    z TestBeta.test_logpdf_ticket_1866c                 C   s$   g d}t ttjj|dddd d S )NrU   ro   r  r   r   rW  )r   r   rX  )r  r   r3   r  r   r  r.   r.   r/   test_fit_bad_keyword_args  s   
z"TestBeta.test_fit_bad_keyword_argsc                 C   s"   g d}t ttjj|ddd d S )Nr  ro   )fafix_a)r  r   r3   r  r   r  r.   r.   r/   #test_fit_duplicated_fixed_parameter"  s   z,TestBeta.test_fit_duplicated_fixed_parameterzOverflow, see gh-14901reasonc                 C   s$   d\}}}t tj|||d d S )N)g?g     R@g   0xAgx)>)r   r3   r  r   )rh   rT  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?)rX   rY   r   r  r   r   )r`   r   r3   r  r  r   r   )rh   inv_R
count_listrT  invr   r.   r.   r/   test_issue_127944  s   
zTestBeta.test_issue_12794c           	      C   sb   d}t dd}d}d| |d || }}}tj|||}tj|||}t|d|  d S )Nh㈵>r   r  r   )r`   r   r3   r  r   rf   r   )	rh   alpha_2count_nobsr\  r,   r-   r  r   r.   r.   r/   test_issue_12796F  s   zTestBeta.test_issue_12796c                 C   s   d\}}t tjd||tj d\}}t tjd||tj d\}}t tjd||d t tjd||d d\}}t tjd||d t tjd	||d d S )
Nr  r   )r  r   r   )r   r~   r~   +ph  )r~   r   r7  )r   r3   r  r_   r`   r   )rh   r,   r-   r.   r.   r/   rl  R  s   zTestBeta.test_endpointsz!Does not warn on special codepathc                 C   sJ   d\}}}t t tj||| W d    d S 1 sw   Y  d S )N)gףp=
?g   vH7B  @0B)r   warnsrX  r3   r  r   )rh   r\  r,   r-   r.   r.   r/   test_boost_eval_issue_14606i  s   
"z$TestBeta.test_boost_eval_issue_14606r   a, b)r        )@)r  r  c                 C   s,   d}z	|||| W d S  t y   Y d S w )Nr   )OverflowError)rh   r   r,   r-   rT  r.   r.   r/    test_beta_ppf_with_subnormal_a_bo  s   z)TestBeta.test_beta_ppf_with_subnormal_a_br  ))ro   ro   gο)r  r   g )r   r  g&׾k )r   r   g*)Mc                 C   s   t t|| | d S rj   r   r3   r  rA   r  r.   r.   r/   rP    rU  zTestBeta.test_entropyza, b, ref, tol))r   rX   gCpr3  )rX   r  g8EOr   )g    NAg    NAg(4Fr  )g    SAg   SAg8TAUrh  )r  g   _Bg[VVuD&r  )r  r  gR#Lrw   )r]   r  g?r5r  )r]   r  <Fr3  )r]   r  guRTc\r3  )r~   r  gL4r  )r~   r  6Er3  )r~   r  g.fq>\r3  )rX   r  gnQc}4r  )rX   r  g{C Er3  )rX   r  %\r3  )r  r]   r  r3  )r  r~   r  r3  )r  rX   r  r3  c                 C   s   t t|| ||d d S r  r  )rh   r,   r-   ra  rV  r.   r.   r/   r    s   $zTestBeta.test_extreme_entropyN)r   r   r   r  r  r  r  r   r   skipifMACOS_INTELr  r  r  rl  xfailr  r   r3   r  r   r  r  rP  r  r.   r.   r.   r/   r    s4    



 
r  c                   @   s   e Zd Zg dZdd Zdd Zejdg ddd	 Z	ejd
edd Z
ejdeg d dd Zejdddgdd Zdd Zdd Zdd ZdS )TestBetaPrime))rz        Y@r  D>?)r  r  r  m嗽?)r   r  rU   gPK?)r   r  r  g%p?)r  r  rU   g#|/?)r  r  r  gsM
<)r  r  r  $5Є*?)^ 9^;r  rU   gompP?)r  r  r  g7j"!9)r  r  r  z^J?)r^  r  rU   gܷ"+>)r^  r  r  grNs: )r^  r  r  gK>c                 C   sZ   d\}}t g d}t||}tt ||  t|	|t 
|| d S )Nr  r  )r`   r   r3   r  r   rG  r   r   r   r_   r   r  r.   r.   r/   r    s
    zTestBetaPrime.test_logpdfc                    s   t jddd}t|d d\ tg d}t j| }tt|  t j	j
 fdd|D }t||dd	d
 d S )Nr   r  r[  rt   r  r  c                    s   g | ]
}t j| qS r.   )r3   r  )r:   r.  r  r  gen_cdfr.   r/   r<         z*TestBetaPrime.test_cdf.<locals>.<listcomp>-=r  )r3   r  rf   r   r`   r   r   rG  r   r?   _cdf_singler   )rh   rW   r  cdfs_gr.   r  r/   r?    s   
zTestBetaPrime.test_cdfzp, a, b, expected))rq         ?r  gV)?)r  r  r  gWJB9*=)rt  r  r  gOG J<)r  rK        @gΣ01)      ?rK  r  g8ǘ`?)>q?r  rU   gMDc                 C   "   t j|||}t||dd d S rc  )r3   r  r   r   )rh   rT  r,   r-   rQ   rW   r.   r.   r/   r    s   
zTestBetaPrime.test_ppfz
x, a, b, pc                 C   s   t tj||||dd d S rc  )r   r3   r  r   )rh   rW   r,   r-   rT  r.   r.   r/   test_ppf_gh_17631  r  zTestBetaPrime.test_ppf_gh_17631zx, a, b, expected))r  r  r  r  )r  r  rU   gV[?)rz  r  rU   r  c                 C   r{  rc  )r   r3   r  rf   )rh   rW   r,   r-   rQ   r.   r.   r/   test_cdf_gh_17631  s   zTestBetaPrime.test_cdf_gh_17631)r  r  rU   g%?)r  r  r  goXr?c                 C   s.   t j|||}|dk sJ t||dd d S )Nr7  gh㈵>rx   )r3   r  rf   r   )rh   rW   r,   r-   rQ   r8  r.   r.   r/   test_cdf_extreme_tails  s   z$TestBetaPrime.test_cdf_extreme_tailsc                 C   sB   g d}g d}g d}g d}t j|||}t||dd d S )N)r~   r   r]   r  r  r  r  r  r  r  r  r  r  r  )r   r]   r   rU   rU   rU   rU   r  r  r  r  r  r  r  )r  r  ꌠ9Y>)Frz  r  r  r^  rz  r  r  r  r^  r  r  )g/:g  U/7gKH9g<![a?gw 4?g)J?g5?r  r  r  r  g%?gsM
<r  r  rx   )r3   r  r   r   )rh   r,   r-   rW   ra  	sf_valuesr.   r.   r/   r  )  s   zTestBetaPrime.test_sfc                 C   s.   t jjg dddd t jddd d d S )N)rU   rK  r[  r  皙?r   r   r}  r  r  )r3   r  r   rl   r.   r.   r/   test_fit_stats_gh18274>  s   z$TestBetaPrime.test_fit_stats_gh18274c                 C   s.   t jdg}tdddgd}t|| d S )NgooB?r]   r  gffffff@r~   )r`   r   r3   r  r  r   )rh   ra  r   r.   r.   r/   test_moment_gh18634E  s   
z!TestBetaPrime.test_moment_gh18634N)r   r   r   cdf_valsr  r?  r   r   r   r  r  r  r  r  r  r  r.   r.   r.   r/   r    s4    
	



r  c                
   @   s   e Z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g ddd Zej	dg dej	dg dej	d	g dej	dddgej	dddgej	dddgdd ZdS )	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  rG  g
CTb?r   rX   gBΖ?)r3   r  r_   r   r  r.   r.   r/   r6  R  s   
zTestGamma.test_pdfc                 C      t jdd}t|d d S ri  )r3   r  r   r   r  r.   r.   r/   r  Z  s   zTestGamma.test_logpdfc                 C   s"   g d}t ttjj|ddd d S )Nr  r   rW  )r   rX  )r  r   r3   r  r   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 )
Nr  r   gplC@r3  r   r  rY   g1}t@r   )r`   iscloser3   r  r  rl   r.   r.   r/   r  d  s   
zTestGamma.test_isfr\   r7  r8  c                 C   s.   t jj|d |d d|d}t|ddd d S )N   r*  r   rG  g>S*r   rx   )r3   r  r[  r   rh   r\   r  r.   r.   r/   r\  z  s   zTestGamma.test_delta_cdfza, ref, rtol))r  gt.rw   )r]   r  rw   )rY   gX>k-־@r   )r  gwM7@rw   )g NgmCg%og$6@rw   )r  oܘ#]@rw   c                 C   s   t tj|||d d S r  )r   r3   r  rA   )rh   r,   ra  ry   r.   r.   r/   rP    rO  zTestGamma.test_entropyr,   )rq   r   r  r[   )rq   r   r  r  TFr   rz  c                 C   s8  t jd}tjj|||d|d}i }	|r||	d< |r||	d< |r%||	d< dt|	 }
|
dkrWd	}tjt	|d
 tjj
|fddi|	 W d    d S 1 sPw   Y  d S tjj
|fddi|	}tj| }|
dkrvt| t | |
dkrt|dt |d  |
dkrt|dt |d  d S d S )Nr   rY   r|  r  r   r   r   r   r   r   r   r  r   r]   )r`   r   r   r3   r  r   r   r   r   r   r   r   r   r  )rh   r,   r[   r\   r  r   rz  r   r   r   rn  r  thetar;   r.   r.   r/   test_fit_mm  s:   

zTestGamma.test_fit_mmN)r   r   r   r6  r  r  r  r   r   r   r\  rP  r  r.   r.   r.   r/   r  Q  s$    


r  c                  C   s:   d} t jd| d  d| d  ddd}t|dd d S )	Nr  g;f?r]   r   r   rZ   r7  gV{q@)r3   r  r   r_   )jitterZr.   r.   r/   test_pdf_overflow_gh19616  s   "r  c                   @   sj   e Z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	dd Z
dS )
TestDgammac                 C   s~   t jd}d}|jd|d}|jd|d}tj||}tjt 	||d }t
|| t|}t
|||dd d S )Nl   OP($ rX   rK  )r  r   r]   r  rx   )r`   r   r   normalr  r3   dgammar_   r  r   r   )rh   r   r   rW   r,   r   ra  r;   r.   r.   r/   r6    s   

zTestDgamma.test_pdfzx, a, expected))ru  r   ggrU>)r  r   g$IC<)ir~   g2Wj<)r  g~)A.=)r~   r   gf?c                 C   sx   t j||}t||dd t j||}t||dd t j| |}t||dd t j||}t|| dd d S r  )r3   r  rf   r   r   r   r  )rh   rW   r,   rQ   rf   r   r   r  r.   r.   r/   test_cdf_ppf_sf_isf_tail  s   z#TestDgamma.test_cdf_ppf_sf_isf_tailr  ))r  gmqn @)?g?)r  gx?c                 C   r  rc  r   r3   r  rA   r  r.   r.   r/   rP       zTestDgamma.test_entropy))r^  r  )r  g>_)rw  g5i)r  go@)rf  g4Fa3@)r  grO]@c                 C   r  r  r  r  r.   r.   r/   test_entropy_entreme_values  s   z&TestDgamma.test_entropy_entreme_valuesc                 C   sL   t g d}tj|}tt|D ]}|| tj|| ks#J qd S )N)r   r~   r  rw  )r`   r   r3   r  rA   r  r   )rh   rW   r8  r  r.   r.   r/   test_entropy_array_input  s
   z#TestDgamma.test_entropy_array_inputN)r   r   r   r6  r   r   r   r  rP  r  r  r.   r.   r.   r/   r    s    



r  c                   @   6   e Zd Zdd Zdd Zejdg ddd Zd	S )
TestChi2c                 C   s4   t tjddddd t tjddddd d S )Nr   gޞw1D?r4  r:  rY   g6:֜?r   r3   chi2r_   rl   r.   r.   r/   r    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  rx   ro   gQ8@r  gܐ؆0guu[9=rU   g8-*@)r3   r  r   r   )rh   r  rW   r.   r.   r/   r  #  s   zTestChi2.test_ppfr  ))r  gܫ>)r   gƯʉ?)rY   gn>@)   g͔v0@)rf  g9:3@c                 C   r  r   )r   r3   r  rA   r  r.   r.   r/   rP  ;  r  zTestChi2.test_entropyN)	r   r   r   r  r  r   r   r   rP  r.   r.   r.   r/   r    s    r  c                   @   r  )TestGumbelLc                 C   r^  Nr  rv  )r`   r<  r3   r  rf   r   r   ra  r.   r.   r/   r{  G  rb  zTestGumbelL.test_cdf_ppfc                 C   sH   t dd}tj|}tj|}t |}t| }t	|| d S r  )
r`   r<  r3   r  r  r,  r   r   expm1r   )rh   rW   r8  r  ur  r.   r.   r/   r.  M  s   
zTestGumbelL.test_logcdf_logsfc                 C   r^  )Nru  r~   )r`   r<  r3   r  r   r  r   ra  r.   r.   r/   rZ  U  rb  zTestGumbelL.test_sf_isfr[   r   r   c                 C   s2   t jjd|d}t jj||d\}}t|| d S )NrY   )r   r[   r   )r3   r  r   r   r   )rh   r[   r   
fitted_locr   r.   r.   r/   test_fit_fixed_param[  s   z TestGumbelL.test_fit_fixed_paramN)
r   r   r   r{  r.  rZ  r   r   r   r  r.   r.   r.   r/   r  E  s    r  c                   @   r  )TestGumbelRc                 C      t tjdddd d S )Nr!  ?~T}%m;r3  rx   )r   r3   r  r   rl   r.   r.   r/   r  f     
zTestGumbelR.test_sfc                 C   r  )Nr  r  r3  rx   )r   r3   r  r  rl   r.   r.   r/   r  o  r  zTestGumbelR.test_isfN)r   r   r   r  r  r.   r.   r.   r/   r  d  s    	r  c                   @   s`  e Zd Zejdddd Zejdd Zejdd Zejd	d
 Zej	
dedejdej	jdgej	
dddgej	
dg dej	
dddgdd Zej	jej	
dddgdd Zdd Zej	jd d!ej	
d"d#d$gej	
d%ddgd&d' Zd(d) Zd*d+ Zd,d- Zej	
d.eg d/g d0g d1ejg d2g d3g d4ej	jdejg d5ed6d7d8ed9dd:ej	jdgd;d< Zej	
d.eg d/g d0g d1ejg d2g d3g d4ej	jdejg d5ed6d7d8ed9dd:ej	jdgd=d> Zej	
d?d@dgej	
dAdBdCgdDdE Zej	
dFdGdHgdIdHggdJdK Zej	
dLdMd@ejejejfgdNdOggdPdQ Zej	
dRg dSej	
dTej j!dUedVd@dWdXfej j"dUedVd@dWdXfej j!dYed@dZdWdUfej j"dYed@dZdWdXfgd[d\ Z#ej	
d]g d^d_d` Z$ej	jej	
d]g dadbdc Z%ddS )eTestLevyStableT)autousec                 C   s(   dt j_dt j_dt j_t jjt j_dS )z2Setup default parameters for levy_stable generatorS1	piecewiseN)r3   levy_stableparameterizationcdf_default_methodpdf_default_method_levy_stable	_QUAD_EPSquad_epsrl   r.   r.   r/   reset_levy_stable_paramsz  s   z'TestLevyStable.reset_levy_stable_paramsc                 C   *   t ttjd }t jj|jdd}|S )a  Sample data points for pdf computed with Nolan's stablec

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

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

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

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

        Typically inputs for stablec:

            stablec.exe <<
            1 # pdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-pdf-sample-data.npyx,p,alpha,beta,pctr  r`   r  r   r  r  r  r  Trt  r.   r.   r/   nolan_pdf_sample_data  s   z$TestLevyStable.nolan_pdf_sample_datac                 C   r  )a#  Sample data points for cdf computed with Nolan's stablec

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

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

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

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

        and the equivalent for the right tail

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

        Typically inputs for stablec:

            stablec.exe <<
            2 # cdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-cdf-sample-data.npyr  r  r  rt  r.   r.   r/   nolan_cdf_sample_data  s   %z$TestLevyStable.nolan_cdf_sample_datac                 C   s   t ttjd }|S )a&  Sample data where loc, scale are different from 0, 1

        Data extracted in similar way to pdf/cdf above using
        Nolan's stablec but set to an arbitrary location scale of
        (2, 3) for various important parameters alpha, beta and for
        parameterisations S0 and S1.
        z1data/levy_stable/stable-loc-scale-sample-data.npy)r`   r  r   r  r  rt  r.   r.   r/   nolan_loc_scale_sample_data  s   	z*TestLevyStable.nolan_loc_scale_sample_datasample_sizer!  r  marksr  S0r  z
alpha,beta))r7  r   )r7  r   )r  r   )r  ro   zgamma,deltar   r   r  c           
      C   sF   |t j_t j||||d}t |j|dd|j\}}	|	dks!J d S )N)r  r  r\   r[   r   r   r  )r3   r  r  r  r   rf   )
rh   r  r  r  r  r  r  lsr   rT  r.   r.   r/   r/    s   zTestLevyStable.test_rvsr  ro   r   c                 C   sZ   t jd d}d}d}tjj||||dd}tj|d||||fd\}}|d	ks+J d
S )z3Additional test cases for rvs for alpha equal to 1.h:r7  ro   r  rT  r[   r\   r   r  r  rq   N)r`   r   r   r3   r  r   r  )rh   r  r  r[   r\   rW   statrT  r.   r.   r/   test_rvs_alpha1  s   

zTestLevyStable.test_rvs_alpha1c                 C   s   g d}t j|\}}}}t|dddd t|dd t|dd	 t|d
d |g d }t j|\}}}	}
t|d t|d t|
dd	 t|	dd	 d S )N)wgr  rt   rt   rt   rt   羼 u?r  r  r  r  67',?r  r  r  r  tA}˜.?r  r  r  r  Gz?r   rq   rF  )\(̿r]   gۧ1?r   g9]c?)r  r  r  r  r  r   gv?r  )r3   r  rm  r   r   r   rh   rW   alpha1beta1loc1scale1rl  alpha2beta2r&  r'  r.   r.   r/   rr  	  s   

zTestLevyStable.test_fitzUnknown problem with fitstart.r  zalpha,beta,delta,gamma)r  rO  r]   r   )r7  rO  r]   r   parametrizationc                 C   sZ   |t j_t jj||||ddd}t j|}|\}}	}
}t||||g||	|
|gdd dS )z7Test that fit agrees with rvs for each parametrization.r  r   r|  rq   rx   N)r3   r  r$  r   rm  r   )rh   r  r  r  r  r$  r   r   	alpha_obsbeta_obs	delta_obs	gamma_obsr.   r.   r/   test_fit_rvs!  s   


zTestLevyStable.test_fit_rvsc           
      C   s~   t g d}tj|\}}}}tj| \}}}}	t|d |dks'J t|| t||  t||  t|	| d S )Nr   r   r   r   rX   rX   rX   r  r  rY   rY   r   r   )r`   r   r3   r  rm  r   r   )
rh   rW   r  r  r   r!  r"  r#  r&  r'  r.   r.   r/   test_fit_beta_flip:  s   

z!TestLevyStable.test_fit_beta_flipc                 C   sr   d}t g d}tj| \}}}}tj| | \}}}	}
t|| t|| t|	||  t|
| d S )Nr   r*  )r`   r   r3   r  rm  r   )rh   SHIFTrW   r  r  r   r!  r"  r#  r&  r'  r.   r.   r/   test_fit_delta_shiftF  s   

z#TestLevyStable.test_fit_delta_shiftc                 C   s   g d}t j|\}}}}|dk sJ d| |t|k s+J dt| d| g d}t j|\}}}	}
|dksDJ d| |	t|ksVJ dt| d|	 d S )	N)r   r   r   r   rX   rX   rX   r  r     r.  r   zExpected alpha < 1, got zExpected loc < z, got )r   r   r   r   rX   rX   rX   r  r     r/  zExpected alpha > 1, got zExpected loc > )r3   r  rm  r  r#  r  r.   r.   r/   test_fit_loc_extrapQ  s   $(z"TestLevyStable.test_fit_loc_extrapz pct_range,alpha_range,beta_range)rq   ro   r  )rU   r   r]   )r   r   r   )rq   r  ro   r  r  )rU   ro   r   r  r]   )gr   r   r[  r  r   )rq   r  rU   rK  ffffff?ro   ?r   r   r  r  rU   r]   r  r      c                    s  |}t  }|jdko|jdkd|j|j|jg}dd fddgdd	 fd
dgdd	 fddgdd fddgdd fddgdd fddgg}t|D ]\}	\}
}}|
tj_	|durs||| n|}t
 }|td tjj|d |d |d ddd}tjdd( t|g d|t||d  t||d  t|d  g}W d   n1 sw   Y  ||d |kt|B  }d |	 d!|
 d"| d#|jj d$| 
}t||d ||d%d& W d   n1 sw   Y  q^dS )'z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnir\  c              	      s  t | d t | d  @ t | d @ | d dk| d dk@ | d dk| d dk@ | d dk@ B | d dkt | d d	d
g@ B | d dkt | d ddg@ B | d dkt | d ddg@ B | d dkt | d ddg@ t t | d g d@ B | d dkt | d dg@ t t | d dg@ B | d dkt | d ddg@ t t | d g d@ B | d dk| d dk@ | d dk@ B | d dk| d dk@ | d dk@ B | d dk| d dk@ | d dk@ B | d dkt | d dg@ t t | d g d@ B | d dkt | d ddg@ t t | d g d@ B | d dkt | d d	d
g@ t t | d ddg@ B | d dkB  @ S )Npctr  r  r   ro   r   r  rO  rq   r  r[  r  r  r  rU   rK  r   )ro   r  r  r1  r2  )gٿ333333ӿr[  rO  ro   r9  r7  rU   r  r[  rO  )r   r   r7  r  r  )r`   isinr   rc  alpha_range
beta_range	pct_ranger.   r/   rH     s   











 
%


*


/


4
9
>
Cz7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>r  r  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr8  r  r  r  r7  r`   r;  r<  r=  r.   r/   rH        

c                    s:   | d dk @ t | d @ d v @ t | d @ S )Nr  r7  r8  r  rA  r<  r>  r?  is_linux_32r@  r.   r/   rH     s   
g&.=c                    s<   t | d t | d  @ t | d @ | d dk@ S )Nr8  r  r  r  rA  r<  r=  r.   r/   rH        
fft-simpsonrw  c                    s<   | d dkt | d @ t | d  @ t | d @ S )Nr  r  r8  r  rA  r<  r=  r.   r/   rH     s   
r  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk @ S )Nr8  r  r  r   r  rA  r<  r=  r.   r/   rH     rB  Nz2Density calculations experimental for FFT method.*rW   r  r  r   r   r\   r[   r  rv  calcabserrrelerrrT  rK  z	pdf test  failed with method 'z' [platform: z]

Ferr_msgverbose)platformunamesystemmachinejoin	processorr*  r3   r  r  r   recordrX  r_   r`   r  r   r   isnanr   r   r   )rh   r
  r@  r>  r?  r   rR  platform_desctestsixdefault_methodry   filter_funcsubdatasuprT  subdata2failuresmessager.   rC  r/   test_pdf_nolan_samples]  s   
O
	 

z%TestLevyStable.test_pdf_nolan_samplesc                    s  |}dd fddgdd fddgdd fd	dgdd
 fddgdd fddgdd fddgg}t |D ]\}\}}	}
|tj_|
durY||
| n|}t }}|td tjj|d |d |d ddd}tj	dd( t
|g d|t||d  t||d  t|d  g}W d   n1 sw   Y  ||d |	kt|B  }d| d| d|jj d | }t||d |	|d!d" W d   n1 sw   Y  qDdS )#z4 Test cdf values against Nolan's stablec.exe output.r  r  c                    s   t | d t | d  @ t | d @ | d dkt | d g d@ | d dk@ | d dkt | d g d@ | d dk@ B  @ S 	Nr8  r  r  r7  )r9  r  r  rq   rU   r  r[  r  rA  r<  r=  r.   r/   rH   Q  s$   



z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>r  c                    s   t | d t | d  @ t | d @ | d dkt | d g d@ | d dk@ @ | d dkt | d g d@ | d dk@ B S rd  rA  r<  r=  r.   r/   rH   f  s"   


	
rF  rw  c                    s<   t | d t | d  @ t | d @ | d dk@ S )Nr8  r  r  333333?rA  r<  r=  r.   r/   rH   x  rE  r  c                    H   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr8  r  r  r  rf  rA  r<  r=  r.   r/   rH     rB  r  c                    rg  )Nr8  r  r  r  r  rA  r<  r=  r.   r/   rH     rB  rq   c                    rg  )Nr8  r  r  r7  r  rA  r<  r=  r.   r/   rH     rB  Nz[Cumulative density calculations experimental for FFT method. Use piecewise method instead.*rW   r  r  r   r   rG  r  rv  rH  rT  rK  z	cdf test rL  z'
rM  FrN  )r*  r3   r  r   r   rW  rX  rf   r`   r  r   r   rX  r   r   r   )rh   r  r@  r>  r?  r   rZ  r[  r\  ry   r]  r^  r_  rT  r`  ra  rb  r.   r=  r/   test_cdf_nolan_samples4  s   	

N

z%TestLevyStable.test_cdf_nolan_samplesr  r   r  r_   rf   c           
      C   s   t  }|jdkodt  d v }|r|dkrtd |}dtj_dtj_	||d |k }d| tj_
|d	v s;J |dkrCtjjntjj}||d
 |d |d ddd}	t|	|| d dS )zGTests for pdf and cdf where loc, scale are different from 0, 1
        r4  32bitr   r_   z4Test unstable on some platforms; see gh-17839, 17859r  r  S)r_   rf   rW   r  r  r]   r   rG  rw  N)rQ  rR  rS  architecturer   r   r3   r  r   r  r  r_   rf   r   )
rh   r  r  r  rR  rD  r   r^  r  r  r.   r.   r/   test_location_scale  s    
z"TestLevyStable.test_location_scalezmethod,decimal_placesr7  r   r  c              	   C   s   t g d}t g d}t g d}t jddA t %}|jtdd |tj_tjj	|d|dd	d
}t
|||| W d   n1 sGw   Y  W d   dS W d   dS 1 s_w   Y  dS )z sample points extracted from Tables and Graphs of Stable
        Probability Density Functions - Donald R Holt - 1973 - p 187.
        )r   r   r   r   r   r   r   r   r]   r]   r]   r]   r   r   r   r   r   r   r   r   )gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g?gDioɴ?g r?gH?g+?gHPs?gX ?g&?g0*?gv/?ga2U0*?)r   rK  ro   r   r   rK  ro   r   r   rK  ro   r   r   rK  ro   r   r   rK  ro   r   r  r   zDensity calculation unstable.*)categoryrb  r   r   rG  N)r`   r   r  r   rL   rX  r3   r  r  r_   r   )rh   r   decimal_placesxsdensitybetasr_  r_   r.   r.   r/   'test_pdf_alpha_equals_one_beta_non_zero  s(   Pz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerozparams,expected)r  r  r   r   )r]   r   rX   r  )rX   r  r   r   c                 C   s4   t jj |d |d |d |d dd}t|| d S )Nr   r   r]   r   r  r  )r3   r  r   )rh   rD  rQ   observedr.   r.   r/   r    s
   zTestLevyStable.test_statsr  )rK  ro   r   zfunction,beta,points,expectedr7  r  rX   rt   r  r  c                 C   s@   d|  k rdk sJ  J t ||||dtt|| dS )a\  Ensure the pdf/cdf routines do not return nan outside support.

        This distribution's support becomes truncated in a few special cases:
            support is [mu, infty) if alpha < 1 and beta = 1
            support is (-infty, mu] if alpha < 1 and beta = -1
        Otherwise, the support is all reals. Here, mu is zero by default.
        r   r   r  r  N)r   r`   r+  r   )rh   r  r  r  r@  rQ   r.   r.   r/   !test_distribution_outside_support  s
   (z0TestLevyStable.test_distribution_outside_supportzx,alpha,beta,expected))r   /iZ?s0?gz5F?)r   ~H?|/mg>m?)r   .d5?L,ٿg깃\?)r   >?ЀjoؿgA]4?)r   pa2?Յ пgqQ?c                 C   $   dt j_tt jj|||d| dS )a  Test pdf for x equal to zeta.

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

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

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

        Reference values taken from MATLAB
        https://www.mathworks.com/help/stats/stable-distribution.html
        Afc=ru  Nr3   r  r  r   r_   rh   rW   r  r  rQ   r.   r.   r/   test_x_equal_zetaJ  s
   -z TestLevyStable.test_x_equal_zeta)
)r  rw  rx  gz¶?)r  ry  rz  gV?)r  r{  r|  gRE)3\?)r  r}  r~  gB?)r  r  r  g/^?)-C6rw  rx  gH?)r  ry  rz  gn?)r  r{  r|  gx\?)r  r}  r~  gVM%?)r  r  r  gm?c                 C   r  )a  Test pdf for x near zeta.

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

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

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

        Reference values taken from MATLAB
        https://www.mathworks.com/help/stats/stable-distribution.html
        r  ru  Nr  r  r.   r.   r/   test_x_near_zeta~  s
   "zTestLevyStable.test_x_near_zetaN)&r   r   r   r   r  r  r
  r  r  r   r   r  r  r/  r  rr  r  r)  r+  r-  r0  r`   r<  r   rc  rh  rl  rs  r   r   r  r3   r  rf   r_   rv  r  r  r.   r.   r.   r/   r  y  s   


!
+

 C
| 
 

r  c                   @   r  )TestArrayArgumentc                 C   r  r  r  rl   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~   rZ  r  )r3   rH  r   r`   r   r  r   r'  rh   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  rp  )r3   r  r_  r   lowerrp  rl   r.   r.   r/   test_docstrings  s
   zTestDocstring.test_docstringsc                 C   s   t   t   d S rj   )r3   r?   r>   rl   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  c                  C   s   t g d} t| dk| d\}}t|g d t|dg tddk| d\}}t||  t|dgt|   t| dk| d\}}t||  t|dgt|   d S )N)r   r   r]   r   r]   r   r   r   r]   )r   r]   r]   r   r   r   )r   r   r   r`   r   r,   r-   ry  r.   r.   r/   test_args_reduce  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j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  rl   r.   r.   r/   r    r  zTestFitMethod.setup_method)r  rH  r  z	dist,argsc                 C   sz   || j v rtd|  tdddddtjg}tdddddtjg}tt|}t	t
|j|dd t	t
|j|dd d	S )
r^  z"%s fit known to fail or deprecatedrN  rO  rP  rQ  rR  r   rs  N)fitSkipNonFiniter   r   r`   r   r   r   r  r3   r  r   r   )rh   r;   r  rW   r8  distfuncr.   r.   r/   !test_fit_w_non_finite_data_values  s   

z/TestFitMethod.test_fit_w_non_finite_data_valuesc              	   C   s   t jd t jdd8 tjjddddd}t t |t d d	 	 }t
t tjj|d
dd|d
dgdd W d    d S 1 sGw   Y  d S )Ni90  r  rm  rK  rt         4@r  r  r]   r   r}  rh  r   )r`   r   r   r  r3   r  r   r  rr  r   r   r   r   )rh   rW   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   r9  r   r]   r   rs  )r`   r   r3   rH  r   r   r  r   rh   rW   r[   r\   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   r9  r   r   r~   r:  r   r   r   r]   r}  )r`   r   rr  r   r3   r  r   r   r   digammar   )rh   rW   meanlogr   r,   r[   r\   rG   r   r   ry  r.   r.   r/   test_fix_fit_gamma  s6   






z TestFitMethod.test_fix_fit_gammac              	   C   s  dd }t g d}tjj|ddd\}}}}t|d t|d t||||ddgdd t g d}tjj|d	ddd
\}}}}t|d	 t|d t|d ||||\}}t|ddd d| }	tjj|	d	ddd\}
}}}t|d	 t|d t|d ||
||	\}}t|ddd t|
| tt	tjj|ddd t g d}tt	tjj|ddd tt	tjj|ddd	d tt	tjj|ddd	d tt	tjj|ddd	dd d S )Nc                 S   sj   t |}t| }td|  }t| | }||| t|    ||| t|   g}|S r   )r   r`   rr  rL  r   psi)r,   r-   rW   rS  s1r  psiabr   r.   r.   r/   mlefunc%  s   z0TestFitMethod.test_fix_fit_beta.<locals>.mlefunc)r  rK  ro   r   r   r}  r  r   r]   )r   r   r   rw  )r   r   r   ro   r  )r   r   r   )r   r   r   r   )r   r   r   r   )
r`   r   r3   r  r   r   r   r   r  r   )rh   r  rW   r,   r-   r[   r\   dadbrl  r%  b2r&  r'  r8  r.   r.   r/   test_fix_fit_beta"  s:   









zTestFitMethod.test_fix_fit_betac                 C   s   t g d}tj|\}}t|d t|d tjj|dd\}}t|d t|d tjj|dd\}}t|d t|d d S )N)r]   r]   r   r   r   r   r   r   r]   r   rs  r   r   r   )r`   r   r3   r  r   r   r  r.   r.   r/   test_expon_fitY  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   rX   r#     r  r   r   r  rx   r9  r}  r]   r   )r   fix_s)r`   r   rr  r3   r  r   r   rY  r   r   r   r  )rh   rW   lnxm1r'  r[   r\   r.   r.   r/   test_lognorm_fith  s    




zTestFitMethod.test_lognorm_fitc                 C   s   t g d}tj|\}}t||  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)r7  r  r        "@r   r   rX   rs  rs   r8  )r`   r   r3   r  r   r   r  rs  r#  r  r   r  r.   r.   r/   test_uniform_fit|  s   


zTestFitMethod.test_uniform_fitr   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=  rY   r   r   r  )r   r   )r  r   r  r  )r  r   r=  )r   r   )r  r   )r  r   r   r]   )r  r   r   r   r   )r  r   r   r   r   )r  r   r   r   )r  r   r   r  )	r3   r  r   r   r   r  r   r   r  )rh   r   r,   r-   rW   res_1res_2res_3res_4res_5aabbr[  ssr   r.   r.   r/   test_fshapes  s.   zTestFitMethod.test_fshapesc                 C   s@   t j}|jddd}tdd}tt|j|fi |d|i d S )Nr]   rY   )ri  r   i)enikibenikir   )r3   rh  r   r   r  r   r   )rh   r   r;   r   r  r.   r.   r/   test_extra_params  s   
"zTestFitMethod.test_extra_paramsN)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    s$    

	&7&r  c                   @   r@  )
TestFrozenc                 C   r  r  r  rl   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  rZ   r  rK  r]   )r3   rH  r_   r   rf   r   r  r   rH  r   rB  rY  rA   r  r,   r-   )rh   r;   frozenresult_fr(  r.   r.   r/   rI    sJ   
















zTestFrozen.test_normc                 C   s  d}t j}t |}|d}|d|}t|| |d}|d|}t|| |d}|d|}t|| |d}|d|}t|| |d}|d|}t|| | }||}t|| |	 }|	|}t|| |
 }|
|}t|| | }||}t|| | }||}t|| |d}|d|}t|| t|j|jj t|j|jj d S )Nrs   r  rK  r/  r]   )r3   r  r_   r   rf   r   r  r   rH  r   rB  rY  rA   r  r,   r;   r-   )rh   r,   r;   r  r  r(  r.   r.   r/   
test_gamma  sL   






















zTestFrozen.test_gammac                 C   s8   t d}|d}|j dd |d}t|| d S )Nr   r]   r  r  )r3   r  r  r   )rh   r  m1r8  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  rt   r/  rU   r   r  r  ro   )r3   r  r;   r  r   r_   r`   r   r,   r-   r   r   r  r   )rh   ry  r  r,   r-   rv1r.   r.   r/   r  >  s4   



zTestFrozen.test_abc                 C   s   t ttjd d S )N	rv_frozen)r   r+   r3   r4   rl   r.   r.   r/   test_rv_frozen_in_namespacej  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   )r3   rH  r   r+   r   r   	get_stater`   r   rG  r   )rh   r  rndmr.   r.   r/   test_random_staten  s   
zTestFrozen.test_random_statec           
      C   s   t dd}t d}t jg dg dfd}|||fD ]H}d|_|jdd	 t|}|jdd	}t|}|jdd	}t	|| |
d
|
d
g}	t	|	d |	d  t	||	d ||	d  qd S )Ngdsz@g@e?r  )r   r   r]   r   r:  r  r   r   r  ro   r   r   )r3   r  r`  r>   r   r   pickledumpsloadsr   r   rf   )
rh   r  poissr  distfnrG   r0	unpickledr1mediansr.   r.   r/   test_pickling|  s&   




zTestFrozen.test_picklingc              
   C   s   dd }t jdddd}tjddd |j|d	dd
d}t jj|dddd	dd
d}W d    n1 s4w   Y  t|| t jddd}||}t jj|ddd}t|| d S )Nc                 S      | S rj   r.   r   r.   r.   r/   r        z$TestFrozen.test_expect.<locals>.funcr]   r   r   r?  r  )r  divider   T)r   ubconditionalr]   r  r[   r\   r   r  r  rZ  )r   r  r[   )r3   r  r`   r  r   r   r`  )rh   r   gmgm_val	gamma_valrT  p_valpoisson_valr.   r.   r/   test_expect  s   

zTestFrozen.test_expectN)r   r   r   r  rI  r  r  r  r  r  r  r  r.   r.   r.   r/   r    s    34,r  c                   @   s|   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd ZdS )
TestExpectc                 C   s   t jjdd ddd}t|ddd t jjd	d ddd}t|ddd t jjd
ddd}t jjdddd}t jjdd dd||d}t|ddd t jjdd dd||dd}t|ddd d S )Nc                 S      | d | d  S )Nr~   r.   r   r.   r.   r/   rH     rI   z&TestExpect.test_norm.<locals>.<lambda>r~   r]   rZ   r   r4  r:  c                 S   r  rj   r.   r   r.   r.   r/   rH     r   r  r  c                 S   r   r   r.   r   r.   r.   r/   rH     r   r[   r\   r   r  r   c                 S   r   r   r.   r   r.   r.   r/   rH     r   Tr[   r\   r   r  r  r7  )r3   rH  r   r   r   )rh   r  r  r   r  prob90prob90cr.   r.   r/   rI    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/   rH     rI   z&TestExpect.test_beta.<locals>.<lambda>rZ  r~   r]   )r  r[   r\   qq?r  r:  c                 S   r  rj   r.   r   r.   r.   r/   rH     r   r8  rs   r  r  rX   rZ   r  c                 S   r   )Nr7  r.   r   r.   r.   r/   rH     r   )rX   rX   Fr  r   c                 S   r   r   r.   r   r.   r.   r/   rH     r   Tr7  )r3   r  r   r   r   )rh   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 )Nr  rX   r   r8  rZ  c                 S   r  rj   r.   r   r.   r.   r/   rH     r   z+TestExpect.test_hypergeom.<locals>.<lambda>)r  rX   r   r  r  r:  c                 S      | d d S Nr  r]   r.   r   r.   r.   r/   rH         r4  c                 S   r  r  r.   r   r.   r.   r/   rH     r  r~   )r  r[   r   r  r   c                 S   r   r   r.   r   r.   r.   r/   rH     r   r9  r9  c                 S   r   r   r.   r   r.   r.   r/   rH     r   T)r  r[   r   r  r  c                 S   r   r   r.   r   r.   r.   r/   rH     r   r   )r  r   r  )r3   r  r   r   r4  rL  )
rh   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/   rH     r   z)TestExpect.test_poisson.<locals>.<lambda>r  r   F)r  r   r  r   r]   r4  r:  c                 S   r   r   r.   r   r.   r.   r/   rH     r   T)r3   r`  r   rf   r   )rh   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  r  )ro   r4  r:  )r3   genhalflogisticr   r   )rh   halflogres1r  r.   r.   r/   test_genhalflogistic  s
   zTestExpect.test_genhalflogisticc                 C   sv   t ttjdd t ttjjdd dd t ttjjdd dd t ttjjdd dd d S )	Nr  Gz?c                 S   r   r   r.   r   r.   r.   r/   rH     r   z/TestExpect.test_rice_overflow.<locals>.<lambda>)r  r  c                 S   r   r  r.   r   r.   r.   r/   rH     r   c                 S   r   Nr   r.   r   r.   r.   r/   rH     r   )r   r`   rG  r3   ricer_   r   rl   r.   r.   r/   test_rice_overflow  s   "zTestExpect.test_rice_overflowc                 C   sp   d\}}t jjdd |fd}t|||d  td|  dd t jjdd |f|d	}t||| dd d S )
N)r[  r   c                 S   r  rj   r.   rT   r.   r.   r/   rH     r   z(TestExpect.test_logser.<locals>.<lambda>r  r7  rw   r   c                 S   r  rj   r.   r  r.   r.   r/   rH     r   r  )r3   r  r   r   r`   rr  )rh   rT  r[   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  r  c                 S   r  rj   r.   r   r.   r.   r/   rH     r   z)TestExpect.test_skellam.<locals>.<lambda>r  c                 S   r  r  r.   r   r.   r.   r/   rH      r  r  r   r]   )r3   r  r   r   )rh   rb  p2r  r8  r.   r.   r/   test_skellam  s
   zTestExpect.test_skellamc                 C   sL   d\}}t jdd ||f}t|tdd t||D ||  dd d S )N)r   q   c                 S   r  rj   r.   r   r.   r.   r/   rH   (  r   z)TestExpect.test_randint.<locals>.<lambda>c                 s   s    | ]}|V  qd S rj   r.   r:   r   r.   r.   r/   r  *  s    z*TestExpect.test_randint.<locals>.<genexpr>rw   r   )r3   r%  r   r   rL  r  )rh   lohir   r.   r.   r/   test_randint$  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/   rH   /  r  z&TestExpect.test_zipf.<locals>.<lambda>r  )r	   rX  r3   r/  r   rl   r.   r.   r/   	test_zipf,  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/   rH   3  r   z/TestExpect.test_discrete_kwds.<locals>.<lambda>r  r  c                 S   r   r   r.   r   r.   r.   r/   rH   4  r   r      rh  )r  maxcount	chunksize	tolerancer4  r:  )r3   r`  r   r   )rh   n0n1r.   r.   r/   test_discrete_kwds1  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~   rX   r   r  r   r#  r]   r.   rP  r.   r.   r/   poiss_moment5;  s   0z-TestExpect.test_moment.<locals>.poiss_moment5)r~   r  r~   r  rx   )r3   r`  r  r   )rh   r  r  m5r.   r.   r/   test_moment8  s
   zTestExpect.test_momentc                 C   sn   t tjjdddd t tjjdddd t tjjdddd t tjjddd	 t tjjd
dd
 d S )Nr0  r7  rZ   r  rX   rU   )   r  r  U   rZ  )r   r3   rH  r   r  r`  rl   r.   r.   r/   test_challenging_cases_gh8928B  s
   z(TestExpect.test_challenging_cases_gh8928c                 C   s   t j}|jddd}t|jddd| t|jddddd| t|jddddd|d	  t|jddddd
d| t|jdddddd t|jdddddd t|jddddd
dd d S )NrX   r~   rZ   r  r  r  r  r4  r  Tr  r  g433333@g433333r9  )r3   r  r   r   r   )rh   r;   ra  r.   r.   r/   test_lb_ub_gh15855K  s"   zTestExpect.test_lb_ub_gh15855N)r   r   r   rI  r  r  r  r  r   r  r  r  r  r  r  r  r  r.   r.   r.   r/   r    s    "
		
	r  c                   @   <   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestNctc                 C   s@   t dd}t|dd t dd}t|dddd d S )Nr~   r   ro   r   g K?rX   r:  )r3   nctr   rf   r   r  r.   r.   r/   test_nc_parameterb  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  rU   r   )gMp^j?g6].ftv?gȳ'ς?gu?)g!Y<a?g]d1p?go|?g?)gHdY?g2Ԥg?g}o/u?g .mr?rw  rx   )r3   r  r_   r`   r   r<  r   r   )rh   r   rQ   r.   r.   r/   test_broadcastingj  s   zTestNct.test_broadcastingc                 C   s   t dd}t| d d S )Nr   r   rs   )r3   r  r   rB  r  r.   r.   r/   test_variance_gh_issue_2401r  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 )Nr   r[  r  )r  ncr  r  r  )r3   r  r   r`   r   r   rG  r   r  r.   r.   r/   test_nct_inf_momentsz  s   "zTestNct.test_nct_inf_momentsc                 C   s   t jdd}t j dd}ddg}t||d dd t||dd t jdd}t j dd}d	d
g}t||d dd t||dd d S )Nr   r]   g@ @g*dn?r   r  rx   r   gqI  @gL) ?r  )r3   r  r   r   )rh   nct_mean_df_1000nct_stats_df_1000expected_stats_df_1000nct_mean	nct_statsr  r.   r.   r/   test_nct_stats_large_df_values  s   
z&TestNct.test_nct_stats_large_df_valuesc                 C   s   t tjddtdd d S )Nr]   i   r   )r   r3   r  rf   r   rl   r.   r.   r/   test_cdf_large_nc  r  zTestNct.test_cdf_large_ncN)	r   r   r   r  r  r   r"  r(  r)  r.   r.   r.   r/   r  a  s    r  c                   @   r  )
TestRecipInvGaussc                 C   s   t jdd}|dksJ d S )Nr   r  rt   )r3   recipinvgaussr_   rk  r.   r.   r/   test_pdf_endpoint  s   z#TestRecipInvGauss.test_pdf_endpointc                 C   s"   t jdd}|tj ksJ d S )Nr   r  )r3   r+  r   r`   r   rf  r.   r.   r/   test_logpdf_endpoint  r  z&TestRecipInvGauss.test_logpdf_endpointc                 C   s$   t jdd}d}t||dd d S )Nr  ro   g9V9s;r3  rx   )r3   r+  rf   r   rh   rT  rQ   r.   r.   r/   test_cdf_small_x  s   z"TestRecipInvGauss.test_cdf_small_xc                 C   s"   t jdd}d}t||d d S )NP   ro   glH<r  )r3   r+  r   r   r.  r.   r.   r/   test_sf_large_x  s   z!TestRecipInvGauss.test_sf_large_xN)r   r   r   r,  r-  r/  r1  r.   r.   r.   r/   r*    s
    r*  c                   @   rn  )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  r7  r8  rt   r-   )rU   rU   ro   r   r   r  r  rh  r  )r   r`   rG  r3   r  r_   r   r   rf   r  r   r   )rh   rW   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  r3  r   )r   r~   )r-   r   )r3   r  r   r   r   r'  r  r.   r.   r/   test_rice_rvs  s   zTestRice.test_rice_rvsc                 C   s   t jtdddtddd}g d}t|| tddd}t jj|ddd}g d	}t|| tj jd
tddd}g d}t|| d S )NrX      )g/Ƹ?g[jǊ\?g 	?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?rU   r   g     @_@r   rG  )	g<~@gwd
@gC?@gb
0@g` A@@g'NxP@g33-a@g4pv@g$F@ro      )gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g<
uQ@giff T@g9r[V@g3bXQ Y@gqxJ[@g`*DD ^@g@`@gdAa@)r3   r  rf   r`   r   r   r   r2   )rh   rf   cdf_expprobabilitiesr   ppf_expr.   r.   r/   test_rice_gh9836  s   "

zTestRice.test_rice_gh9836N)r   r   r   r4  r5  r;  r.   r.   r.   r/   r2    s    r2  c                   @   rn  )
TestErlangc                 C   r  r  r  rl   r.   r.   r/   r    r  zTestErlang.setup_methodc              	   C   s   t  6 t dt tttjjddddd g d}tjj|dd}tj	j|dd}t
||d	d
 W d    d S 1 s=w   Y  d S )NrQ  r  r   r   r   r  )ro   r7  rs   r=  r?  r  rx   )rU  rV  rW  rX  r  r3   erlangr   r   r  r   )rh   r   result_erlangresult_gammar.   r.   r/   test_erlang_runtimewarning  s   
"z%TestErlang.test_erlang_runtimewarningc                 C   s.   t tjjdddgdtjjdddgd d S )Nro   r   r   r1  )r   r3   r=  r_   r  rl   r.   r.   r/   test_gh_pr_10949_argcheck#  s   z$TestErlang.test_gh_pr_10949_argcheckN)r   r   r   r  r@  rA  r.   r.   r.   r/   r<    s    r<  c                   @   sp   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	ejdddgddggdd Z
dd Zdd ZdS )TestRayleighc                 C   r  )Nr  r  rl   r.   r.   r/   r  )  r  zTestRayleigh.setup_methodc                 C   r  )Nr!  g)Zx)r3   r  r   r   rh   r8  r.   r.   r/   r  -     zTestRayleigh.test_logpdfc                 C   r  )Nr!  i)r3   r  r,  r   rC  r.   r.   r/   r:  1  rD  zTestRayleigh.test_logsfrY  )gB)Q?got|?)gS2P?g3?c                 C   s   t jjd||d}dd }|||}t jj||d\}}t|| t|| t jj|dd\}}t|d t j|\}}t|||| d S )Nr*  rh  c                 S   s"   t | | d dt|   d S )Nr]   ro   )r`   rL  r   )r   r   r.   r.   r/   rB  :  s   "z(TestRayleigh.test_fit.<locals>.scale_mler   r  rs  )r3   r  r   r   r   )rh   r   rx  r   rB  scale_expectr[   r\   r.   r.   r/   rr  5  s   



zTestRayleigh.test_fitr  rq   g̡=E?g@1d?c                 C   s"   t jjd||d}tt j| d S )Nr*  rh  )r3   r  r   r   )rh   r   rx  r   r.   r.   r/    test_fit_comparison_super_methodN  s   z-TestRayleigh.test_fit_comparison_super_methodc                 C   s   t tj d S rj   )r  r3   r  rl   r.   r.   r/   r  V  r  zTestRayleigh.test_fit_warningsc           	      C   s   t jd}d\}}}tjj||||d}tj|\}}|t |k s&J tjj||d\}}|t |k s9J ||ks?J d S )Ni  )r!  r&  r   r   rs  )r`   r   r   r3   r  r   r   r  )	rh   r   r[   r\   r   r   r   r   r   r.   r.   r/   test_fit_gh17088Y  s   
zTestRayleigh.test_fit_gh17088N)r   r   r   r  r  r:  r   r   r   rr  rF  r  rG  r.   r.   r.   r/   rB  (  s    


rB  c                   @   sX   e Zd Zdd Zdd Zdd Zejdg dd	d
 Z	ejdg ddd Z
dS )TestExponWeibc                 C   sB   d}d}d}t j|||}t j|||}t||gddg d S )NrU   r7  r  g:23W+g~`9k)r3   	exponweibr_   r   r   )rh   rW   r,   ry  rT  r  r.   r.   r/   test_pdf_logpdfh  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 )Nrv  r   r   r   rY   )r`   rw  r3   rI  r_   weibull_minr   r   rh   rW   r,   ry  rT  rQ   r  r.   r.   r/   test_a_is_1s  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   rX   )r`   rw  r3   rI  r_   r  r   r   rL  r.   r.   r/   test_a_is_1_c_is_1  s   
z TestExponWeib.test_a_is_1_c_is_1zx, a, c, ref))r   r  r   g=J ?)r!  r  r   g$+PR>)r)  r  r   g><)r*  r  r   ggX.X:)r*        ?r   gRy9)r   rO  r  g'vR0=)g_QPr/  r  gQ:<c                 C   r  rc  )r3   rI  r   r   )rh   rW   r,   ry  ra  r   r.   r.   r/   r       zTestExponWeib.test_sfzp, a, c, ref))rK  r  r   g;y$(@)gMg<r  r   gdbq^@)r  r   r]   gE@)gvIh%L=rO  r   g/7@)rR  r/  r  gTWTOc                 C   r  rS  )r3   rI  r  r   )rh   rT  r,   ry  ra  r  r.   r.   r/   r    s   	zTestExponWeib.test_isfN)r   r   r   rJ  rM  rN  r   r   r   r  r  r.   r.   r.   r/   rH  f  s    

rH  c                   @   r  )TestFatigueLifec                 C   r:  )Nr  r  X9r   rx   )r3   r  r   r   r  r.   r.   r/   test_sf_tail  s   zTestFatigueLife.test_sf_tailc                 C   s$   d}t j|d}t|ddd d S )NrR  r  r  r   rx   )r3   r  r  r   )rh   rT  r\  r.   r.   r/   test_isf_tail  s   zTestFatigueLife.test_isf_tailN)r   r   r   rS  rT  r.   r.   r.   r/   rQ    s    rQ  c                   @   sX   e Zd Zdd Zdd Zejdddgdd	 Zd
d Z	ejdddgdd Z
dS )TestWeibullc                 C   r  ri  )r3   rK  r   r   rC  r.   r.   r/   r       zTestWeibull.test_logpdfc           
      C   sP  d}d}d}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|t	
d  t jj|||d}t|tt	
d  t jj|||d}t|td t jj|||d}	t|	d t jjdddd}t|td	 t jjdddd}	t|	d	 d
}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|td t jj|||d}t|d t jj|||d}t|t	
d  t jj|||d}	t|	tt	
d  t jjdddd}t|t	
d  t jjdddd}	t|	tt	
d  d S )Nr  rs   r  rG  rq  r   r  r]   r  r  g&.gCe )r3   rK  r_   r   r`   r   r   rr  rf   r   r  r  r   r,  weibull_max)
rh   rW   r,   r-   rT  r<  ry  lcrG   r  r.   r.   r/   test_with_maxima_distrib  sH   


z$TestWeibull.test_with_maxima_distribr\   r7  rU   c                 C   s*   t jj|d |d d|d}t|d d S )Nr  r   r   rG  g>)r3   rK  r[  r   r  r.   r.   r/   r\  @  s   zTestWeibull.test_delta_cdfc                 C   s   t jd}d\}}}t|||}|jd|d}tjj|ddd\}}}	tjj|ddd\}
}}||  kr<dks?J  J ||
ksEJ tjj|ddd	d
\}}}|dksXJ t|||}|jdd}t |t|f}t	|| d S )Nl   > )r]   r  ro   rY   r   r  r   r   r  r  r  r!  r  )
r`   r   r   r3   rK  r   r   r   rC  r   )rh   r   ry  r[   r\   r;   r   c2r&  r'  c3r)  r*  c4r,  r-  r.  r   ra  r.   r.   r/   test_fit_minU  s   
zTestWeibull.test_fit_minrg  )r!  r   r  )r   r   gq뮕qH)c                 C   rb  rS  )r   r3   rK  r   r  rk  r.   r.   r/   rZ  s  s   zTestWeibull.test_sf_isfN)r   r   r   r  rY  r   r   r   r\  r]  rZ  r.   r.   r.   r/   rU    s    T

rU  c                   @   r  )TestDweibullc                 C   sR   t jd}d|jddd }tj|}tj|t d }t	||dd d S )N   q>~). rX   rY   rK  ro   rw   rx   )
r`   r   r   r  r3   dweibullrA   rK  rr  r   )rh   r   ry  r   ra  r.   r.   r/   rP  |  s
   zTestDweibull.test_entropyc                 C   s\   t jd}d|jddd }d|  }tj||}dtj|| }t	||dd d S )Nr_  rX   r   rK  ro   rw   rx   )
r`   r   r   r  r  r3   r`  r   rK  r   )rh   r   ry  rW   r   ra  r.   r.   r/   r    s   zTestDweibull.test_sfN)r   r   r   rP  r  r.   r.   r.   r/   r^  {  s    r^  c                   @   r@  )TestTruncWeibullc                 C   s(   t jddgddd}t|ddg d S )NrU   rs   g)\(?gףp=
?rt   )r3   truncweibull_minr_   r   rC  r.   r.   r/   test_pdf_bounds     z TestTruncWeibull.test_pdf_boundsc                 C   s>   t jdddtj}t|d t jdddd}t|d d S )Nrs   r7  rt   r=  g~?)r3   rb  r   r`   r   r   r   rC  r.   r.   r/   r    s   
zTestTruncWeibull.test_logpdfc                 C   s(   t jddgddd}t|ddg d S )Nrt   r7  rs   rU   )r3   rb  r   r   rC  r.   r.   r/   test_ppf_bounds  rd  z TestTruncWeibull.test_ppf_boundsc                 C   :   g d}t j|ddd}t j|ddd}t|| d S N)rt   rU   rK  ro   r   r   r7  rs   rt   r  )r3   rb  r   rf   r   rh   r\  rW   q_outr.   r.   r/   test_cdf_to_ppf     z TestTruncWeibull.test_cdf_to_ppfc                 C   rf  rg  )r3   rb  r  r   r   rh  r.   r.   r/   test_sf_to_isf  rk  zTestTruncWeibull.test_sf_to_isfc                    s  dd d fddt jd }t|d t jd }tfdd	 \}}t|| t jd
 }tfdd	 \}}t|| t jd }tfdd	 \}}t|| t jd }	tfdd	 \}
}t|	|
 d S )Nrs   r7  r  c                    s   | | t j|   S rj   )r3   rb  r_   )rW   rS  r  r.   r/   xnpdf  s   z)TestTruncWeibull.test_munp.<locals>.xnpdfr   r   c                    
    | dS r   r.   r   rm  r.   r/   rH        
 z,TestTruncWeibull.test_munp.<locals>.<lambda>r]   c                    rn  r  r.   r   ro  r.   r/   rH     rp  r   c                    rn  r  r.   r   ro  r.   r/   rH     rp  r   c                    rn  )Nr   r.   r   ro  r.   r/   rH     rp  )r3   rb  r  r   r   r   )rh   r  r  m1_expectedr   r8  m2_expectedm3m3_expectedr9  m4_expectedr.   )r,   r-   ry  rm  r/   	test_munp  s$   



zTestTruncWeibull.test_munpc                 C   s   d}d}d}t dt dt dt d    }tj||||}t|d tj||||}t|t d  tj	d|||}t|| tj
||||}t|d tj||||}	t|	t d  tjd|||}
t|
| d S )Nr7  r  rs   r   ro   r  )r`   r  rr  r   r3   rb  rf   r   r  r   r   r,  r  )rh   r,   r-   ry  x_medrf   rX  r   r   r  r  r.   r.   r/   test_reference_values  s    *


z&TestTruncWeibull.test_reference_valuesc                 C   s  d}d}d}t j}d}tjj|||d}tjj|||||d}t|| tjj|||d}tjj|||||d}	t||	 tjj|||d}
tjj|||||d}t|
| tjj	|||d}tjj	|||||d}t|| tjj
|||d}tjj
|||||d}t|| tjj|||d}tjj|||||d}t|| tjj
dd||dd}t|t d	 tjjdd||dd}t|d	 d S )
Nr  rs   rt   r  rG  r  r]   r   r  )r`   r   r3   rK  r_   rb  r   r   rf   r  r   r,  r   )rh   rW   ry  r,   r-   r\   rT  p_truncr<  lp_truncrf   	cdf_truncrX  lc_truncrG   s_truncr  ls_truncr.   r.   r/   test_compare_weibull_min  s6   





z)TestTruncWeibull.test_compare_weibull_minc           
      C   s   d\}}}t ||d}tj||||}tj||||}tj||tj|| }tj||| }tj||tj|| | }	t j|| t j||	 d S )N)r  rK  r  rY   )	r`   r<  r3   rb  r_   rf   rK  rC  r   )
rh   ry  r,   r-   rW   rA  r  rH  rB  r  r.   r.   r/   test_compare_weibull_min2  s   
 z*TestTruncWeibull.test_compare_weibull_min2N)r   r   r   rc  r  re  rj  rl  rv  rx  r  r  r.   r.   r.   r/   ra    s    )ra  c                   @   r  )
	TestRdistc                 C   s0   t j}g d}t|||dd|dd d S )Nr  g     @r~   r:  )r3   rdistr   rf   r   )rh   r  r  r.   r.   r/   test_rdist_cdf_gh1285"  s
   
zTestRdist.test_rdist_cdf_gh1285c                 C   sN   t ddd}d}tdt|d |d |d d  t|| d S )NgGzr  rX   g@ro   r]   r   )r`   r<  r   r3   r  r_   r  )rh   rW   ry  r.   r.   r/   test_rdist_beta)  s
   &zTestRdist.test_rdist_betarg  ))r  i  g?)rU      g;|bZ?)ro   i  g79)r   iU  g޻S/c                 C   ri  rS  )r   r3   r  r   rk  r.   r.   r/   test_rdist_sf7  s   
zTestRdist.test_rdist_sfN)	r   r   r   r  r  r   r   r   r  r.   r.   r.   r/   r  !  s    	r  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[  ro   r   r   r   )r   r3   r   r_   triangrf   )rh   modesmoderW   r.   r.   r/   test_reduces_to_triangE  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   rX   )r`   r<  r   r3   r   r_   r  rf   r  r.   r.   r/   test_reduces_to_uniformN  s   "z%TestTrapezoid.test_reduces_to_uniformc                 C   s  t tjdddd t tjdddd t tjdddd t tjdddd t tjd	ddd
 t tjdddd t tjdddd
 t tjd	ddd t tjdddd t tjdddd t tjdddd t tjdddd d S )Nr   r]   r   ro   r   r  r  r7  rU   g      ?r  r   rO  r  g      ?)r   r3   r   r_   rf   rl   r.   r.   r/   
test_casesS  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  r   r]   r   r]   c                    sT   | d  | d     | d   | d        | d  | d  S )Nr]   r   r.   )rS  r,   r-   ry  drO  r.   r/   r  n  s    z6TestTrapezoid.test_moments_and_entropy.<locals>.momentr   ro   r  r:  r   r  r9  r   r   )r`   rr  r   r3   r   r   rB  rA   )	rh   rb  r  r[   r\   r  r   rB  rA   r.   r  r/   test_moments_and_entropyg  s&   0> z&TestTrapezoid.test_moments_and_entropyc                 C   s`  t g d}t ddgd d d f }t g d}tj|||}t |||\}}}t j|j|jd}t 	|j}	t
|	| | | D ]\}
}}}tj|||||
< qIt|||jdd t tjj||dd	}t ||\}}t |jd
f}t 	|j}	t
|	| | D ]\}
}}tjj||dd	||
< qt||j|jdd d S )Nre  ro   r  )r  rK  r   r  rw   r   r  r  r   )r`   r   r3   r   r_   broadcast_arraysemptyr   r   r   r   ravelr   r@  r'  r   r	  )rh   ry  r  rW   r  ccddrz  r   indr  rk  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  )r`   r<  r   r3   rB   r_   r  r  r.   r.   r/   
test_trapz  s   "zTestTrapezoid.test_trapzN)	r   r   r   r  r  r  r  r  r  r.   r.   r.   r/   r  D  s    	r  c                   @   rg  )
TestTriangc                 C   s"  t jdd ttjddd ttjddd ttjddd ttjddd ttjddd ttjddd	 ttjddd ttjddd
 ttjddd ttjddd ttjddd ttjddd W d    d S 1 sw   Y  d S )Nraiserm  r   rs   ro   r7  r   rt   r]   r   rK  )r`   r  r   r3   r  r_   rf   rl   r.   r.   r/   test_edge_cases  s   "zTestTriang.test_edge_casesN)r   r   r   r  r.   r.   r.   r/   r    r  r  c                   @   s@   e Zd Zejdddgdd Zejdg ddd	 Zd
S )TestMaxwellrr  )r  gCR5&.)rq   g7q?c                 C   r  rc  )r   r3   maxwellr   ru  r.   r.   r/   r    rv  zTestMaxwell.test_sfr  ))r  g1!@)g    ?g?)g      <gCuJ!@c                 C   r  rv   )r   r3   r  r  r  r.   r.   r/   r    r  zTestMaxwell.test_isfNr  r.   r.   r.   r/   r    s    
r  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   r7  r  )r   r3   mielker  r`   r   r   rG  )rh   rT   rG   r.   r.   r/   r    s    zTestMielke.test_momentsc                 C   s@   t ddd}d\}}ttj|||| tj||| d S )Nrq   rY   r!  )g@gHzG@)r`   r<  r   r3   burrr_   r  )rh   rW   rT   rG   r.   r.   r/   test_burr_equivalence  s   *z TestMielke.test_burr_equivalenceN)r   r   r   r  r  r.   r.   r.   r/   r    r  r  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   )ro   r]   )r   r   )r]   ro   r  ro   r7  )r   r]   rs   c                 S   r  r.   r  r  r.   r.   r/   r<     r  z0TestBurr.test_endpoints_7491.<locals>.<listcomp>c                 S   r  r.   r.   r  r.   r.   r/   r<     r  c                 S   r  r.   )r   r,   r  r.   r.   r/   r<     r  c                 S   s   g | ]
\}}}t |qS r.   )r`   rr  r  r.   r.   r/   r<     r  )r3   fiskr  burr12r   )rh   r   r  r  r.   r.   r/   test_endpoints_7491  s   






	
zTestBurr.test_endpoints_7491c                 C   s<   d\}}t ||  \}}d\}}t|| t|| d S )N)r8  r   )g4U?g&MI?)r3   r  r   )rh   ry  r  r   variancemean_hcvariance_hcr.   r.   r/   test_burr_stats_9544  s
   
zTestBurr.test_burr_stats_9544c           	      C   sF  d\}}t ||  \}}tt| tt| d\}}t ||  \}}tt| tt| d\}}t jtg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d\}}t jg d||\}}}}tt| tt| tt| tt| d S )N)ro   r   )r  r   ri  )r  r   )r  r   )r  r   )r3   r  r   r`   rX  rG  _munpr   )	rh   ry  r  r   r  e1e2e3e4r.   r.   r/   test_burr_nan_mean_var_9544  sL   "z$TestBurr.test_burr_nan_mean_var_9544c                 C   s6   d\}}g d}g d}t tj||||dd d S )N)r8  r  )rU   r  r2  rs  )g+&?gI$_@gKT@gؗVAr3  rx   )r   r3   r  r  )rh   ry  r  r\  ra  r.   r.   r/   test_burr_isf$  s   zTestBurr.test_burr_isfN)r   r   r   r  r  r  r  r.   r.   r.   r/   r    s
    *r  c                   @   s.   e Zd Zejdddgdd Zdd ZdS )	
TestBurr12zscale, expected)r7  gd~)r  gR톇T c                 C   s(   t jjdddd|d}t||dd d S )Ng     jAg     jAr   r   rG  r   rx   )r3   r  r[  r   )rh   r\   rQ   r  r.   r.   r/   r\  1  s   zTestBurr12.test_delta_cdfc           	      C   sp   d\}}t jd }dt jd d  }t jd d|d   }t j}||||g}t||d	}t||d
d d S )Nr  r   r   r]   r  r   r  r  r  r3  rx   )r`   ra   r   r3   r  r   )	rh   ry  r  r   rB  rC  r  ra  r   r.   r.   r/   test_moments_edgeH  s   
zTestBurr12.test_moments_edgeN)r   r   r   r   r   r   r\  r  r.   r.   r.   r/   r  /  s    
r  c                   @   s  e Zd Zg dZg dZg dZeeeefZg dZ	ddddd	ej
gZg d
Zeeee	eeeZddddej
dfddej
dfddej
dfgZdd Zejjdd ZejeZdZeejeeZe !eZ"W d   n1 sww   Y  ej#de"d dd Z$ej#de"d dd Z%ejjej&dej#de"d d d! Z'd"d# Z(ejj)d$d% Z*ej#d&ed'd( Z+ejjej&dd)d* Z,ejj)d+d, Z-d-d. Z.d/d0 Z/d1d2 Z0dS )3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`"@r0  gʡEs@g|?5^@g/$@gV-@g/$@gF@g?5^I@)gRV@gffffffl@gp@g     r@gʡ @gHzG/@gQ82@gQ3@g!rh@g     @g+@gʡEs @gjt@gB`"[@g@gnJ@gV-@gFx@gsh|?@g+N@g/$@g @g@gGz@)gfffff"@i  i
  i  gHzG2@g(\A@gQC@gfffffE@g @gNbX9"@gHz$@g(\&@g-@gn@@gw/@g=
ףp @gJ+@g-'@gn@gHz@gV-@gnJ@g$@g/ݤ@)r  r  re  r   r   rX   r  x   )r]   r   r4  r  )rU   r   i)#  gupm1f?)r   rX   r   g?<-=A?gv"?r   gd暕?ga-A?c                 C   s<   | j D ]\}}|\}}}tj|||}t||dd qd S )Nr  rx   )r   r3   studentized_rangerf   r   )rh   pvkr\  
p_expectedr  rT   res_pr.   r.   r/   test_cdf_against_tables  s
   
z,TestStudentizedRange.test_cdf_against_tablesc                 C   s<   | j D ]\}}|\}}}tj|||}t||dd qd S )NMb@?rx   )r   r3   r  r   r   )rh   r  
q_expectedrT  r  rT   res_qr.   r.   r/   test_ppf_against_tables  s
   
z,TestStudentizedRange.test_ppf_against_tablesz&data/studentized_range_mpmath_ref.jsonN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\  rT   r  expected_atolexpected_rtolr  )r3   r  rf   r   rh   r  r  r  qkvr   r.   r.   r/   test_cdf_against_mp     
z(TestStudentizedRange.test_cdf_against_mppdf_datac                 C   r  r  )r3   r  r_   r   r  r.   r.   r/   test_pdf_against_mp  r  z(TestStudentizedRange.test_pdf_against_mpz+intermittent RuntimeWarning: invalid value.moment_datac                 C   sz   |d }|d }|d |d |d f}t jdd tjj| }W d    n1 s*w   Y  t|||d |d	 d
 d S )Nr  r  r  rT   r  r  r  r  r  r  )r`   r  r3   r  r  r   )rh   r  r  r  mkvr   r.   r.   r/   test_moment_against_mp  s   
z+TestStudentizedRange.test_moment_against_mpc                 C   s4   d\}}t tjjdtj||fd}t|d d d S )Nr   rX   r   r  r   )r   r3   r  r_   r`   r   r   )rh   rT   r  r   r.   r.   r/   test_pdf_integration  s   z)TestStudentizedRange.test_pdf_integrationc                 C   s\   d\}}t jdddd}tj|||dd  }tj|||}t||}t||dd d S )	Nr  r   rX   rq   )stepr   r  rx   )r`   r   r3   r  rf   r_   r   r   )rh   rT   r  rW   y_cdf	y_pdf_rawy_pdf_cumulativer.   r.   r/   test_pdf_against_cdf  s   
z)TestStudentizedRange.test_pdf_against_cdfr_case_resultc                 C   sV   |\}}}}t jdd tj|||}W d    n1 sw   Y  t|| d S )Nr  r  )r`   r  r3   r  rf   r   )rh   r  r\  rT   r  r_resr   r.   r.   r/   test_cdf_against_r  s
   z'TestStudentizedRange.test_cdf_against_rc                 C   s   t jdd tjddgddgddg}W d    n1 sw   Y  t|jd	 tjt	d
d tjdddgg d W d    d S 1 sIw   Y  d S )Nr  r  r   r]   r   r~   rX   r  r  z...could not be broadcast...r   )rX   r  r9  )
r`   r  r3   r  r  r   r'  r   r   r   r  r.   r.   r/   test_moment_vectorization  s   "z.TestStudentizedRange.test_moment_vectorizationc              	   C   s   t  /}tjdd |t tjg d\}}}}W d    n1 s&w   Y  W d    n1 s5w   Y  ttj	|| d S )Nr  r  r   )
r   r`   r  rL   r   r3   r  rm  r   	_argcheck)rh   r_  rT   r  r   r.   r.   r/   test_fitstart_valid  s   
 z(TestStudentizedRange.test_fitstart_validc                 C   sh   t jddtj}t jddd}t||ddd t jddtj}t jddd}t||ddd d S )Nr   rX   韆 r  r  )r3   r  r_   r`   r   r   rf   )rh   r   
res_finiter.   r.   r/   test_infinite_df  s   z%TestStudentizedRange.test_infinite_dfc                 C   s   t jddd}t jddd}t jddd}ttt||ddd t||ddd t jddd}t jddd}t jddd}ttt||ddd t||ddd d S )Nr   rX   r   r  i r  r  )r3   r  r_   r  AssertionErrorr   rf   )rh   r   r  
res_sanityr.   r.   r/   test_df_cutoff  s   

z#TestStudentizedRange.test_df_cutoffc                 C   s8   d\}}}t j|||}t|ddd |dksJ d S )N)gaRA@r   iS  r   r  r   )r3   r  r   r   )rh   r\  rT   r  rT  r.   r.   r/   test_clipping  s   
z"TestStudentizedRange.test_clipping)1r   r   r   q05q01q001r`   r  qspsr   vskslistr   r$   r   r_datar  r   r   r  r  ospathdirnamer  path_prefixrelative_pathopenrU  filejsonr  pregenerated_datar   r  r  xfail_on_32bitr  r  r   r  r  r  r  r  r  r  r.   r.   r.   r/   r  W  sX    









r  c                   C   sR   t tjddddd t tjddddd t tjjdd	d
ddddd d S )Ng2g?rX   test_540_567)r;  rO  g2gk?g;B.?gͣh?gHŎ*?rZ   g.y?)r   r3   rH  rf   r.   r.   r.   r/   r    s   
r  c                   C   s   t tjdddd d S )Nrt   r]   ro   r4  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      r8  rV   r  r  rt   r  r  rs   r   r   r]   )r`   r<  r  r   r3   r'   r_   r   r   rX  r   )rW   rb  rT  r.   r.   r/   test_regression_tukey_lambda,  s   "	r  zdocstrings strippedr  c                   C   s$   t dtjjv t dtjjv  d S )Nzpdf(x, mu, loc=0, scale=1)zpmf(x,)r   r3   r`  r_  r.   r.   r.   r/   test_regression_ticket_1421A  s   r  c                   C   s  t jdd tt tjdt j tt tjdt j tt tj	dt j tt tj
dt j tt tjdt j tt tjdt j tt tjdt j tt tjdt j tt tjt jd tt tjt jd tt tj	t jd tt tj
t jd tt tjt jd tt tjt jd tt tjt jd tt tjt jd W d    d S 1 sw   Y  d S )Nr  r  r   ro   )r`   r  r   rX  r3   r  r  r   rf   r,  r   r_   r   r   r  rp  r4  r  r.   r.   r.   r/    test_nan_arguments_gh_issue_1362G  s$   "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.  )rK  rt   ro   r   r   r]   rY   r  r  r  rt   r   r:  ro   )r   r[   rK  )r   r[   r  r   rs   r   )r`   r   r   r   r3   r  r   r  r   r   rH  r  r   )truerW   rD  r[   r   rQ   r.   r.   r/   test_frozen_fit_ticket_1536\  s(     r  c                  C   s<   t jd tjjdd} tj| }d}t||dd d S )Ni	 rY   r  )g
ףp=
?gʡE?r   r:  )r`   r   r   r3   r  r   r   r   )r   rD  rQ   r.   r.   r/   test_regression_ticket_1530x  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   6Ar7  r   r  )r`   r   r   r  r3   r  r   r   )rW   offsetr[   r\   r.   r.   r/   test_gh_pr_4806  s   r  c                  C   s   t jj ddd} dtjd d ddg}t| |dd t jj d	dd} g d
}t| |dd t jj ddd} g d}t| |dd d S )Nr   r  r  r]   r   r  rX   r:  g
ףp=
	@)r   gz5v?r   gRTgQ?)r   gNg @r   gJFٻ)r3   r'   r`   ra   r   )r  rQ   r.   r.   r/   "test_tukeylambda_stats_ticket_1545  s   r  c                   C   s   t ttjdd d S )Nr  r  )r   r`   rG  r3   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))
    )r7  )ro   r  rt   r  )rs   )gUUUUUU?r  g^cQg333333r  r  N)r3   rq  r   )rY  r,   
exact_mvskr  r.   r.   r/   test_powerlaw_stats  s   r  c                  C   s   t jdd} t| d d S )Nr   r   rt   )r3   rq  r   r   rT  r.   r.   r/   test_powerlaw_edge  rV  r
  c                  C   sh   t jdd} t| d t jdg d} t| tjddg t jdg d} t| tjdtj g d S )Nr   r   rt   )rK  r7  r  r7  )r3   r  r   r   r_   r`   r   r	  r.   r.   r/   test_exponpow_edge  s   
r  c                  C   s   t jddd} t| d d S )Nr   r   r7  )r3   gengammar_   r   r	  r.   r.   r/   test_gengamma_edge  s   r  za, c, ref, tol))g    `6Ar   g2j!@rw   )r  r   ggA@rw   )r  r   r  rw   )r9  r   g #@r   )g    `FAr  gI~mrw   )gl$W}Lr^  g.I#Urw   c                 C   s   t tj| |||d d S r  )r   r3   r  rA   )r,   ry  ra  rV  r.   r.   r/   test_gengamma_extreme_entropy  s   r  c                  C   s@   t jddd} | dksJ t jddd}|tj ksJ d S )Nr   r   r   rt   )r3   r  r_   r   r`   r   )rT  r  r.   r.   r/   !test_gengamma_endpoint_with_neg_c  s   r  c                  C   s8   t jddd} t| d t jddd} t| d d S )Nr   r  r7  g>rX   gqq?)r3   r  r  r   r	  r.   r.   r/   test_gengamma_munp  s   
r  c               	   C   s   t g d} t jdd6 t }|td |td tj	|  W d    n1 s.w   Y  W d    d S W d    d S 1 sFw   Y  d S )N)0g>X*ȿgPix#?g=?g&^?goϿg뵏˿gO_ZQ?g\?g~?g)/?gRܶ?g핚οgH߃[g?gS"gm_ пg7k?g#BF?gKU=?gT?gZg[Qs?g2?g6Hwƭ8?g*-
?ga]?g'?g޻?g?J_ ?g~sw?g0FfͿgg"@ӿg?%:˿g&zM?g?Gg	F?g~,g HgW2ҿgTzy?gwmǿg @gW=ֿg	't?g".v1glg.Hꮿg,?g*˿r  r  z:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integer)
r`   r   r  r   rL   r   rX  r3   r  r   )r  r_  r.   r.   r/   test_ksone_fit_freeze  s    "r  c                  C   s   t ttddd } g d}tt | |dd tt | d j|dd tj| d d	 j	}t 
tj| tj|  }t||d	d d S )
Nr   r  r   )gDB.g8_$g%`OAgjhwHRgWMB@v`g7VY}igۦx\Arg	xg#g/dg3$gegd)gNq{3gيGǓgr4g37'
gfFg?dJgضg2,
gm%gӅJgz;pgɿ{gk2gij<%giVSͶgBR4g
Q/Mrh  r   y        +=y        |=r  )r`   r   r  r  r   r3   rH  r  realimagr   r   )rW   rQ   derivderiv_expectedr.   r.   r/   test_norm_logcdf  s   	r  c                  C   sT   t g d} t g d}tj| }t||dd tj|}t|| dd d S )N)r   r7  ro   rU   rq   r  )g~V1?ro  gba"?g܄4ťY?rp  g$%+Ir  rx   r   )r`   r   r3   r  rf   r   r   )rW   rQ   r8  rz  r.   r.   r/   test_levy_cdf_ppf6  s   r  c                  C   :   t g d} t g d}tj| }t||dd d S )N)rf  r~  gMraB3Gr  )gep[>g}XEQ=gѭEG<g?_%~:r3  rx   )r`   r   r3   r  r   r   rW   rQ   r8  r.   r.   r/   test_levy_sfN     r  zp, expected_isf))r2  gj1e2H)rh  g6C)r  gnE@)r(  g!^x1?)re  gZ?)g   ?g:}!Nu?c                 C   s   t j| }t||dd d S )Nr  r   )r3   r  r  r   )rT  expected_isfrW   r.   r.   r/   test_levy_isfe  s   r  c                  C   r  )N)gMb{Gzg{Gztg~jtX)g#]<gOul2;gޢا6g̅7=!r   rx   )r`   r   r3   r  r   r   r  r.   r.   r/   test_levy_l_sfq  r  r  c                  C   s8   t g d} tj| }tj|}t|| dd d S )N)g [n<rK  r  rR  rx   )r`   r   r3   r  r  r   r   )rT  rW   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@r  rY   r   r   )r   r3   r  r  r   r.   r.   r.   r/   test_hypergeom_interval_1802  s   r"  c                  C   sr  t jd t jdddd} tttjj| dddd	 tttjj| ddd
dd	 tttjj| ddd
d tttjj| ddddd tttjj	ddddd tttjj
| ddddd tttjj| ddddd tttjjddddd tttjjddddd tttjj| ddddd tj| dd tj| ddd
 tjdd tjddd
 tjddd
d tj	ddd
d tjtjj	dddd tjj| ddd	 tttjj| ddd
 tttjj| ddd
d	 tttjj| ddd	 tttjj| dd
ddd	 tttjj| dd
ddd tttjj| dd
dddd	 tttjj| dd
ddddd	 tj| dd
ddd d S )Nr   rU   r  r~   numr]   r   r7  rZ  r   ro   rZ   rs   r  r  r  r9  rG  )r`   r   r   r<  r  r   r3   r  r_   r   rf   r   rA   r   r  r4  r  rI  r  r   r.   r.   r/   test_distribution_too_many_args  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 )	Nr  r  r  r]   gYZ@r  r   rF  )r3   ncx2rf   r`   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 )NrQ  r   iT  i^  r]   r   r  r   r9  gsq6)rU  rV  rW  rX  r   r3   r&  r_   r`   r   r   r   r  r   r   )logvalr.   r.   r/   test_ncx2_tails_pdf  s   

"r*  zmethod, expectedrf   gu%>g	;Q=r_   g<x>gRz\R>r   gʎK$/gԆX1r   gfHu@ge:@c                 C   s,   t tj| dddgdd}t||dd d S )NrU   r   r   rX   )r!  r  rw   r   )r  r3   r&  r   )r   rQ   r(  r.   r.   r/   test_ncx2_zero_nc  s   r+  c                  C   s4   t jjdddd} t jjddd}t| |dd d S )NrX   r   r   )r  r!  r   )r  r   rw   r   )r3   r&  r   r  r   )r(  rQ   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 )NrX   r~   r  r   r  r!  r   )r`   r   r   r3   r&  rf   )r!  r.   r.   r/   test_ncx2_gh12731  s   r.  c                  C   sB   t g d} d\}}tjj| ||d}g d}t||dd d S )N)gю]	@gj%@gb	y/7@g H@gIZ@gXl@g'/2?8@gݰmА@gU@gy]`'@g@g*\@g48c@)r  gh ?8@r-  )r7  r7  r7  r7  r7  g?gy[qD?rt   rt   rt   rt   rt   rt   r  r   )r`   r   r3   r&  r   r   )rW   nurb  r   sf_expectedr.   r.   r/   test_ncx2_gh8665  s
   
r1  c               	   C   sx   d} d}t jtjd| |tjd| |dd}tj|| |}tj|| | t d|  d|  }t||d	d
 d S )Ni,  i  r  re  r  r#  r]   r   r  r   )	r`   r<  r3   r&  r   r_   rH  r  r   )r  r!  rW   ncx2_pdfgauss_approxr.   r.   r/   test_ncx2_gh11777   s   &r4  zx, c, expected))r]   r   g|1q?)r]   r]   g~?)r  r   V<3T1=) 7yQCr   u	lY<)r  g   vHGBg^b!*1=)r  r  gS?c                 C      t j| |}t||d d S Nry  )r3   
foldcauchyr   r   rW   ry  rQ   r   r.   r.   r/   test_foldcauchy_sf/   s   r<  r  ))r]   g?)r  r5  )r6  r7  )g6ްPg8R#/c                 C   s   t j| }t||d d S r9  )r3   r  r   r   )rW   rQ   r   r.   r.   r/   test_halfcauchy_sf=   s   r=  zp, expected))g?g*wӄZ>)333333?gN9?)ro   r7  )rq   g8<,O@)r3  g:B)gl ׶w/gMb}[Pc                 C   s   t j| }t|| d S rj   )r3   r  r  r   )rT  rQ   rW   r.   r.   r/   test_halfcauchy_isfI   s   r?  c                  C   s"   t jddd} t| dd d S )Nr   r   rG  )r3   rj  r   rf   r  r.   r.   r/   test_foldnorm_zeroU   s   r@  ))r]   r   gwo{?)r  r   gGd-P/)rX   r#  gof?)r  r#  gOul";c                 C   r8  )Nr3  )r3   rj  r   r   r;  r.   r.   r/   test_foldnorm_sfi   s   rA  c                  C   s   t j g ddd} t j ddgdd}tdd |D }t||  t j g d} t j dd	g}td
d |D }t||  d S )N)rt   ro   r7  r   ro   r7  c                 s   s     | ]}t jt j|f V  qd S rj   r`   r2  r   r  r.   r.   r/   r  x   r  z-test_stats_shapes_argcheck.<locals>.<genexpr>)r]   r>  r   r]   r>  c                 s   s     | ]}t j|t jf V  qd S rj   rB  r  r.   r.   r/   r  ~   r  )r3   r  tupler   r  )mv3mv2mv2_augmentedr.   r.   r/   test_stats_shapes_argchecks   s   
rG  c                   @   rg  )
_distr_genc                 C   r   Nr  r.   rh   rW   r,   r.   r.   r/   _pdf   r  z_distr_gen._pdfNr   r   r   rK  r.   r.   r.   r/   rH     r  rH  c                   @   rg  )_distr2_genc                 C      d| | S rI  r.   rJ  r.   r.   r/   _cdf      z_distr2_gen._cdfN)r   r   r   rO  r.   r.   r.   r/   rM     r  rM  c                   @   r  )_distr3_genc                 C   s   || S rj   r.   rh   rW   r,   r-   r.   r.   r/   rK     s   z_distr3_gen._pdfc                 C   rN  rI  r.   rJ  r.   r.   r/   rO     s   z_distr3_gen._cdfNr   r   r   rK  rO  r.   r.   r.   r/   rQ     r  rQ  c                   @   r  )_distr6_genc                 C   s   || | S rj   r.   rR  r.   r.   r/   rK     rP  z_distr6_gen._pdfc                 C   rN  rI  r.   rR  r.   r.   r/   rO     rP  z_distr6_gen._cdfNrS  r.   r.   r.   r/   rT     s    rT  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   r1  r  rH  r   r_   rh   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 )NrV  ArW  r   r1  )rH  r  r   r_   r   rY  r.   r.   r/   test_wrong_shapes_1   s    z1TestSubclassingExplicitShapes.test_wrong_shapes_1c                 C   s4   t ddd}tdddd}tt|jdfi | d S )NrV  za, b, crW  r   r]   r   r  )rH  r   r  r   r_   )rh   rZ  r  r.   r.   r/   test_wrong_shapes_2   s   z1TestSubclassingExplicitShapes.test_wrong_shapes_2c                 C   "   t ddd}tttfi | d S )NrV  r  rW  )r   r  r   rH  rh   r  r.   r.   r/   test_shapes_string      z0TestSubclassingExplicitShapes.test_shapes_stringc                 C   r_  )NrV  z(!)rW  r   r  SyntaxErrorrH  r`  r.   r.   r/   test_shapes_identifiers_1   rb  z7TestSubclassingExplicitShapes.test_shapes_identifiers_1c                 C   r_  )NrV  4chanrW  rc  r`  r.   r.   r/   test_shapes_identifiers_2      z7TestSubclassingExplicitShapes.test_shapes_identifiers_2c                 C   r_  )NrV  zm(fti)rW  rc  r`  r.   r.   r/   test_shapes_identifiers_3   rh  z7TestSubclassingExplicitShapes.test_shapes_identifiers_3c                 C   r_  )NrV  za=2rW  rc  r`  r.   r.   r/   "test_shapes_identifiers_nodefaults   rh  z@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaultsc                 C   r_  )NrV  z*argsrW  rc  r`  r.   r.   r/   test_shapes_args   rh  z.TestSubclassingExplicitShapes.test_shapes_argsc                 C   r_  )NrV  z**kwargsrW  rc  r`  r.   r.   r/   test_shapes_kwargs   rh  z0TestSubclassingExplicitShapes.test_shapes_kwargsc                 C   r_  )NrV  za, b, c, lambdarW  rc  r`  r.   r.   r/   test_shapes_keywords   rb  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                   @   rg  )zFTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_genc                 S      t j|| S rj   r3   rH  rK  rJ  r.   r.   r/   rK     r  zKTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_gen._pdfNrL  r.   r.   r.   r/   	_dist_gen   r  rp  r,   r   ro   r]   r1  r3   r?   r   r_   rH  rh   rp  r;   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                   @   rg  )zSTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_genc                 S   rn  rj   ro  rJ  r.   r.   r/   rK     r  zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_gen._pdfNrL  r.   r.   r.   r/   rp     r  rp  r  rq  ro   r   r]   r  )r3   r?   r  r   r_   r   rs  r.   r.   r/   "test_shapes_signature_inconsistent   s   
"z@TestSubclassingExplicitShapes.test_shapes_signature_inconsistentc                 C   sz   G dd dt j}|dd}t|jdddt jdd  t|ddt jdd  tt|jdfi tdd d S )	Nc                   @   rg  )z?TestSubclassingExplicitShapes.test_star_args.<locals>._dist_genc                 W   s   |d }t j|| S Nr   ro  )rh   rW   r  extra_kwargr.   r.   r/   rK     s   zDTestSubclassingExplicitShapes.test_star_args.<locals>._dist_gen._pdfNrL  r.   r.   r.   r/   rp     r  rp  rw  rq  ro   !   rw  )xxx)r3   r?   r   r_   rH  r  r   r   rs  r.   r.   r/   test_star_args   s
   
  z,TestSubclassingExplicitShapes.test_star_argsc                 C   sj   G dd dt j}|dd}t|jddddt jdd d  t|dddt jdd d  d S )	Nc                   @   rg  )zATestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_genc                 W   s   |d }t j|| | S rv  ro  )rh   rW   r  r  rw  r.   r.   r/   rK     s   zFTestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_gen._pdfNrL  r.   r.   r.   r/   rp     r  rp  zoffset, extra_kwargrq  ro   o   rx  )r  rw  rr  rs  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                   @   rg  )zBTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_genc                 _   s   | dd}tj|| S )Nrw  r   )popr3   rH  rK  )rh   rW   r  kwargsrw  r.   r.   r/   rK  	!  s   zGTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_gen._pdfNrL  r.   r.   r.   r/   rH  !  r  rH  rw  rq  r   r   ry  rr  )rh   rH  r;   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                   @   rg  )zITestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_genc                 S   s   t j|S rj   )r3   rH  r_   r  r.   r.   r/   rK  !  rP  zNTestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_gen._pdfNrL  r.   r.   r.   r/   rp  !  r  rp   rq  ro   rr  rs  r.   r.   r/   test_shapes_empty_string!  s   
z6TestSubclassingExplicitShapes.test_shapes_empty_stringN)r   r   r   r[  r]  r^  ra  re  rg  ri  rj  rk  rl  rm  rt  ru  r{  r}  r  r  r.   r.   r.   r/   rU     s$    		rU  c                   @   sl   e Zd Zdd Zdd Zejjedddd Z	ejjeddd	d
 Z
dd Zdd Zdd Zdd ZdS )TestSubclassingNoShapesc                 C   s"   t dd}t|jdddd d S )NrV  r  r   r1  r  rX  rY  r.   r.   r/   test_only__pdf !  s   
z&TestSubclassingNoShapes.test_only__pdfc                 C   s"   t dd}t|jdddd d S )NrV  r  r   r1  )rM  r   r_   rY  r.   r.   r/   test_only__cdf$!  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 )NrV  r  r   r,   zlogpdf\(x, a, loc=0, scale=1\))	rH  r   numargsr   refindallr_  r   r   rh   rZ  r   r.   r.   r/   test_signature_inspection)!  s   
z1TestSubclassingNoShapes.test_signature_inspectionc                 C   sD   t dd}t|jd t|jd td|j}tt|dk d S )NrV  r  r]   r  z!logpdf\(x, a, b, loc=0, scale=1\)r   )	rT  r   r  r   r  r  r_  r   r   r  r.   r.   r/   test_signature_inspection_2args4!  s   
z7TestSubclassingNoShapes.test_signature_inspection_2argsc                 C   s   t ttdd d S )NrV  r  )r  r   rQ  rl   r.   r.   r/   0test_signature_inspection_2args_incorrect_shapes>!  r6   zHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapesc                 C   .   G dd dt j}tt|fi tdd d S )Nc                   @   s   e Zd ZdddZdS )z>TestSubclassingNoShapes.test_defaults_raise.<locals>._dist_genr  c                 S   r   rI  r.   rJ  r.   r.   r/   rK  E!  r  zCTestSubclassingNoShapes.test_defaults_raise.<locals>._dist_gen._pdfN)r  rL  r.   r.   r.   r/   rp  D!  s    rp  rV  r  r3   r?   r  r   r   rh   rp  r.   r.   r/   test_defaults_raiseB!     z+TestSubclassingNoShapes.test_defaults_raisec                 C   r  )Nc                   @   rg  )z>TestSubclassingNoShapes.test_starargs_raise.<locals>._dist_genc                 W   r   rI  r.   )rh   rW   r,   r  r.   r.   r/   rK  L!  r  zCTestSubclassingNoShapes.test_starargs_raise.<locals>._dist_gen._pdfNrL  r.   r.   r.   r/   rp  K!  r  rp  rV  r  r  r  r.   r.   r/   test_starargs_raiseI!  r  z+TestSubclassingNoShapes.test_starargs_raisec                 C   r  )Nc                   @   rg  )z<TestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_genc                 [   r   rI  r.   )rh   rW   r,   r  r.   r.   r/   rK  S!  r  zATestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_gen._pdfNrL  r.   r.   r.   r/   rp  R!  r  rp  rV  r  r  r  r.   r.   r/   test_kwargs_raiseP!  r  z)TestSubclassingNoShapes.test_kwargs_raiseN)r   r   r   r  r  r   r   r  DOCSTRINGS_STRIPPEDr  r  r  r  r  r  r.   r.   r.   r/   r  !  s    


	r  r  c                  C   sT   g d} t jD ] }tt |}t|t jt jfr'| D ]}tt||j	d u  qqd S )N)z,\s*,z\(\s*,z^\s*:)
r3   rK   r  r)  r>   r?   r   r  searchr_  )badonesdistnamer;   regexr.   r.   r/   r  X!  s   

r  c                   C   s4   t tjtjddd t tjtjddd d S )NrX   r  r   r   rU   r   )r   r3   r  r   r`   r   r&  rO  r.   r.   r.   r/   test_infinite_inputb!  s   r  c                  C   &   t jt jddd} t| d d S r]  )r3   lomaxr   rf   r   r	  r.   r.   r/   test_lomax_accuracyg!  ra  r  c                  C   r  r]  )r3   r  r   rf   r   r	  r.   r.   r/   test_truncexpon_accuracym!  ra  r  c                  C   s*   t jt jddd} t| ddd d S )Nr  r   r  r#  r:  )r3   r  r  r   r   r	  r.   r.   r/   test_rayleigh_accuracys!  s   r  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)rW  alwaysro   r   rt   N)rU  rV  rW  r3   r  rf   r_   r   r   r`   r   r   r   )r  number_of_warnings_thrownr.   r.   r/    test_genextreme_give_no_warningsy!  s   
"r  c                  C   s   d} t jd}t|d|  d dd t jd}t|| d dd t jd}t|d t jjd	d
d}t|| d td
 d dd t jd
}t|d|  d dd t jd}t|d|  d dd d S )Ngox?r  r]   r   r3  rx   r   r7  r  rX   rG  r   r  r  r  )r3   r  rA   r   r   r`   rr  )euler_gammarO  r.   r.   r/   test_genextreme_entropy!  s   
 r  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 )	Nr   r  g'b%4gQ@r  gؗҜ;r   g.l6?)r3   r  r   r   r  )rW   rG   rl  r.   r.   r/   test_genextreme_sf_isf!  s   




r  c                  C   s"   d} t j| dd}t|d d S )Nr_  r]   r   gH&8>)r3   r  r   r   )probr  r.   r.   r/   test_burr12_ppf_small_arg!  s   	r  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  r8  r3  Nr   r7  rs   )r  r  )gC,d	Ɣ?gH㸘?g5?gM"M#w?gɫs^?g @?gƴ?g@w?ɫs^?|?q ?g C?r  r  gJó?g,BV\ۤ?g;?g#ek?g%ǓE?g(Ȍx?g>J>r  rx   r  )g#{`?gdf?g Jq?gSS){?g'	w?uL? T)?cAJ?GTn?R1#?gA]P?r  r  r  r  gvӢ?gKq?gL?g
	N<!?gAw>ro   )r  r  r[   r\   )g=aO}?gI8?g#T?aW)?ǓI?
J?E?d۳?GTn?8?R1#?kP?g(*T?r  r  r  r  r  r  r  r  )gD
)?g:3P?g9?g?S[?r  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?r  ğ@ _?y}D?焂Rr/?N?YjhG?a0L?4f?<@?@CH?g	ސF?g5+-#?g?g?q ?r  )g}'v?r  g*V?r  gr/0+?r  g[8	?r  gΥ?r  gY?r  g#)a?r  g?̔?r  g]ؚ?r  g|c ?r  )r`   r<  r3   crystalballr_   r   r   rf   )r  
calculatedrQ   r.   r.   r/   test_crystalball_function!  s&   r  c                  C   s  t g d} t g d}t g d}tjd| |}t||dd t g d}t dd	t jd
dg}|| }tjd| |}t||dd t t jt jt jddg}|| }tjd| |}	t||	dd t t jt jt jt jdg}|| }
tjd| |}t|
|dd t t jt jt jt jdg}|| }tjd| |}t||dd t t jt jt jt jdg}|| }tjd| |}t||dd dS )zg
    All values are calculated using the pdf formula and the integrate function
    of Mathematica
    )rs   r7  r  rs   r  )r  r  rs   r=  r  )r7  r7  r7  r7  r7  r   r  rx   )gԚh@g[&@gͪ@g2dQ@gn6-@g?ޫV&̿g BgQCRgQF\ jr   g
@gn(@r]   g?Җ)r   gMg'#@r   g('UHr~   N)r`   r   r3   r  r  r   r   )r  r  expected_0th_momentcalculated_0th_momentrH  r,   expected_1th_momentcalculated_1th_momentexpected_2th_momentcalculated_2th_momentexpected_3th_momentcalculated_3th_momentexpected_4th_momentcalculated_4th_momentexpected_5th_momentcalculated_5th_momentr.   r.   r/   !test_crystalball_function_moments"  s4   r  c                  C   sR   t dd} |  }d\}}}t|||}tt| ||}t||dd d S )Nr]   r   )ir  r
  r\  rx   )	r3   r  rA   r`   r<  r   r   r_   r   )cbr  r	  r
  r
  rW   r  r.   r.   r/   test_crystalball_entropyM"  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 )Nr  )r  dispxtolftol)r"   )r   x0r  r  r.   r.   r/   rB  o"  s   z&test_invweibull_fit.<locals>.optimizer)r   r  r]   r  r0  r   r  r   r~   r   rX   r9  @   c   )r   rB  g`?r  rx   g [@N)r.   r   )r`   r   r3   r
  r   r   )rB  rW   ry  r[   r\   r.   r.   r/   test_invweibull_fitX"  s   
r  ))r   r  g7Ըh?)r   r  gz]r>)r   g     "@goBڱ9)rf  r  g$=cC;c                 C       t j| |}t||dd d S rv   )r3   r
  r   r   )rW   ry  rQ   rE  r.   r.   r/   test_invweibull_sfz"  s   r  zp, c, expected)ro   r  g9?)geK<r~   g@c                 C   r  rv   )r3   r
  r  r   )rT  ry  rQ   rE  r.   r.   r/   test_invweibull_isf"  s   r  z	df1,df2,x)r   r  r7  r  r   r  r  rw  r  c                 C   sh   d}t j|| |}t j|| ||}t||dd t j|| |}t j|| ||}t||dd d S )Nr   r3  rx   r  )r3   r  rf   r  r   r_   )df1df2rW   r!  expected_cdfcalculated_cdfr{   calculated_pdfr.   r.   r/   test_ncf_edge_case"  s   
r  c                  C   s"   t jddd} t| ddd d S )Nr]   r9  r   g     `E@r3  rx   )r3   r  rB  r   )r  r.   r.   r/   test_ncf_variance"     r  c                  C   s.   t jdddd} d}t|tj| dd d S )Nr  r9  rx  gffffff>@g&4I,)?)decimals)r3   r  rf   r   r`   round)	scipy_val	check_valr.   r.   r/   test_ncf_cdf_spotcheck"  s   r  r  z(On some 32-bit the warning is not raisedc                     sx   t ddd} d| d< d tt tjj| g R  } fdd| D }W d    n1 s0w   Y  t|| d S )Nr   r   r&  r_  )rU   r]   r~   r   r   c                    s    g | ]}t jj|g R  qS r.   )r3   r  r   )r:   xiparr.   r/   r<   "  s     z,test_ncf_ppf_issue_17026.<locals>.<listcomp>)	r`   r<  r   r  rX  r3   r  r   r   )rW   r\  q0r.   r  r/   test_ncf_ppf_issue_17026"  s   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   r]   r]   r   r   r   r   r   r   r   r~   r~   r~   r~   r~   r9  r9  r9  r9  r  r  r  r   r   r  r   binsr7  r  r  {   r|  r!  )
r`   r   r   	histogramr3   r@   templaterH  r   norm_template)rh   r  r   norm_histogramr.   r.   r/   r  "  s   
zTestHistogram.setup_methodc                 C   s   t g d}t g d}t| j|| t| jdd t| jdd t| jdd t| jdd t d	d
d}t| j|t	j
j|ddddd d S )Nrt   ro   r7  r  rs   r  r  r  r=  r  r8        @ra  r  r  r  r        !@r  r~  )rt   rt   r1  r1  {Gz?r  Q?r  {Gz?r  r  r  r  r  r  r  r  r  rt   rt   r  r  r  r  rt   r/  r   r]   rX   r7  r  rZ   rU   rx   )r`   r   r   r   r  r_   r   r<  r  r3   rH  )rh   r  
pdf_valuesrW   r.   r.   r/   r6  "  s   
zTestHistogram.test_pdfc                 C   s   t g d}t g d}t| j|| t| j|dd |dd  t ddd}t| j| j|| t ddd}t| j| j|| t d	dd
}t| j|t	j
j|ddddd d S )Nr  )rt   rt   rt   r  r1  r  r  
ףp=
?Q?{Gz?rO  ro   r  (\?RQ?=
ףp=?)\(?r!  r7  r7  r]   r   r7  r  rY   rt   r   rX   r  rZ   rU   rx   )r`   r   r   r   r  rf   r   r<  r  r3   rH  )rh   r  
cdf_valuesrW   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$kd%| dd	 tt|d&kd| dd	 tt|d&kd| dd	 tt|d&kd d S )'Nr  r  r   r7  rt   rs   r1  r  rx   r  r  r  r  rU   r  r  r=  r 	  r  r	  r8  rO  r  r  ro   ra  r  r  r	  r  r	  r  r	  r  r	  r  r!  r  )r  r   r   r`   rL  r   )rh   r
  r  r.   r.   r/   r/  #  s(   zTestHistogram.test_rvsc                 C   s6   t dD ]}t| j|tdd|dd qd S )Nr   r7  r  r  rx   )r  r   r  r  r3   rH  r  r]  r.   r.   r/   rv  #  s
   zTestHistogram.test_munpc                 C   s$   t | j tjjddddd d S )Nr7  r  rZ   r  rx   )r   r  rA   r3   rH  rl   r.   r.   r/   rP  !#  s   

zTestHistogram.test_entropyN)	r   r   r   r  r6  r{  r/  rv  rP  r.   r.   r.   r/   r  "  s    r  c                  C   s   ddgg d} }t j| |fdd}tj|ddgddg | dks(J t j| |fdd}tj|ddgd	 | d
ksEJ d}tjt	|d t | |f}| d
ks^J W d    n1 shw   Y  t | g df}| dks~J d S )Nr   )r   r   r  F)rq  ro   r  r  Tg'^P?g     H@z(Bin widths are not constant. Assuming...r   r	  )
r3   r@   r`   rC  r   r_   rH  r   r  rX  )countsr  r;   rb  r.   r.   r/   test_histogram_non_uniform&#  s   r	  c                   @   s6   e Zd Zdd Zejdddgdd Zdd	 Zd
S )TestLogUniformc                 C   s   t jd}tdd}|jd|d}t jd}tdd}|jd|d}t|| t jt 	|dd\}}d|
   krK|   krKd	ksNJ  J t t |d
 dks\J d S )N   0o[ r  r   r  r   rX   r  rn  iL  r   )r`   r   r   r3   
loguniformr   
reciprocalr   r  log10r  r#  r   rH  )rh   r   r  r   rv2r   r-  r   r.   r.   r/   
test_alias>#  s   
. zTestLogUniform.test_aliasr   r#  r  c                 C   sn   t jd}tjjddd|d}tjj||d\}}}}|dks"J tjj|d|d\}}}}|dks5J d S )	Nr
	  rU   r   r   r   r"  r]   r  )r`   r   r   r3   r	  r   r   )rh   r   r   r   r,   r-   r[   r\   r.   r.   r/   test_fit_overrideO#  s   z TestLogUniform.test_fit_overridec           
      C   s   t jd}d\}}t||}|jdddd}t|||| |j	dd}t|||| dt 
dd	 }||}t|d d
 |dd   d || t |t |  }	t| |	 d S )Nl   eVi
P )gN~hgZbtir   r   r   r  r/  i8r  r   rX   )r`   r   r   r3   r	  r  r   rf   r   r   r   r_   rr  r   )
rh   r   r,   r-   r;   rf   r   rW   r_   r   r.   r.   r/   test_overflow\#  s   
zTestLogUniform.test_overflowN)	r   r   r   r	  r   r   r   r	  r	  r.   r.   r.   r/   r		  =#  s
    
r		  c                   @   s  e Zd Zdd Zejdddgddgdd	ggd
d Zejdddgdd Zejdg ddd Z	ejdg ddd Z
ejdg ddd Zejdg ddd  Zejdg d!d"d# Zejdg d$d%d& Zejdg d'd(d) Zd*S )+	TestArgusc                 C   s2   t jjdddd}tt d | dd d S )Nr!  r   E  r   r   r:  )r3   argusr   r   r   r  r.   r.   r/   test_argus_rvs_large_chit#  s    z"TestArgus.test_argus_rvs_large_chizchi, random_staterU   r	  r     r     c                 C   s6   t jj|d|d}t |d|f\}}t|dk d S )Nr   r   r	  r  r3   r	  r   r  r   )rh   r}  r   rW   r   rT  r.   r.   r/   r/  y#  s   zTestArgus.test_rvsr}  r  r  c                 C   s6   t jj|ddd}t |dd \}}t|dk d S )Nr   ie r   c                 S   s   dd| d  d  S )Nr   r]   r  r.   r   r.   r.   r/   rH   #  r=   z.TestArgus.test_rvs_small_chi.<locals>.<lambda>r  r	  )rh   r}  rc  r   rT  r.   r.   r/   test_rvs_small_chi#  s   zTestArgus.test_rvs_small_chizchi, expected_mean))r   g щi?)rX   g.憃?)r  g\paP?)r  g	?)r  g,6?c                 C   s"   t jj|dd}t||dd d S )Nr   rG  r   rx   )r3   r	  r   r   )rh   r}  expected_meanr  r.   r.   r/   r  #  r  zTestArgus.test_meanzchi, expected_var, rtol))r   gLH'B?r   )rX   go$?r  )r  g
=>rh  )r  g2W>rh  )r  gb~P>rh  c                 C   s"   t jj|dd}t|||d d S )Nr   rG  rx   )r3   r	  rB  r   )rh   r}  expected_varry   r  r.   r.   r/   r  #  r  zTestArgus.test_varzchi, expected, rtol))r   gwM?r3  )ro   gj?r3  )rU   gHEA`!?r3  )rq   gcف>rw   )r  gF=r3  )r  g߹Q#B=r3  )r  g0ޟ<r3  )r  g*W%:rw   c                 C   s   t t|||d d S r  )r   r    )rh   r}  rQ   ry   r.   r.   r/   test_argus_phi_small_chi#  s   
z"TestArgus.test_argus_phi_small_chizchi, expected))ro   )g-\/?g+p7c?g5Ϧ\?)r  )g
f?gi{?ٸ?gZ@7?)rU   )gB	?g]?gR{?)rq   )glͅw?g,?g[Z=?)r  )gz,?g]?gѪ1?)r  )g8<?gE-?gI?)r  )g~7?g7B.?g9?)r  )g;?g9B.?g}5?c                 C   *   t g d}ttj|||dd d S )NrU   ro   r   r   rx   )r`   r   r   r3   r	  r_   rh   r}  rQ   rW   r.   r.   r/   test_pdf_small_chi#     zTestArgus.test_pdf_small_chi))ro   )gQ߹?e?grJ,?g򺗄?)r  )gΎd?g?gh?)rU   )g|
o?gvb?g+@?)rq   )g̈́On?ge?gC|[3?)r  )g!?m?g{jiH?gu53?)r  )g~m?g0-.?g3?)r  )g~m?g7;B.?gŗ3?)r  )g~m?g9B.?gŗ3?c                 C   r	  )Nr	  r3  rx   )r`   r   r   r3   r	  r   r	  r.   r.   r/   test_sf_small_chi#  r!	  zTestArgus.test_sf_small_chi))ro   )g+&?gk?gμm/?)r  )g?CL\f?g^N?g]AͭR?)rU   )ga>$?g;Lf?gaW?)rq   )gx?g 43n?gwY?)r  )go7🤎?g
+-oGn?gIQ9Y?)r  )gT?gGn?g@̋Y?)r  )gU?g{Gn?giG͋Y?)r  )gDU?g {Gn?gH͋Y?c                 C   r	  )Nr	  r  rx   )r`   r   r   r3   r	  rf   r	  r.   r.   r/   test_cdf_small_chi#  r!	  zTestArgus.test_cdf_small_chi))ro   )gQ)?g6{?r  )gB`"۹?)g?g8%?r  )rU   )g388?gV%?r   )rq   )g*j?gRS%?r   )r  )g!|?gZ%?r   )r  )gy[|?gG%?r   )r  )g"3|?gW%?r   )r  )g!3|?gW%?r   c                 C   s"   t jj |dd}t|||d d S )Nr  r  rx   )r3   r	  r   )rh   r}  rQ   ry   r.  r.   r.   r/   test_stats_small_chi#  rP  zTestArgus.test_stats_small_chiN)r   r   r   r	  r   r   r   r/  r	  r  r  r	  r 	  r"	  r#	  r$	  r.   r.   r.   r/   r	  s#  sT    

	


	






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	dd Z
ejdg ddd Zejjddejdg dejdg dejdg ddd Zejdg dejdg ddd ZdS )TestNakagamic                 C   s$   d}d}t j||}t|d d S )Nr  r  gM+)r3   nakagamir   r   )rh   r/  rW   r  r.   r.   r/   r  #  s   zTestNakagami.test_logpdfc                 C   sD   d}d}t j||}t|ddd t j||}t||dd d S )Nr  r8  g"S+:r   rx   )r3   r&	  r   r   r  )rh   r/  r  r   rk  r.   r.   r/   rZ  #  s   zTestNakagami.test_sf_isfzm, ref))r~   g|Bd븿)ro   r  )rX   g/ۿc                 C   r  )Ng^~z=rx   r   r3   r&	  rA   rh   r  ra  r.   r.   r/   rP  $  r  zTestNakagami.test_entropy))r^  g}Ô%I)r  gq_)g    ScAgB4U)g    cAgu1U)r  gb>%)r  gWҙ\c                 C   s   t tj|| d S rj   r'	  r(	  r.   r.   r/   test_extreme_nu$$  s   zTestNakagami.test_extreme_nuc                 C   s0   t tjdsJ t tjdsJ d S )Nr  r^  )r`   rG  r3   r&	  _entropyrl   r.   r.   r/   test_entropy_overflow+$  s   z"TestNakagami.test_entropy_overflowznu, ref))r  g2H?)r  g:U?)r  g>c                 C   r  r  )r   r3   r&	  r   )rh   r/  ra  r.   r.   r/   r  /$  s   
zTestNakagami.test_meanz+Fit of nakagami not reliable, see gh-10908.r  r/  )r  r  r  r[   )rr   rX   #   r\   )r  r~   r  c           
         s   d t jj |||ddt j\}}}t||dd t||dd t||dd fdd} fdd	} fd
d}	t||||ddd t||||ddd t|	|||ddd d S )NrY   9  r   r/  r[   r\   r   r  rx   c                    s<   d|  d t d |   d|  |d  t  |   S )Nr   r   r]   r`   rL  r/  r[   r\   )r  r.   r/   	dlogl_dnuJ$  s   z(TestNakagami.test_fit.<locals>.dlogl_dnuc                    sN    dt |  td|   dt t | |   t | | d  S )Nr   r   r]   )r`   rr  r   rL  r0	  r
  r  r.   r/   
dlogl_dlocN$  s
   z)TestNakagami.test_fit.<locals>.dlogl_dlocc                    s2   d  |  | d|  |d  t | d   S )Nr   r]   r   r/	  r0	  r2	  r.   r/   dlogl_dscaleS$  s    z+TestNakagami.test_fit.<locals>.dlogl_dscaler   r  r   )r3   r&	  r   r   r   )
rh   r/  r[   r\   nu_estloc_est	scale_estr1	  r3	  r4	  r.   r2	  r/   rr  ;$  s   zTestNakagami.test_fitc                 C   s   d}d}t jj||||dd}t jj||d\}}}t|}	tt|| d }
t||dd t||	dd t||
dd d S )	Nro   rY   r-	  r.	  r?  r]   r\  rx   )	r3   r&	  r   r   r`   r  r  r   r   )rh   r[   r\   r/  rS  r  r5	  r6	  r7	  loc_theo
scale_theor.   r.   r/   test_fit_nu[$  s   
zTestNakagami.test_fit_nuN)r   r   r   r  rZ  r   r   r   rP  r)	  r+	  r  r  rr  r:	  r.   r.   r.   r/   r%	  #  s0    


r%	  c                   @   rn  )TestWrapCauchyc                 C   sr   t ddgddgg}t dgdgg}tj||}|jdks"J dd	 t ||fD }t| |d
d d S )NQ?rK  ro   r   r7  r=  r  c                 S   s   g | ]\}}t j||qS r.   )r3   
wrapcauchyrf   )r:   rk  r  r.   r.   r/   r<   y$  s    z>TestWrapCauchy.test_cdf_shape_broadcasting.<locals>.<listcomp>r   rx   )	r`   r   r3   r=	  rf   r'  nditerr   r  )rh   ry  rW   rT  scalar_valuesr.   r.   r/   test_cdf_shape_broadcastingq$  s   z*TestWrapCauchy.test_cdf_shape_broadcastingc                 C   s"   t jtjd}t|ddd d S )Nr<	  ro   r3  rx   )r3   r=	  rf   r`   ra   r   rk  r.   r.   r/   test_cdf_center}$  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 )Nr7  r=  r   r   r   r]   )r3   r=	  rf   r   r`   arctantanra   )rh   rk  rl  ry  rT  crr.   r.   r/   r?  $  s   (6zTestWrapCauchy.test_cdfN)r   r   r   r@	  rA	  r?  r.   r.   r.   r/   r;	  o$  s    r;	  c                  C   sV   G dd dt j} | dd}ttdd |  W d    d S 1 s$w   Y  d S )Nc                   @   rg  )z/test_rvs_no_size_error.<locals>.rvs_no_size_genc                 S   r   r   r.   rl   r.   r.   r/   _rvs$  r  z4test_rvs_no_size_error.<locals>.rvs_no_size_gen._rvsN)r   r   r   rE	  r.   r.   r.   r/   rvs_no_size_gen$  r  rF	  rvs_no_sizer  z_rvs\(\) got (an|\d) unexpectedr   )r3   r?   r  r   r   )rF	  rG	  r.   r.   r/   test_rvs_no_size_error$  s
   

"rH	  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  )$skip_test_support_gh13294_regressionr   r   r  r3   r)  r?   r   supportr   r`   r   )r  r  r;   a0b0r   r!  a1b1r,   r-   r.   r.   r/   test_support_gh13294_regression$  s"   

rP	  c                  C   sX  t jg dg d\} }ttj tj tj tjg}ttjtjtjtjg}t| | t|| | j|jks<J |j|jksDJ t jg g \}}tg tg }}t|| t|| |j|jksjJ |j|jksrJ t jg ddg\}}	tdtjg }
tdtjg }t||
 t|	| |j|
jksJ |	j|jksJ d S )N)r   r   r   r   )r   r   r   r   r   r   )	r3   rH  rK	  r`   r   r   r   r   r'  )rL	  rM	  ex_a0ex_b0rN	  rO	  ex_a1ex_b1r%  r  ex_a2ex_b2r.   r.   r/   ,test_support_broadcasting_gh13294_regression$  s(    





rW	  c                  C   sn   ddg} dgdgdgg}t tj| |ddgddgddgg td} td}tj| |jdks5J d S )	Nrt   r7  rs   r  r=  r  r8   r  )r   r3   rH  rB  r`   r  r'  rZ   r.   r.   r/   *test_stats_broadcasting_gh14953_regression$  s   &

rX	  )gn!	g:I"<)gQ	@gE?c                 C   s*   t tj| | t tj|  | d S rj   )r   r3   cosinerf   r   )rW   rQ   r.   r.   r/   test_cosine_cdf_sf$  s   rZ	  ))r  gkM6O)r  g0ӭ!	)r>  g;'u(@c                 C   s*   t tj| | t tj| |  d S rj   )r   r3   rY	  r   r  )rT  rQ   r.   r.   r/   test_cosine_ppf_isf$  s   r[	  c                  C   s$   t jtj tjg} t| d d S )NgrB)r3   rY	  r   r`   ra   r
   )r  r.   r.   r/   test_cosine_logpdf_endpoints$  s   r\	  c                  C   sT   dd t D } dd tD }| |ksJ dd tD }dd tD }||ks(J d S )Nc                 S   s   h | ]\}}t |tr|qS r.   )r)  rD   r:   r  r   r.   r.   r/   	<setcomp>$  s    
z*test_distr_params_lists.<locals>.<setcomp>c                 S      h | ]\}}|qS r.   r.   r]	  r.   r.   r/   r^	  $  r=   c                 S   r_	  r.   r.   r]	  r.   r.   r/   r^	  $  r=   c                 S   r_	  r.   r.   r]	  r.   r.   r/   r^	  $  r=   )r   r   r   r   )discrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamesr.   r.   r/   test_distr_params_lists$  s   rd	  c                   C   sB   t jjddd t jjddddksJ t jdddksJ d S )Nr   rT   r3  r   )r  r,   r  )r3   r  _statsr  r  r.   r.   r.   r/   test_moment_order_4$  s   rf	  c                
   @   s   e Zd Zejdd Zejdg ddd Zejdg dd	d
 Z	ejdej
ddejjdej
ddejjdej
ddejjdgdd ZdS )TestRelativisticBWc                 C   r  )a&  Sample data points for pdf computed with CERN's ROOT

        See - https://root.cern/

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

        pdf calculated for Z0 Boson, W Boson, and Higgs Boson for
        x in `np.linspace(0, 200, 401)`.
        z-data/rel_breitwigner_pdf_sample_data_ROOT.npyzx,pdf,rho,gammar  r  rt  r.   r.   r/   ROOT_pdf_sample_data%  s   z'TestRelativisticBW.ROOT_pdf_sample_datazrho,gamma,rtol))qVEB@gj+@rR  )FC@Gz @r3  )ND@_LU?ru  c                 C   sN   ||d |k|d |k@  }|d |d }}t |tjj|||d|d d S )Nrhor  rW   r_   rG  rx   )r   r3   rel_breitwignerr_   )rh   rh	  ro	  r  ry   r   rW   r_   r.   r.   r/   test_pdf_against_ROOT'%  s   


z(TestRelativisticBW.test_pdf_against_ROOTzrho, Gamma, rtol))ri	  rj	  ru  )rk	  rl	  ru  )rm	  rn	  g&.>c           	      C   s\   dd }t ddd}tjj|||d}tjj|||d}|||| |}t|||d d S )Nc                 S   sx   t |d |d |d   }dt d | | | t jt |d |   }|| d |d  d |d |d    S r  )r`   r  ra   )Er	  Gammar  rT   r.   r.   r/   r_   @%  s
   (zFTestRelativisticBW.test_pdf_against_simple_implementation.<locals>.pdfr  r  rX   rG  rx   )r`   r<  r3   rp	  r   r_   r   )	rh   ro	  rs	  ry   r_   rT  rW   r   ra  r.   r.   r/   &test_pdf_against_simple_implementation8%  s   z9TestRelativisticBW.test_pdf_against_simple_implementationz	rho,gammari	  rj	  r  rk	  rl	  rm	  rn	  c                 C   s   d}t j|}tjj||d|d}tjj|dd}t|d |d f||fdd |d	 dks1J tjj|d|d
}t|d |dd |d	 |d fd|fksQJ dS )zpTests fit for cases where floc is set.

        `rel_breitwigner` has special handling for these cases.
        l   s;
rl# r   )r\   r   r   r   r   r]   r  rx   r   r}  rq   N)r`   r   r   r3   rp	  r   r   r   )rh   ro	  r  r   r   r   r   r.   r.   r/   test_fit_flocL%  s    z TestRelativisticBW.test_fit_flocN)r   r   r   r   r  rh	  r   r   rq	  rt	  r  r  r   ru	  r.   r.   r.   r/   rg	  %  s.    






rg	  c                   @   rQ  )TestJohnsonSUr  )r  r  r  r  g={?g?5mV>gn?g\}\1@)g`fo@g$ں_@r   r   gvUgN<fj?gwCg~l
@c                 C   s4   t jj |d d ddi}t||dd  dd d S )Nr   r  r  r3  rx   )r3   rT  r   )rh   r  r   r.   r.   r/   test_moment_gh18071m%  s   z!TestJohnsonSU.test_moment_gh18071N)r   r   r   r   r   r   rw	  r.   r.   r.   r/   rv	  l%  s    rv	  c                   @   sd   e Zd Zdd Zejdddgejdddgejdddgejdddgd	d
 ZdS )TestTruncParetoc                 C   sT   d\}}t dd}t|||}t||t|| }t|| d S )N)?333333@ry	  rz	  )r`   r<  r3   truncparetor_   r  rf   r   )rh   r-   ry  rW   r   ra  r.   r.   r/   r6  }%  s
    zTestTruncPareto.test_pdfr   TFrz  r  rl  c                 C   s   t jd}d\}}}}	tj||||	d}
|
jd|d}i }|r$||d< |r*|	|d< |r0||d< |r6||d	< |rd|rd|rd|rdd
}tjt|d tjj	|fi | W d    d S 1 s]w   Y  d S t
tj|fi | d S )Nl   Z#Lm )ry	  rz	  r   r  rZ   r   r   r   r   r   r   r   r   )r`   r   r   r3   r{	  r   r   r   r   r   r   )rh   r   rz  r  rl  r   r-   ry  r[   r\   r;   r   r   rb  r.   r.   r/   rr  %  s&   "zTestTruncPareto.test_fitN)r   r   r   r6  r   r   r   rr  r.   r.   r.   r/   rx	  |%  s    rx	  c                   @   rg  )
TestKappa3c                 C   s.   dt jdd }t jdd}t|| d S )Nr   ro   g     j@)r3   kappa3rf   r   r   )rh   sf0r  r.   r.   r/   r  %  s   zTestKappa3.test_sfN)r   r   r   r  r.   r.   r.   r/   r|	  %  r  r|	  r  ))r}	  NNNN)rg  NNNN)r  NNNN)r  NNNN)r  NNNNc                 C   s   | \}}}}}t d}|pd}|pd}|pd}|pd}tt|}tt| }|| }	t ||}
|	|	|
}t	||
||d dt ||d }
|	|	|
}t	||
||d d S )	Nro   iir   r  r  r   r  )
r`   r	  r  r3   r   r   rw  r   r  r   )r  r  lp1lp2r   ry   lpmr;   rD  dist_frozenra  r   r.   r.   r/   test_sf_isf_overrides%  s   	

r	  rj   )NF(  r_  rU  r  r  r  pathlibr   r  r  rQ  numpy.testingr   r   r   r   r   r   r	   r
   r   r   r   r  r&  r`   r   r   numpy.lib.recfunctionsr   r2   r   scipy._lib._utilr   rz  r   r   r   r   scipy.statsr3   !scipy.stats._distn_infrastructurer   scipy.stats.distributionsscipy.specialr   r   r   scipy.stats._distr_paramsr   r   test_discrete_basicr   r   scipy.stats._continuous_distnsr   r    scipy.optimizer!   r"   r#   	itertoolsr$   flagsoptimizer  rT  r  rJ	  r0   r5   rR   rS   r   r  r   r   r  r  rA  rh  ro  rt  r|  r  r  r  r  r  r  r6  r;  rR  r\  rf  rn  r  r  r  r  r  r  r  r3  rQ  r[  r]  r  r  r  r  r  r  r  r  r.  r4  r<  rW  re  rp  ry  r  r  r  r  r  r  r  r  ra   rH  r  rI  rV  r]  r`  rw  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r*  r2  r<  rB  rH  rQ  rU  r^  ra  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r  r  r  r  r  r  r  r  r  r   r"  r%  r(  r*  r+  r,  r.  r1  r4  r<  r=  r?  r@  rA  rG  r?   rH  rM  rQ  rT  rU  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r	  r		  r	  r%	  r;	  rH	  rP	  rW	  rX	  rZ	  r[	  r\	  rd	  rf	  rg	  rv	  rx	  r|	  r	  r.   r.   r.   r/   <module>   s   , J"
J	
2H KFD**D">#  @ $[X(% wX?* $ p9W<37+f %-5		$ v22: 3 kS*      5
 p i ;A%E>h  #^U( E	
&
	
(





	x;	,G.
"

a6y 

Y&