a
    Qer                    @   s  d Z ddlZddlZddlZddlZddlmZ ddlZddlZddl	Z	ddl
mZmZmZmZmZmZmZmZmZmZ ddlZddlmZ ddlZddlZddlmZmZ ddlmZ ddlmZ dd	l m!Z! dd
l"m#Z#m$Z$m%Z%m&Z& ddl'm(Z( ddl)m*Z* ddl+Zddl,m-Z-m.Z.m/Z/ ddl0m1Z1m2Z2 ddl3m4Z4m5Z5 ddl6m7Z7m8Z8 ddl9m:Z:m;Z; ddl<m=Z= ej>j?dkZ@ej	dkoe	A dkZBddgZCdddZDdd ZEdd ZFG dd dZGddd ZHd!d" ZIejJKd#g d$d%d& ZLG d'd( d(ZMG d)d* d*ZNG d+d, d,ZOG d-d. d.ZPG d/d0 d0ZQG d1d2 d2ZRG d3d4 d4ZSG d5d6 d6ZTG d7d8 d8ZUG d9d: d:ZVG d;d< d<ZWG d=d> d>ZXG d?d@ d@ZYG dAdB dBZZG dCdD dDZ[G dEdF dFZ\G dGdH dHZ]G dIdJ dJZ^G dKdL dLZ_G dMdN dNZ`G dOdP dPZaG dQdR dRZbG dSdT dTZcG dUdV dVZdG dWdX dXZeG dYdZ dZZfG d[d\ d\ZgG d]d^ d^ZhG d_d` d`ZiG dadb dbZjG dcdd ddZkG dedf dfZlG dgdh dhZmG didj djZnG dkdl dlZoG dmdn dnZpG dodp dpZqG dqdr drZrG dsdt dtZsG dudv dvZtG dwdx dxZuG dydz dzZvG d{d| d|ZwG d}d~ d~ZxG dd dZyG dd dZzG dd dZ{dde|ddej}   dde|ddej}   dde|ddej}   dde|ddej}   dde|ddej}   g	fde|ddej}  dde|ddej}   dde|ddej}   d dde|ddej}   d dde|ddej}   d g	fdde|dej}  ddde|dej}   ddde|dej}   ddde|dej}   ddde|dej}   ddde|dej}   ddde|dej}   dgfgZ~G dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG ddĄ dăZG ddƄ dƃZG ddȄ dȃZG ddʄ dʃZG dd̄ d̃ZG dd΄ d΃ZddЄ ZG dd҄ d҃ZG ddԄ dԃZG ddք dփZG dd؄ d؃ZG ddڄ dڃZG dd܄ d܃ZG ddބ dރZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZG dd dZdd Zdd Zdd  ZejJje@dddd Zdd Zdd Zd	d
 Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZejJKdg ddd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( ZejJKd)g d*d+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 ZÐd5d6 ZĐd7d8 ZejJKd9d:ed;d<gfd=ed>d?gfd@edAdBgfdCedDdEgfgdFdG ZƐdHdI ZǐdJdK ZȐdLdM ZɐdNdO ZejJKdPg dQdRdS ZejJKdTg dUdVdW ZejJKdXg dYdZd[ Z͐d\d] ZejJKdPg d^d_d` Zϐdadb ZG dcdd dde(jуZG dedf dfe(jуZG dgdh dhe(jуZG didj dje(jуZG dkdl dlZG dmdn dnZejJje@doddpdq Zؐdrds Zِdtdu Zڐdvdw Zېdxdy Zܐdzd{ Zݐd|d} Zސd~d Zߐdd Zdd Zdd Zdd Zdd ZejJKdPg 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de5e2 dd Zdd Zdd ZejJKdTddgdd ZejJKdXg ddd Zdd Zdd ZdÐdĄ ZG dŐdƄ dƃZG dǐdȄ dȃZG dɐdʄ dʃZdS (  z!
Test functions for stats module
    N)Path)
assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_assert_warnsassert_array_lesssuppress_warningsIS_PYPY)raises)	typecodesarray)rec_append_fields)special)check_random_state)IntegrationWarningquad	trapezoidcumulative_trapezoid)
argsreduce)xlogy	polygammaentr)distcontinvdistcont   )distdiscreteinvdistdiscrete)FitDataError
_argus_phi)rootfmin)productdarwinx86_64tukeylambdapearson3c                 C   s,   |d u r|  d| }t t| ||d d S )Nz does not have attribute msg)r   hasattr)abr*    r.   X/var/www/sunrise/env/lib/python3.9/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattr4   s    r0   c                   C   s   t tjjd d S )NZf_gen)r0   scipystatsdistributionsr.   r.   r.   r/   test_api_regression:   s    r4   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   s   g | ]}|d  qS r   r.   .0distr.   r.   r/   
<listcomp>A       z0test_distributions_submodule.<locals>.<listcomp>c                 S   s   g | ]}|d  qS r5   r.   r6   r.   r.   r/   r9   B   r:   )rv_discreterv_continuousrv_histogramentropytrapzc                 S   s   t | d S )N<)str
startswithsr.   r.   r/   <lambda>I   r:   z.test_distributions_submodule.<locals>.<lambda>)setr1   r2   r3   __all__r   r   filter)actualZ
continuousZdiscreteotherexpectedr.   r.   r/   test_distributions_submodule?   s    rL   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ejd(d)ej dejgejd*g d+d,d- Zd.d/ Zejjejd(d)ej d0ej gd1d2 Zejd3d4dgd5d6 Zd7S )8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   )r2   vonmisesr   pdfnppirN   LrD   rQ   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 )NrT   r   rW   )r2   rX   r   cdfrZ   r[   r\   r.   r.   r/   check_vonmises_cdf_periodicV   s    zHTestVonMises.test_vonmises_periodic.<locals>.check_vonmises_cdf_periodicr   r   rR   r.   )selfrN   rQ   r_   ra   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   r2   Zvonmises_liner,   rZ   r[   r-   rb   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         ?)r2   rX   r   r`   )rb   r^   r.   r.   r/   test_vonmises_numericalg   s    
z$TestVonMises.test_vonmises_numericalzx, kappa, expected_pdf))rO   {Gz?g|65?)rO         9@g?U?)rO   rg   g"?)       @rj   gDfI?)rl   rk   g1<)rl   rg           c                 C   s    t j||}t||dd d S NV瞯<rtol)r2   rX   rY   r   )rb   rQ   kappaexpected_pdfrY   r.   r.   r/   test_vonmises_pdfu   s    zTestVonMises.test_vonmises_pdfzkappa, expected_entropy))r   gA	?)   g,eޞ?)rS   gBb9d22)  g
G )  gc                 C   s   t j|}t||dd d S NvIh%<=rp   )r2   rX   r>   r   )rb   rr   Zexpected_entropyr>   r.   r.   r/   test_vonmises_entropy   s    z"TestVonMises.test_vonmises_entropyc                 C   s   t td}tj|}tj|}tj|}tjddddj|d}tjddtj ddj|d}tjdddtj t | d dj|d}t	||dd t	||dd d S )	NZvon_mises_rvsr   r   rT   random_staterW   ro   atol)
abshashrZ   randomdefault_rngr2   rX   rvsr[   r   )rb   seedZrng1Zrng2Zrng3Zrvs1rvs2Zrvs3r.   r.   r/   test_vonmises_rvs_gh4598   s    z%TestVonMises.test_vonmises_rvs_gh4598zx, kappa, expected_logpdf))rO   rj   gEJ?)rO   rk   goι?)rO   rg   g0,)rl   rj   gdty)rl   rk   gʹw[A)rl   rg   gc                 C   s    t j||}t||dd d S rn   )r2   rX   logpdfr   )rb   rQ   rr   Zexpected_logpdfr   r.   r.   r/   test_vonmises_logpdf   s    z!TestVonMises.test_vonmises_logpdfc                 C   s  t jd}|dd \}}}tj||ddd }t|d t |jt j	sVJ ||dt j
  f}tj||djd	d g|R  }t|d t |jt j	sJ ||dt j
  f}tj||djd
d g|R ddi}tt ||dt j
   t |jt jsJ dS )a   
        Test that the vonmises expectation values are
        computed correctly.  This test checks that the
        numeric integration estimates the correct normalization
        (1) and mean angle (loc).  These expectations are
        independent of the chosen 2pi interval.
           kD +xNn    rR   rU   rr   c                 S   s   dS Nr   r.   rQ   r.   r.   r/   rE      r:   z3TestVonMises.test_vonmises_expect.<locals>.<lambda>r   rW   c                 S   s   dS r   r.   r   r.   r.   r/   rE      r:   c                 S   s   t d|  S )Ny              ?)rZ   expr   r.   r.   r/   rE      r:   Zcomplex_funcN)rZ   r   r   r2   rX   expectr   
issubdtypedtypeZfloatingr[   angleZcomplexfloating)rb   rngrU   rr   lbresZboundsr.   r.   r/   test_vonmises_expect   s"    
 
z!TestVonMises.test_vonmises_expectrvs_locrW   	rvs_shape)r   rS       חAfix_locTF	fix_shapec                 C   sp   |r|rt d tjd}tjj|d||d}ddi}|rF||d< |rR||d< ttj|tjj	fi | d S )	NzNothing to fit.r   rv   )sizerU   r|   fscaler   flocf0)
pytestskiprZ   r   r   r2   rX   r   _assert_less_or_close_loglikennlf)rb   r   r   r   r   r   datakwdsr.   r.   r/   test_fit_MLE_comp_optimizer   s     
z(TestVonMises.test_fit_MLE_comp_optimizerrU         	kappa_tol))rO   皙?)      Y@rj   )g     j@rj   c                 C   s   t jd}|\}}tj||djd|d}tj|\}}}	|	dksJJ t t |t 	|g}
t t |t 	|g}t 
|
|}t|d|dd t|||d d S )	Nr   r   順 r{   r   r   r~   rq   rp   )rZ   r   r   r2   rX   r   fitr   cossinZarccosdotr   )rb   r   rU   r   rr   tolr   	kappa_fitloc_fit	scale_fitZloc_vecZloc_fit_vecr   r.   r.   r/   test_vonmises_fit_all   s    z"TestVonMises.test_vonmises_fit_allc                 C   sr   t jd}dt j }d}tj||djd|d}tjj||d\}}}||ksTJ |dks`J t||d	d
 d S )Nr         ?rR   r   r   r{   r   r   rj   rp   )	rZ   r   r   r[   r2   rX   r   r   r   )rb   r   rU   rr   r   r   r   r   r.   r.   r/   test_vonmises_fit_shape   s    
z$TestVonMises.test_vonmises_fit_shapec                 C   sX   g d}t |}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^lsFr   r   )r   r   )
rZ   asarrayr2   rX   r   finfofloatZtinyr   r   )rb   rU   r   r   r   r   r.   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sJ t j |  k rt jk sn J d S )	Nr   rh   rR   r   r   r{      r   )	rZ   r   r   r2   rX   r[   r   r   r   )rb   r   r   r   Zshifted_datar   r   r   Zkappa_fit_shiftedZloc_fit_shifted_r.   r.   r/    test_vonmises_fit_unwrapped_data  s    

z-TestVonMises.test_vonmises_fit_unwrapped_dataN)__name__
__module____qualname__r   markparametrizerZ   r[   rc   rf   ri   rt   rz   r   r   r   xslowr   r   r   r   r   r.   r.   r.   r/   rM   N   sD   



rM   c                 K   s   |du r| j }| j|fi |}tt| | j|fi |}|||}|||}||ksltj||ddslJ d|v r|d |d ksJ d|v r|d |d ksJ 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.
    Nro   rp   r   r   r   )r   r   supertyperZ   allclose)r8   r   funcr   Zmle_analyticalZnumerical_optZll_mle_analyticalZll_numerical_optr.   r.   r/   r     s    

r   c                 C   s  ddg}| j r2t| j d}|g dd | 7 }tt|tt|}g d}tjt	dd" | j
|fi | W d    n1 s0    Y  tjtdd | 
tjg W d    n1 s0    Y  tjtdd | 
tjg W d    n1 s0    Y  tjtd	d | j
|d
d W d    n1 s@0    Y  tjtdd0 | j
|gdgt|d  R   W d    n1 s0    Y  d S )Nr   r   ,)r   f1f2r   rW   r   3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:rW   )Zextra_keywordzToo many positional arguments.r   )shapeslensplitdictziprZ   aranger   r   RuntimeErrorr   
ValueErrornaninf	TypeError)r8   paramZnshapesZ	all_fixedr   r.   r.   r/   assert_fit_warnings/  s,    0,..r   r8   )alpha	betaprimefatiguelifeinvgammainvgauss
invweibull	johnsonsblevylevy_llognormgibratpowerlognormrayleighZ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   getattrr2   r   rY   r,   r   r   rZ   r   r-   )r8   dctargsr.   r.   r/   test_supportF  s    
r   c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestRandIntc                 C   s   t jd d S N  rZ   r   r   re   r.   r.   r/   setup_methodY  s    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 )Nru      rS   r   rW   2   
AllInteger   .   r)   r   )r2   randintr   r   numpyallr   shaper   charr   
isinstanceZ
ScalarTypereprr   rb   valsvalr.   r.   r/   test_rvs\  s     zTestRandInt.test_rvsc                 C   sF   t jdd }t |dk|dk @ dd}tj|dd}t|| d S )Nr   $   ru   r   {Gz?)r   r_wherer2   r   pmfr   )rb   rN   outr  r.   r.   r/   test_pdfi  s    zTestRandInt.test_pdfc                 C   sd   t ddd}t|}t|dk|dkgd|d d d	 gd}tj|dd}t||d
d d S )Nr   r
  rS   r   ru         ?      @r   rk      decimal)	rZ   linspacer   floorselectr2   r   r`   r   )rb   rQ   rN   r  r  r.   r.   r/   test_cdfo  s
    
*zTestRandInt.test_cdfN)r   r   r   r   r	  r  r  r.   r.   r.   r/   r   X  s   r   c                   @   sT   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   s   t jd d S r   r   re   r.   r.   r/   r   x  s    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 NrR         ?r   r   r   r   r   )r2   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 )NrS   r   r   r  ro   rq   r~   r2   r  r  r   )rb   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 )NrW   rh   )r   rh   r   rm   r  )	r2   r  rZ   r   sumr   r>   r   r   )rb   r-   
expected_p
expected_hhr.   r.   r/   test_entropy  s    

zTestBinom.test_entropyc                 C   sh   t  L t dt ttjddd d ttjddd d W d    n1 sZ0    Y  d S )NerrorrW   r   np)	warningscatch_warningssimplefilterRuntimeWarningr   r2   r  meanstdre   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?r  )qr,  r-  )r2   r  ppfrb   r,  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   r+  缉ؗҜ<r}   )rZ   r   r2   r  r  poissonr   )rb   r,  r-  rQ   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}   )r2   r  r  r`   r   )rb   r,  r-  rr   r<  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   rw   +?r   r:  r}   r!  )rb   r   r.   r.   r/   test_pmf_gh15101  s    zTestBinom.test_pmf_gh15101N)r   r   r   r   r	  r$  r)  r4  r9  r=  r?  rA  r.   r.   r.   r/   r  w  s   		r  c                   @   s   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   )r2   ZarcsinerY   r   rZ   r   rb   r-  r.   r.   r/   test_endpoints  s    zTestArcsine.test_endpointsN)r   r   r   rE  r.   r.   r.   r/   rB    s   rB  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestBernoullic                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestBernoulli.setup_methodc                 C   s   t jjddd}tt|dkt|dk@  tt|dk t|jjt	d v  t jd}tt
|t t dd}tt
|tj t|jjt	d v  d S )Nr  r   r   r   r   r   r   )r2   	bernoullir   r   r   r  r  r   r  r   r  r  r  r  r.   r.   r/   r	    s     zTestBernoulli.test_rvsc                 C   st   t d}dtd dtd  }| }t|| t d}| }t|d t d}| }t|d d S )Nr         пr  rm   r  )r2   rG  rZ   logr>   r   r   )rb   r-   r'  r(  r.   r.   r/   r)    s    




zTestBernoulli.test_entropyN)r   r   r   r   r	  r)  r.   r.   r.   r/   rF    s   rF  c                   @   s   e Zd Zdd ZdS )TestBradfordc                 C   s:   d}t dd}tj||}tj||}t|| d S )NrO   )rZ   logspacer2   Zbradfordr`   r7  r   )rb   crQ   r6  xxr.   r.   r/   test_cdf_ppf  s
    zTestBradford.test_cdf_ppfN)r   r   r   rP  r.   r.   r.   r/   rJ    s   rJ  c                   @   sF   e Zd ZdZdZdd Zdd Zdd Zej	
d	g d
dd ZdS )TestChignT9;g2 >h?@c                 C   s"   t jdd}t|| jdd d S )NrR   r   ro   rp   )r2   chisfr   CHI_SF_10_4rb   rD   r.   r.   r/   test_sf  s    zTestChi.test_sfc                 C   s"   t j| jd}t|ddd d S )Nr   rR   ro   rp   )r2   rR  isfrT  r   rb   rQ   r.   r.   r/   test_isf   s    zTestChi.test_isfc                 C   s"   t jjdd}t|| jdd d S )Nrv   )df-q=rp   )r2   rR  r2  r   CHI_MEAN_1000rX  r.   r.   r/   	test_mean  s    zTestChi.test_meandf, ref))-C6?gQ(݂)r   ńjɮ9?)     @@gWr4'?)    _Bgr$h(?)}Ô%ITgs$h(?c                 C   s   t t| |dd d S rn   )r   r2   rR  r>   rb   rZ  r<  r.   r.   r/   r)    s    zTestChi.test_entropyN)r   r   r   rT  r\  rV  rY  r]  r   r   r   r)  r.   r.   r.   r/   rQ    s   rQ  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )

TestNBinomc                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestNBinom.setup_methodc                 C   s   t jjdddd}tt|dk tt|dk t|jjt	d v  t jdd}tt
|t t ddd}tt
|tj t|jjt	d v  d S r  )r2   nbinomr   r   r   r  r  r   r  r   r  r  r  r  r.   r.   r/   r	     s    zTestNBinom.test_rvsc                 C   sH   t ttjdddtjddd tjjddd}t|d d S )Ni  i  gp=
ף?r   r   )	r   rZ   r   r2   rf  logpmfr  r1   r   )rb   r  r.   r.   r/   r$  +  s
    zTestNBinom.test_pmfc                 C   s@   t jjg dddd}tt jjg dddd}t|| d S )N)r   ru   r   ru   333333@?r+  )r2   rf  logcdfrZ   rI  r`   r   )rb   r  r<  r.   r.   r/   test_logcdf_gh161593  s    zTestNBinom.test_logcdf_gh16159N)r   r   r   r   r	  r$  rk  r.   r.   r.   r/   re    s   re  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   s   t jd d S r   r   re   r.   r.   r/   r   ;  s    zTestGenInvGauss.setup_methodc                 C   s:   t dd}t |jddd|j\}}t|dkd d S )Nffffff@      ?  r   r   r|   r   Tr2   geninvgausskstestr   r`   r   rb   gigr   r-  r.   r.   r/   test_rvs_with_mode_shift>  s    z(TestGenInvGauss.test_rvs_with_mode_shiftc                 C   s:   t dd}t |jddd|j\}}t|dkd d S )N?r  ro  r   rp  r   Trq  rt  r.   r.   r/   test_rvs_without_mode_shiftE  s    z+TestGenInvGauss.test_rvs_without_mode_shiftc                 C   s:   t dd}t |jddd|j\}}t|dkd d S )NrO   皙?ro  r   rp  r   Trq  rt  r.   r.   r/   test_rvs_new_methodL  s    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 )Nro  r   rp  r   r   )r2   rr  r   rs  r`   )r-  r-   ru  r   r.   r.   r/   my_ks_checkU  s    z4TestGenInvGauss.test_rvs_p_zero.<locals>.my_ks_checkr   ry  Trw  rn  )r   )rb   r{  r.   r.   r/   test_rvs_p_zeroS  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      rW   rR   r   rp  r   rn  )r   r2   rr  r   re   r.   r.   r/   test_rvs_negative_p^  s    z#TestGenInvGauss.test_rvs_negative_pc                 C   s   t jjddddd}tt j|ddgdd dkd	 d
tddd }}t jj|dd| |d}t|t 	|| t jj
|dd| |d}t|t 	|
| d S )Nro  r   r   r   )r   r-  r-   r|   r   r   333333?TrS   rj   rR   )r-  r-   rV   )r2   rr  r   r   rs  rZ   r  rY   r   r   r`   )rb   ZigmurQ   Zpdf_igZcdf_igr.   r.   r/   test_invgaussd  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?rj   ru   rR   rh   r   )rZ   r   r  r   r2   rr  rY   )rb   vals_RrQ   r.   r.   r/   
test_pdf_Ro  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   rh   g    >Ar   rW   )r   r2   rr  rY   re   r.   r.   r/   test_pdf_zeroz  s    zTestGenInvGauss.test_pdf_zeroN)r   r   r   r   r   r   slowrv  rx  rz  r|  r~  r  r  r  r.   r.   r.   r/   rl  :  s   




rl  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   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestGenHyperbolic.setup_methodc           
      C   sl   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?rW   rW   r   rh   rn  rT   rR   r   ry   r   )rZ   r   r2   genhyperbolicr  r   rY   
rb   r  lmbdar   betar  deltar   ghrQ   r.   r.   r/   
test_pdf_r  s    
zTestGenHyperbolic.test_pdf_rc           
      C   sl   t g d}d\}}}d\}}||| || f}tj|||d}t ddd}	t||	|ddd	 d S )
N)
g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?r  r  rT   r  rR   r   ư>r   )rZ   r   r2   r  r  r   r`   r  r.   r.   r/   
test_cdf_r  s    
zTestGenHyperbolic.test_cdf_rzx, p, a, b, loc, scale, ref)
)rW   r   rn  rh   rn  g8ɹvF(;)r  rR   rn  r   r   ru   g[Ϡ?)r  rR   rn  g      ?r   r   g ✝`D;)r        ?rn  ):?r   r   gdL;)r   r  rn  r  r   r   gzK^7?)ru         rn  r  r   r   gj?)ru   r  rv     r   r   ga=vG:)   r  rv   r  r   r   g?)(   r  rv   r  r   r   g1bV?)<   r  rv   r  r   r   g?c           	      C   s*   t jj||||||d}t||dd d S NrT   dy=rp   )r2   r  r`   r   )	rb   rQ   r-  r,   r-   rU   rV   r<  r`   r.   r.   r/   test_cdf_mpmath  s    z!TestGenHyperbolic.test_cdf_mpmath))r   r  r  r   r   r   gC!,?)r   r         @      @r   r   g,Ћf?)rK  r   r  r  r   r   r  )   rW   r   rn  rh   rn  gm"چ>),  rR   rn  r   r   ru   g:;)r  r  rv   r  r   r   gw=)K   r  rv   r  r   r   g3Z0&K<c           	      C   s*   t jj||||||d}t||dd d S r  )r2   r  rS  r   )	rb   rQ   r-  r,   r-   rU   rV   r<  rS  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 )rT   )r2   r  moment)r7   ir   r  r  r.   r/   r9     s   z4TestGenHyperbolic.test_moments_r.<locals>.<listcomp>r   ru   r   ry   r   )ranger   )rb   r  r  r   r  Z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  rT   ro  r   rp  r   T)r2   r  rs  r   r`   r   )
rb   r  r   r  r  r  r   r  r   r-  r.   r.   r/   r	    s    
zTestGenHyperbolic.test_rvsc           	      C   s   t ddd}t |dt t jj d }}dt | }}| d ||f}tj|||d}t |	d|	dd	d d t j
f }t||tj||dd
d d S )Nr   r   rR   rW   r   rT   rj   Gz?r   r  r   )rZ   r  float_powerr   float32epssqrtr2   r  r7  newaxisr   rY   t)	rb   rZ  r   r  r  r  r   r  rQ   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   rT   rj   r  r   r  r   )rZ   r   r  r  r2   r  r  r7  r  r   rY   cauchy)	rb   r  r   r  r  r  r   r  rQ   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  rR   )r   r   r   rT   rK  r  r   r   r   dy=r   )rZ   r  r   r  r  r2   r  r  r   rY   laplace)	rb   rU   r  r  r   r  r   r  rQ   r.   r.   r/   test_pdf_laplace   s    
z"TestGenHyperbolic.test_pdf_laplacec           	   	   C   s   t dddt dddt dtd t dddt dddf\}}}}d	}||| || f}tj|||d
}t |d|ddd d t jf }t|	|tj
j	|||||dddd d S )Nr   r  rR   r      r   rS   r   rT   rj   r  r   )r,   r-   rU   rV   ry   r   )rZ   r  r  r  r2   r  r7  r  r   rY   norminvgauss)	rb   r   r  r  r  r  r   r  rQ   r.   r.   r/   test_pdf_norminvgauss5  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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   s   t jd d S r   r   re   r.   r.   r/   r   M  s    zTestNormInvGauss.setup_methodc                 C   s@   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   rh   r,   r-   &.>r}   )rZ   r   r2   r  r`   r   )rb   Zr_cdfx_testvals_cdfr.   r.   r/   
test_cdf_RP  s    zTestNormInvGauss.test_cdf_Rc                 C   s@   t g d}t g d}tjj|ddd}t||dd d S )N)gp϶>g\H55$?geСt&?go NiH?g]u>r  r   rh   r  r  r}   )rZ   r   r2   r  rY   r   )rb   Zr_pdfr  Zvals_pdfr.   r.   r/   r  \  s    zTestNormInvGauss.test_pdf_Rzx, a, b, sf, rtol))r   r   r   !7?ry   )r  r   r   ?=r_  )r   ru   r}  gy5`?r[  )rR   ru   r}  gMLC9r  c                 C   s@   t j|||}t|||d t j|||}t|||d d S Nrp   r2   r  rS  r   rW  )rb   rQ   r,   r-   rS  rq   rD   r  r.   r.   r/   test_sf_isf_mpmathd  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  ry   r:  r   r  rp   r  )rb   rQ   r,   r-   rS  rD   r  r.   r.   r/   test_sf_isf_mpmath_vectorizedq  s    z.TestNormInvGauss.test_sf_isf_mpmath_vectorizedc                 C   s<   t dd}tddd}||}||}t|| d S )Nr   r   r  rW   )r2   r  rZ   r   rS  rW  r   )rb   dstrQ   rS  rW  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   rh   rW   r         @r   r   mvskmoments)rZ   r  r   r2   r  )rb   r,   r-   gammaZ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?rh   r@  )rZ   r   r2   r  r7  r   r`   )rb   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  L  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   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestGeom.setup_methodc                 C   s   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   )r2   geomr   r   r   r  r  r   r  r   r  r  r  r  r.   r.   r/   r	    s    zTestGeom.test_rvsc                 C   sT   t jd}tjjt dd|d}|jt jks4J t 	|t 
t jjksPJ d S )Nl   A: iru   rp  )rZ   r   r   r2   r  r   r   r   int64r  Ziinfoint32max)rb   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   rh   )rh   r   r  )r2   r  r  r   rb   r  r.   r.   r/   r$    s    zTestGeom.test_pmfc                 C   sV   t tjg dd}tjg dd}t||ddd tjdd}t|d d S )Nr   rh   ro   r   r   r   rm   )rZ   rI  r2   r  r  rg  r   r   )rb   r"  r#  r  r.   r.   r/   test_logpmf  s
    zTestGeom.test_logpmfc                 C   sL   t jg dd}t jg dd}tg d}t|| t|d|  d S )Nr   rh   rh   r        ?r   )r2   r  r`   rS  r   r   rb   r  vals_sfrK   r.   r.   r/   test_cdf_sf  s
    
zTestGeom.test_cdf_sfc                 C   sV   t jg dd}t jg dd}tg d}t|t| t|t|  d S )Nr   rh   r  )	r2   r  rj  logsfr   r   rZ   rI  log1pr  r.   r.   r/   test_logcdf_logsf  s
    zTestGeom.test_logcdf_logsfc                 C   s,   t jg dd}tg d}t|| d S )Nr  rh   )r  rl   r  )r2   r  r7  r   r   rb   r  rK   r.   r.   r/   r    s    zTestGeom.test_ppfc                 C   s   t tjddddd d S )N#B;r  +=r}   )r   r2   r  r7  re   r.   r.   r/   test_ppf_underflow  s    zTestGeom.test_ppf_underflowc                 C   s    t d }t|ddd d S )Ng<,Ԛ?g۩@ro   rp   )r2   r  r>   r   )rb   r(  r.   r.   r/   test_entropy_gh18226  s    zTestGeom.test_entropy_gh18226N)r   r   r   r   r	  r  r$  r  r  r  r  r  r  r.   r.   r.   r/   r    s   	
r  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )
TestPlanckc                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestPlanck.setup_methodc                 C   s,   t jg dd}tg d}t|| d S )Nr   r  )g|dy?g8'\>ggrU!>)r2   planckrS  r   r   r  r.   r.   r/   rV    s    zTestPlanck.test_sfc                 C   s,   t jg dd}tg d}t|| d S )N)ra       @@     p@ra  )g    P.g    h>g    TF)r2   r  r  r   r   r  r.   r.   r/   
test_logsf  s    zTestPlanck.test_logsfN)r   r   r   r   rV  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	S )
TestGennormc                 C   s0   g d}t j|d}t j|}t|| d S Nr   r   )r2   gennormrY   r  r   rb   pointspdf1pdf2r.   r.   r/   test_laplace  s    zTestGennorm.test_laplacec                 C   s4   g d}t j|d}t jj|dd}t|| d S Nr   rW   g;f?rV   )r2   r  rY   normr   r  r.   r.   r/   	test_norm  s    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stJ td}|jdd}tjjddd	}t
||jdksJ d S )
Nr   rh   rv   r   rO   r   rW   g;f?rV   r   )rZ   r   r   r2   r  r   rs  r`   Zpvaluer  Zks_2sampr  )rb   r8   r   Zrvs_laplaceZ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s`J t|d d ddf tdjd d	ksJ t|d d ddf tdjd d	ksJ t|d d ddf tdjd d	ksJ d S )
Nr   rh   r  rl   r  )rv   rW   rW   r   r   rO   )rZ   r   r   r2   r  r   rs  r`   )rb   r8   r   r.   r.   r/   test_rvs_broadcasting  s    ...z!TestGennorm.test_rvs_broadcastingN)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S )
TestGibratx, sfx)rn  gD.?)  gJ]b<c                 C   s0   t tj||dd t tj||dd d S )Ng+=rp   )r   r2   r   rS  rW  rb   rQ   sfxr.   r.   r/   test_sf_isf  s    zTestGibrat.test_sf_isfN)r   r   r   r   r   r   r  r.   r.   r.   r/   r    s   
r  c                   @   sH   e Zd Zdd Zejd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   )r2   gompertzr7  r`   r   rD  r.   r.   r/   test_gompertz_accuracy(  s    z#TestGompertz.test_gompertz_accuracyz	x, c, sfx))r   r  g|t?)r   r  g(fMr;)r   ru   g[?)g      @ru   gg[<c                 C   s4   t tj|||dd t tj|||dd d S Nr  rp   )r   r2   r  rS  rW  )rb   rQ   rN  r  r.   r.   r/   r  9  s    zTestGompertz.test_sf_isfc, ref))r_  geUT8?)r   gtqq?)rv   gs{)rb  gN*6c                 C   s   t tj||dd d S r	  )r   r2   r  r>   rb   rN  r<  r.   r.   r/   r)  H  s    zTestGompertz.test_entropyN)	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dS )TestFoldNorm	x, c, ref)r_  :0yE>g:0N<?)r_  r_  g:?c                 C   s   t tj|||dd d S rn   )r   r2   foldnormr`   rb   rQ   rN  r<  r.   r.   r/   r  W  s    zTestFoldNorm.test_cdfN)r   r   r   r   r   r   r  r.   r.   r.   r/   r  P  s   
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 )TestHalfNormr  )r   |N?)rR   Oul2;c                 C   s0   t tj||dd t tj||dd d S r	  )r   r2   halfnormrS  rW  r  r.   r.   r/   r  k  s    zTestHalfNorm.test_sf_isfx, ref))gWw'&l7g;G<^͛7)C]r2<gE~o-<)r  g?c                 C   s   t tj||dd d S rn   )r   r2   r  r`   rb   rQ   r<  r.   r.   r/   r  x  s    zTestHalfNorm.test_cdfN)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g ddd	 Zd
S )TestHalfLogisticr  )rS   ]6)   L-c                 C   s   t tj||dd d S rn   )r   r2   halflogisticrS  r  r.   r.   r/   rV    s    zTestHalfLogistic.test_sfq, ref))r  rS   )r  r  )gv?g   .!>)g?g      <c                 C   s   t tj||dd d S rn   )r   r2   r  rW  rb   r6  r<  r.   r.   r/   rY    s    zTestHalfLogistic.test_isfNr   r   r   r   r   r   rV  rY  r.   r.   r.   r/   r    s   


r  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestHalfgennormc                 C   s0   g d}t j|d}t j|}t|| d S r  )r2   halfgennormrY   exponr   r  r.   r.   r/   
test_expon  s    zTestHalfgennorm.test_exponc                 C   s4   g d}t j|d}t jj|dd}t|| d S r  )r2   r!  rY   r  r   r  r.   r.   r/   test_halfnorm  s    zTestHalfgennorm.test_halfnormc                 C   s6   g d}t j|d}t j|d}t|d|  d S )Nr   g
(?rW   )r2   r!  rY   r  r   r  r.   r.   r/   test_gennorm  s    zTestHalfgennorm.test_gennormN)r   r   r   r#  r$  r%  r.   r.   r.   r/   r     s   r   c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestLaplaceasymmetricc                 C   s6   t g d}tj|d}tj|}t|| d S r  )rZ   r   r2   laplace_asymmetricrY   r  r   r  r.   r.   r/   r    s    z"TestLaplaceasymmetric.test_laplacec                 C   sL   t g d}d}d| }tj||}tj||d  |}t|| d S )Nr   rW   r   )rZ   r   r2   r'  rY   r   )rb   r  rr   Zkapinvr  r  r.   r.   r/   test_asymmetric_laplace_pdf  s    z1TestLaplaceasymmetric.test_asymmetric_laplace_pdfc              	   C   s   t t d t dg}d}tj||}tj||}tj||}t ddg}t ddg}t dd	g}tj||}	|}
tj	||}|}t
t ||||	|ft ||||
|f d S )
N   rR   rW   rO   gMbp?ry  gV-?皙?gMb`?)rZ   r   rI  r2   r'  rY   r`   rS  r7  rW  r   concatenate)rb   r  rr   r  cdf1Zsf1r  cdf2Zsf2Zppf1Zppf2Zisf1Zisf2r.   r.   r/   !test_asymmetric_laplace_log_10_16  s    z7TestLaplaceasymmetric.test_asymmetric_laplace_log_10_16N)r   r   r   r  r(  r.  r.   r.   r.   r/   r&    s   	r&  c                   @   s   e Zd Zdd Zejdg ddd Zejdg ddd	 Zd
d Z	dd Z
dd Zdd Zdd Zdd Zdd Zg dg dg dg ddejdddd gej dd!dd"d gg d#g d$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   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestTruncnorm.setup_method	a, b, ref))r   rS   r`  )333333?ffffff?gܲl)r  g>g+c                 C   s   t tj|||dd d S N绽|=rp   r   r2   	truncnormr>   rb   r,   r-   r<  r.   r.   r/   r)    s    zTestTruncnorm.test_entropy))r  rb  ghiɮ9?)r  rc  r`  )g0.+rc  r`  )}Ô%Irc  Z_2?c                 C   s   t tj|||dd d S r	  r5  r7  r.   r.   r/   test_extreme_entropy  s    z"TestTruncnorm.test_extreme_entropyc              	   C   sJ   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_  rh   H.?r   rW         r  r      rW   rT   r   fO?l@ru   )r2   r6  r7  rZ   r   r   r   r  r.   r.   r/   test_ppf_ticket1131  s
    
z!TestTruncnorm.test_ppf_ticket1131c              	   C   sJ   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 )Nr;  r=  r  r   r>  rW   rT   ru   r@  r?  r   )r2   r6  rW  rZ   r   r   r   r  r.   r.   r/   test_isf_ticket1131  s
    
z!TestTruncnorm.test_isf_ticket1131c                 C   s   d\}}t jj||dddd}t||   k oD|   k oD|k n   d\}}t jj||dddd}t||   k o|   k o|k n   d S )N)ir  r   r   rR   r   )rR      r2   r6  r   r   minr  rb   lowhighrQ   r.   r.   r/   test_gh_2477_small_values  s    .z'TestTruncnorm.test_gh_2477_small_valuesc                 C   sF  d\}}t jj||dddd}t||   koD|   koD|kn  t|||gf 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 o|   k o|k n   d\}}t jj||dddd}t||   k o:|   k o:|k n   d S )	N)rS   rP   r   r   rR   r   )rv     )'  i'  )i)r2   r6  r   r   rE  r  rA   rF  r.   r.   r/   test_gh_2477_large_values  s    <..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 rt g d
}
t|| t||	 t||
 tt 	|
d |
d  |d  t g d}tj
|||}t |t |d |g}t|| |d	k rft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   rL  rl   r   r   r   r   r  r  rm   rm   )r   d._MT
@BKg?r   r   )r   rR  rQ  r   r   rW   rh   r   rh   r  gĖy	@gdv*?g,mj%V?r   )rZ   r   r   r2   r6  r`   rS  rY   r   rI  r7  r   )rb   rG  rH  xvalsxmidcdfssfspdfsexpected_cdfsexpected_sfsexpected_pdfspvalsppfsexpected_ppfsrY   r.   r.   r/   test_gh_9403_nontail_values(  sH    




z)TestTruncnorm.test_gh_9403_nontail_valuesc                 C   s  ddgddgfD ]x\}}t t j ||t jg}|| d }tj|||}tj|||}tj|||}t g d}t g d}	t g d}
|d	k rt 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  irl   rO  rP  )r   pGC@Ff<r   r   )r   rc  rb  r   r   rW   rh   rS  gEC@g i?gspXio)>r   rC  r   )rZ   r   r   r2   r6  r`   rS  rY   r   rI  r7  r   r  )rb   rG  rH  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  rY   Zxvals2r.   r.   r/   test_gh_9403_medium_tail_valuesK  sb    





 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   r2   r6  r`   rZ   r   re   r.   r.   r/   test_cdf_tail_15110_14753z  s    z'TestTruncnorm.test_cdf_tail_15110_14753)r   rm   r  rm   rm   )r  rR   rm   r  rm   gLFu)rN  r   rm   gMFmz%?rm   gſ)r   rW   rm   ghI}?rm   gHNMr   gQ63E?gnl$A?gr1"D?gK8L?gQ63Egr1"D)r   r   gU*? bn?gnA??c3TXʿ)rN  r   gU*ҿrh  gnAri  )r  g"$7"gOxr?gp7`g'>K@casec                 C   sL   |\}}}}}}t jj ||dd\}}	}
}t||	|
|g||||gdd d S )Nr  r  FFg<r}   )r2   r6  r   )rb   rk  r,   r-   m0Zv0s0Zk0mvrD   rN   r.   r.   r/   test_moments  s    zTestTruncnorm.test_momentsc                 C   s0   t jj dtjdd\}}t|d t|d d S )Nr   mvr  g e3E?g:&A?)r2   r6  rZ   r   r   )rb   ro  rp  r.   r.   r/   test_9902_moments  s    
zTestTruncnorm.test_9902_momentsc                 C   sP   d\}}t jj||dddd}t||   k oD|   k oD|k n   d S )N)rR   r   r   r   rR   r   rD  rF  r.   r.   r/   test_gh_1489_trac_962_rvs  s    z'TestTruncnorm.test_gh_1489_trac_962_rvsc                 C   s   ddt j dt j t j dddddg}dddt jddddd	t jt jg}tjj||dt|fd
}t |dt|fkszJ tt ||j	ddk tt |j
dd|k d S )Nr  rR   r  ir  rC  ru   ra  -   r   r   )Zaxis)rZ   r   r2   r6  r   r   r  r   r  rE  r  rF  r.   r.   r/   test_gh_11299_rvs  s    & zTestTruncnorm.test_gh_11299_rvsc                 C   s*   t tjdr&tjjdddtj d d S )Nr   r  r  ru   rp  )r+   rZ   r   r2   r6  r   r   re   r.   r.   r/   test_rvs_Generator  s    z TestTruncnorm.test_rvs_Generatorc                 C   s   t t j t j dt j dg}t t jt jddt jg}t g d}g d}tt|||| tt| | | | d S )NrR   r  )rR         @ry  	   r  )gOul"gځ=!gL!g>EG	f g^K[X)rZ   r   r   r   r2   r6  rj  r  )rb   r,   r-   rQ   rK   r.   r.   r/   test_logcdf_gh17064  s     z!TestTruncnorm.test_logcdf_gh17064c                 C   s$   t ddd}d}t|| d S )Nr   r   ru   gl).0S?)r2   r6  r  r   )rb   r   r<  r.   r.   r/   test_moments_gh18634  s    z"TestTruncnorm.test_moments_gh18634N)r   r   r   r   r   r   r   r)  r:  rA  rB  rI  rM  r_  rd  rf  rZ   r   Z_truncnorm_stats_datar   rq  rs  rt  rv  rw  r{  r|  r.   r.   r.   r/   r/    sZ   


#/#


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
=)rS   gh@X)rv   gh<c                 C   s$   d}t j||}t||dd d S )Nrn  ry   rp   )r2   genlogisticr   r   )rb   rQ   rK   rN  logpr.   r.   r/   test_logpdf  s    zTestGenLogistic.test_logpdfr
  ))r  gTKEl@)r_  gJk$@)r   gsF<?)rc  7~F<?c                 C   s   t tj||dd d S N+<rp   )r   r2   r  r>   r  r.   r.   r/   r)    s    zTestGenLogistic.test_entropyr  )r  rR   g8.)  r  gpT	oc                 C   s   t tj|||dd d S r	  )r   r2   r  rS  r  r.   r.   r/   rV    s    zTestGenLogistic.test_sf	q, c, ref)rj   r  g^ #@)r  rW   gGFf@c                 C   s   t tj|||dd d S NgV瞯<rp   )r   r2   r  rW  rb   r6  rN  r<  r.   r.   r/   rY    s    zTestGenLogistic.test_isf)rh   r  gİ@)r  r  g1a@c                 C   s   t tj|||dd d S r  )r   r2   r  r7  r  r.   r.   r/   r    s    zTestGenLogistic.test_ppf)rS   {Gz?g(?)r   r  g'Tn7c                 C   s   t tj|||dd d S rn   )r   r2   r  rj  r  r.   r.   r/   test_logcdf  s    zTestGenLogistic.test_logcdfN)r   r   r   r   r   r   r  r)  rV  rY  r  r  r.   r.   r.   r/   r}    s(   








r}  c                   @   sT   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 )TestHypergeomc                 C   s   t jd d S r   r   re   r.   r.   r/   r   $  s    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  rR   r   r   r   r   r   )r2   	hypergeomr   r   r   r  r  r   r  r   r  r  r  r  r.   r.   r/   r	  '  s    zTestHypergeom.test_rvsc                 C   s6   d}d}d}|}|}t jd|||}t|dd d S )Ni	  r   r  rW   gkㅒP?rC  )r2   r  r  r   )rb   Mr,  NZtotZgoodZhgpmfr.   r.   r/   test_precision3  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   rW   r   r  rC  rm   )r   r2   r  r  re   r.   r.   r/   	test_args=  s    zTestHypergeom.test_argsc                 C   s.   t dtjdddd  ko"dkn   d S )Nr   r   io i  if0  r  )r   r2   r  r`   re   r.   r.   r/   test_cdf_above_oneF  s    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@@ru        @     @c                    s"   g | ]}t j   |qS r.   )r2   r  rS  )r7   ZeatenZorangesZpearsquantiler.   r/   r9   Q  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)rZ   r   r   r2   r  rS  )rb   Zfruits_eatenr   rK   Z	quantilesres2Z	expected2r.   r  r/   test_precision2J  s    zTestHypergeom.test_precision2c                 C   sd   t ddd}| }tddg}tt|| }t|| t ddd}| }t|d d S )Nr   r   r  r   rm   )	r2   r  r>   rZ   r   r%  r   r   r   )rb   hgr(  r&  r'  r.   r.   r/   r)  ]  s    
zTestHypergeom.test_entropyc                 C   sl   d}d}d}d}t j||||}d}t||dd d}d	}d
}d}t j||||}d}t||dd d S )Nr      cA    .A     j@gor   r  r   @  X  r  g_7	j$r   )r2   r  r  r   rb   rN   r  r,  r  resultrK   r.   r.   r/   r  i  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  )r2   r  rj  r   rZ   r   fullr  r.   r.   r/   r    s8    zTestHypergeom.test_logcdfN)r   r   r   r   r	  r  r  r  r  r)  r  r  r.   r.   r.   r/   r  #  s   
	r  c                   @   sj   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
dS )TestLoggammaz	x, c, cdf))r   rW   g;Y%?)r      gRٲa6_<)gHr  gi|e?)r  g6l?)i+rO   g֬CCf9)ir  g ֺlc                 C   s<   t j||}t||dd t j||}t||dd d S rx   )r2   loggammar`   r   r7  )rb   rQ   rN  r`   r-  yr.   r.   r/   rP    s    zTestLoggamma.test_cdf_ppfzx, c, sf))r   rn  gQOu3;)   rS   g\Z{0)r  r  geɐ?)ig{Gzd?gr0T?c                 C   s<   t j||}t||dd t j||}t||dd d S rx   )r2   r  rS  r   rW  )rb   rQ   rN  rS  rD   r  r.   r.   r/   r    s    zTestLoggamma.test_sf_isfc                 C   s    t jdd}t|ddd d S )NrW   g     @r  rp   )r2   r  r   r   )rb   lpr.   r.   r/   r    s    zTestLoggamma.test_logpdfc                 C   sT   t g ddd}|D ]4\}}}}}tjj|dd}t|||||gdd qd S )N)rh   g"~jg46<@g oŏ      @r  g	h"lxgQ?gZd;333333@g      (@g{/L@g??gгYҿgh|?5?r   ru   Zmsvkr  r   r  )rZ   r   reshaper2   r  r   )rb   tablerN  r2  varskewZkurtcomputedr.   r.   r/   r    s    zTestLoggamma.test_statsrN  rO   r  c                 C   sv   t jj|dd}t| s"J t j|}t t||k t	|}|j
dd}|jd  k rl|jk srn J d S )Nr   r   r@  )Zconfidence_levelrh   )r2   r  r   rZ   isfiniter  medianZ	binomtestZcount_nonzeror   Zproportion_cirG  rH  )rb   rN  rQ   ZmedZbtestcir.   r.   r/   r	    s    zTestLoggamma.test_rvsN)r   r   r   r   r   r   rP  r  r  r  r	  r.   r.   r.   r/   r    s   

r  c                   @   s*   e Zd Zg dZejdedd ZdS )TestJohnsonsu))r  r   r   g?r  )rw   r   r   gH';vIh%,=)r   r   r   g?x7r  rk  c                 C   sF   |\}}}}}t tj||||dd t tj|||||d d S Nr  rp   )r   r2   	johnsonsurS  rW  rb   rk  rQ   r,   r-   rS  r   r.   r.   r/   r  	  s    zTestJohnsonsu.test_sf_isfNr   r   r   casesr   r   r   r  r.   r.   r.   r/   r    s   r  c                   @   s*   e Zd Zg dZejdedd ZdS )TestJohnsonb))r_  r   r   g?Hz>)r<  r   r   g0jA:r  )g!?r   r   gQbF5r  rk  c                 C   sF   |\}}}}}t tj||||dd t tj|||||d d S )Nr  rp   r}   )r   r2   r   rS  rW  r  r.   r.   r/   r    s    zTestJohnsonb.test_sf_isfNr  r.   r.   r.   r/   r    s   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   s2   t dd}tj|}tj|}t|| d S NrK  r  )rZ   r  r2   logisticr`   r7  r   rb   rQ   r  rO  r.   r.   r/   rP  (  s    zTestLogistic.test_cdf_ppfc                 C   s2   t dd}tj|}tj|}t|| d S r  )rZ   r  r2   r  rS  rW  r   r  r.   r.   r/   r  .  s    zTestLogistic.test_sf_isfc                 C   s4   d}d}t tjd| | t tj|| d S )Ng      <gg|EA@r   )r   r2   r  r7  rW  )rb   r-  Zdesiredr.   r.   r/   test_extreme_values4  s    z TestLogistic.test_extreme_valuesc                 C   s*   t jg d}g d}t||dd d S )N)r  r   rR   )gm\  .g9B.gO& $ry   rp   )r2   r  r   r   )rb   r  rK   r.   r.   r/   test_logpdf_basic;  s    zTestLogistic.test_logpdf_basicc                 C   s"   t jddg}t|ddg d S )Nrg   r  )r2   r  r   r   rb   r  r.   r.   r/   test_logpdf_extreme_valuesC  s    z'TestLogistic.test_logpdf_extreme_valueszloc_rvs,scale_rvs)g9x&?gi '?)gB"?gs^&?c                 C   sR   t jjd||d}dd }t|t j||fdj}t j|}t||dd d S )NrS   r   rU   rV   c                 S   s   | \}}t |}tt|| | dt|| |   |d  }t|| | t|| | d t|| | d   | }||fS Nr   rW   )r   rZ   r%  r   )inputr   r,   r-   r,  x1x2r.   r.   r/   r   O  s    z#TestLogistic.test_fit.<locals>.funcr  gKH9r}   )r2   r  r   r"   	_fitstartrQ   r   r   )rb   loc_rvs	scale_rvsr   r   Zexpected_solutionZ
fit_methodr.   r.   r/   test_fitI  s    

zTestLogistic.test_fitc                 C   sB   t jjdddd}tt j| tt j|dd tt j|dd d S )NrS   rh   rW   r  r   r   r   )r2   r  r   r   rb   r   r.   r.   r/   test_fit_comp_optimizera  s    z$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)rL  r     r   r  )     g      g%h9fg?~T}%mgCx^&ْV瞯<rp   )rZ   r   r2   r  rj  r  r   )rb   r  rQ   r  rK   r.   r.   r/   test_logcdfsf_tailsg  s    z TestLogistic.test_logcdfsf_tailsc                 C   s2   t g ddgd  dgd  }ttj| d S )N)	i5%   +   ru  ru  0   6   7   :   ;   r   =   rz  )rZ   r   r   r2   r  r  r.   r.   r/   test_fit_gh_18176u  s    
zTestLogistic.test_fit_gh_18176N)r   r   r   rP  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d	S )

TestLogserc                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestLogser.setup_methodc                 C   s   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   )r2   logserr   r   r   r  r  r   r  r   r  r  r  r  r.   r.   r/   r	    s    zTestLogser.test_rvsc                 C   s   t jdd}t|d d S )Nr   r  g&Y3)r2   r  r  r   rb   ro  r.   r.   r/   test_pmf_small_p  s    zTestLogser.test_pmf_small_pc                 C   s   t jd}t|d d S )Nr  gW  ?)r2   r  r2  r   r  r.   r.   r/   test_mean_small_p  s    zTestLogser.test_mean_small_pN)r   r   r   r   r	  r  r  r.   r.   r.   r/   r  ~  s   r  c                	   @   s   e Zd Zejdddd Zejdej	ej
gejdg dejdg d	ejd
ddgddgfdd Zejdej	dfej
dfgdd ZdS )TestGumbel_r_lfunctionZscopec                 C   s   t jdS r   rZ   r   r   re   r.   r.   r/   r     s    zTestGumbel_r_l.rngr8   r  r   r   r   r  rO   r   ru   zfix_loc, fix_scaleTFc           	      C   sN   |j d|||d}t }|r(|d |d< |r8|d |d< t||fi | d S )NrS   )r   rU   rV   r|   rW   r   r   )r   r   r   )	rb   r8   r  r  r   	fix_scaler   r   r   r.   r.   r/   r    s    
z&TestGumbel_r_l.test_fit_comp_optimizerz	dist, sgnr   r   c                 C   s@   |t g d }||\}}t||d  t|ddd d S )N)r   r   r   r   r   r   r   gW  @g   @g3qtw>r  rp   )rZ   r   r   r   )rb   r8   ZsgnzrU   rV   r.   r.   r/   r    s    zTestGumbel_r_l.test_fitN)r   r   r   r   fixturer   r   r   r2   gumbel_rgumbel_lr  r  r.   r.   r.   r/   r    s   

r  c                   @   s  e Zd Zdd Zdd Zejdddd Zej	d	ej
d
ddgej
dddgej
dddgdd Zej
d
ddgej
dddgej
dddgej
ddd eddgddD ejdddd Zejdddd  Zd!d" Zd#d$ Zd%S )&
TestParetoc                 C   s  t   t dt tjjddd\}}}}t|tj t|tj t|tj	 t|tj	 tjjddd\}}}}t|tj t|tj t|tj	 t|tj	 tjjddd\}}}}t|d t|tj t|tj	 t|tj	 tjjddd\}}}}t|d t|tj t|tj	 t|tj	 tjjd	dd\}}}}t
|d
 t
|d t|tj	 t|tj	 tjjddd\}}}}t
|d t
|d t|tj	 t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t|tj	 tjjddd\}}}}t
|d t
|d t
|dtd  t
|d W d    n1 s0    Y  d S )Nr*  rh   r  r  r  rn  r  rl   r  g?grq@r        @gffffff?gK~?g      2@g۶m۶m?r  UUUUUU?gqq?      $@      @g%I$I?gQ?gUUUUUU@grq?g88Nb@)r.  r/  r0  r1  r2   paretor   rZ   r   r   r   r  rb   ro  rp  rD   rN   r.   r.   r/   r    s^    











zTestPareto.test_statsc                 C   s:   d}d}d}t jj||d|d}|| | }t|| d S )Ng    eArW   rn  r   rT   )r2   r  rS  r   )rb   rQ   r-   rV   r-  rK   r.   r.   r/   rV    s    zTestPareto.test_sfr  r  c                 C   s   t jdS r   r  re   r.   r.   r/   r     s    zTestPareto.rngz2ignore:invalid value encountered in double_scalarsr   r   rW   r   r   	rvs_scaleru   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rv|  krvdks|n J t jjd|||d |d}t jj|dd	\}	}
}t|d |  |d }|jd }t|	|tt	||    t|
d d S )
NrS   r   r-   rV   rU   r|   r   p=
ף?)r   r   )r   fix_b)r   fbrW   r   )
r2   r  r   r   r   rE  r  rZ   r%  rI  )rb   r   r   r  r   r   Zshape_mle_analytical1Zshape_mle_analytical2Zshape_mle_analytical3Zshape_mle_aZ	loc_mle_aZscale_mle_aZ
data_shiftndatar.   r.   r/   r    s,    
zTestPareto.test_fitrO   fix_shape, fix_loc, fix_scalec                 C   s   g | ]}d |v r|qS Fr.   r7   r-  r.   r.   r/   r9   4  s   zTestPareto.<listcomp>TFr   repeatignoreinvalidc           
      C   sV   t jjd||||d}i }	|r&||	d< |r2||	d< |r>||	d< tt j|fi |	 d S )NrS   r  r   r   r   )r2   r  r   r   
rb   r   r   r  r   r   r  r   r   r   r.   r.   r/   r   0  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   rS   ið& rp  )r2   r  r   rZ   r   r   r   )rb   r  locationrV   r   r.   r.   r/   test_fit_known_bad_seedF  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   rW   r   )ru   rW   r   r   r   r   r   )r   r2   r  assert_raisesr    r   re   r.   r.   r/   test_fit_warningsP  s
    
zTestPareto.test_fit_warningsc                 C   s.   t jjddd|d}t|d t j|}d S )Ni~r   rS   )rU   r-   r   r|   r   )r2   r  r   r
   r   )rb   r   r   r   r.   r.   r/   test_negative_dataX  s    
zTestPareto.test_negative_dataN)r   r   r   r  rV  r   r  r   r   filterwarningsr   r  r$   rZ   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$ Zd%d& Zd'S )(TestGenparetoc                 C   sl   dD ]6}t |}tj|\}}t|d tt | qt d}tj|\}}t||gddg d S )Nr  rm   rm          rh   )	rZ   r   r2   	genpareto_get_supportr   r   isposinfr   )rb   rN  r,   r-   r.   r.   r/   test_abc  s    


zTestGenpareto.test_abc                 C   s   t jdd}tddd}t||t j| t||t j| t||t j| tddd}t|	|t j	| d S )Nrm   rN  r   r  r   r  rR   )
r2   r  rZ   r  r   rY   r"  r`   rS  r7  rb   rvrQ   r6  r.   r.   r/   test_c0p  s    zTestGenpareto.test_c0c                 C   s   t jdd}tddd}t||t j| t||t j| t||t j| tddd}t|	|t j	| t|
d	d d S )
Nr=  r  r   r  r   rm   r  rR   r   )r2   r  rZ   r  r   rY   uniformr`   rS  r7  r   r  r.   r.   r/   test_cm1|  s    zTestGenpareto.test_cm1c                 C   s   t jdd}t|tj|tjgddg tt|	tj t jdd}t|tj|tjgddg tt|	tj t jdd}t|tj|tjgddg tt|	tj d S )NrO   r  rm   r  r=  )
r2   r  r   rY   rZ   r   r`   r   isneginfr   rb   r  r.   r.   r/   
test_x_inf  s    """zTestGenpareto.test_x_infc                 C   s   t ddd}dD ]t}tj||}dD ]$}tj||| }t||dd q(tj||}dD ]$}tj||| }t||dd q`qd S )	Nr   rR   r   r   r   r  g+r[  r}   )r  r  )rZ   r  r2   r  rY   r   r`   )rb   rQ   rN  Zpdf0dcZpdfcZcdf0Zcdfcr.   r.   r/   test_c_continuity  s    zTestGenpareto.test_c_continuityc              	   C   s   t jt jddddt jdddddd	t jdddd f }d
D ]<}tj||}dD ]$}tj||| }t||dd qTq>d S Nr[  rj   rO   baser   r   FZendpointr  )rm   r=  r#  r}   )rZ   r  rM  r  r2   r  r7  r   )rb   r6  rN  Zppf0r$  Zppfcr.   r.   r/   test_c_continuity_ppf  s    z#TestGenpareto.test_c_continuity_ppfc              	   C   s   t jt jddddt jdddddd	t jdddd f }d
D ]<}tj||}dD ]$}tj||| }t||dd qTq>d S r&  )rZ   r  rM  r  r2   r  rW  r   )rb   r6  rN  Zisf0r$  Zisfcr.   r.   r/   test_c_continuity_isf  s    z#TestGenpareto.test_c_continuity_isfc              	   C   sj   t jt jddddt jdddddd	t jdddd f }d
D ]&}ttjtj||||dd q>d S )Nr[  rj   rO   r'  r   r   Fr)  r  )r  gC]r2ro   gV瞯Ҽro   r}   )	rZ   r  rM  r  r   r2   r  r`   r7  )rb   r6  rN  r.   r.   r/   test_cdf_ppf_roundtrip  s    z$TestGenpareto.test_cdf_ppf_roundtripc                 C   s    t jdddd}t|d d S )Nrb  rj   r   r   gpEȜ)r2   r  r  r   r  r.   r.   r/   r    s    zTestGenpareto.test_logsfzc, expected_statsr   )r   r   rW   r  r   r  gqq@rR   rW   gqq?g      ?g$I$	?rq?r>  gll0@r   )rh   UUUUUU?r   333333c                 C   s$   t jj |dd}t||ddd d S )Nr  r  ry   ro   r   )r2   r  r   )rb   rN  expected_statsr  r.   r.   r/   r    s    zTestGenpareto.test_statsc                 C   s   t jd}t|ddd d S )Nr  gvǼ
  ?ry   rp   )r2   r  r  r   )rb   rp  r.   r.   r/   test_var  s    zTestGenpareto.test_varN)r   r   r   r  r  r  r!  r%  r*  r+  r,  r  r   r   r   rZ   r  r   r  r1  r.   r.   r.   r/   r  b  s&   

	


r  c                   @   sD   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dS )TestPearson3c                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestPearson3.setup_methodc                 C   s   t jjddd}tt|dk t|jjtd v  t jd}tt	|t
 t dd}tt	|tj t|jjtd v  tt|dk d S )NrO   r   r   ZAllFloatrh   r   )r2   r(   r   r   r   r  r   r  r   r  r   r  r   r  r.   r.   r/   r	    s    zTestPearson3.test_rvsc                 C   s|   t jdg d}t|tg ddd t jdd}t|tdgdd t jg d	d}t|tg d
dd d S )NrW   rm   rO   ry  )gtT?g+q?g?r  r}   rN  rO   ND}i?rN  r   r   r   r   )r4  gj?gdC?gs?g'M?)r2   r(   rY   r   rZ   r   r  r.   r.   r/   r    s    zTestPearson3.test_pdfc                 C   sp   t jdg d}t|tg ddd t jdd}t|dgdd t jg d	d}t|g d
dd d S )NrW   r3  )grE?gTp]0?g~?r  r}   rN  rO   g E&"J?r5  )giZ*J?gh+8w?gcK?g|<x6?gG?)r2   r(   r`   r   rZ   r   r  r.   r.   r/   r    s    
zTestPearson3.test_cdfc                    s@   g d}dd t j|} fdd|D }t|| d S )NrN  r   r   rh   rh   rg  c                    s$   g | ]}t t|j d  qS r5   )r   r2   r(   rY   )r7   r  Zneg_infx_evalr.   r/   r9   	  s   z<TestPearson3.test_negative_cdf_bug_11186.<locals>.<listcomp>)r2   r(   r`   r   )rb   skewsrV  Zint_pdfsr.   r7  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sPJ d S )Nr   rW   r   r  )r2   r(   r  r   r  rZ   number)rb   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 )Nr6  rh   r   rn  r   rW   )r2   r(   r7  r`   r   rZ   r   r  rY   rS  rW  )rb   r9  r8  r   r  rQ   r.   r.   r/   test_ppf_bug_17050	  s    
zTestPearson3.test_ppf_bug_17050N)
r   r   r   r   r	  r  r  r:  r<  r=  r.   r.   r.   r/   r2    s   

r2  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)rm   rO   ry  rh   r  )
gffffffr=  r   皙ɿ皙rO   ry  rh   r  ffffff?)r2   kappa4r`   r  r   rb   rQ   r(  rN   r  Z	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  ru   rR   rm   rN  r   )rZ   r  r2   rB  r`   
genextremer   rC  r.   r.   r/   test_cdf_genextreme2	  s    zTestKappa4.test_cdf_genextremec                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr   rR   r  rm   )rZ   r  r2   rB  r`   r"  r   rC  r.   r.   r/   test_cdf_expon;	  s    zTestKappa4.test_cdf_exponc                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr  ru   rR   rm   )rZ   r  r2   rB  r`   r  r   rC  r.   r.   r/   test_cdf_gumbel_rD	  s    zTestKappa4.test_cdf_gumbel_rc                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr  ru   rR   r=  rm   )rZ   r  r2   rB  r`   r  r   rC  r.   r.   r/   test_cdf_logisticM	  s    zTestKappa4.test_cdf_logisticc                 C   s@   t ddd}d}d}tj|||}tj|}t|| d S )Nr  ru   rR   r  )rZ   r  r2   rB  r`   r  r   rC  r.   r.   r/   test_cdf_uniformV	  s    zTestKappa4.test_cdf_uniformc                 C   s   t dd d S r  )r2   rB  re   r.   r.   r/   test_integers_ctor_	  s    zTestKappa4.test_integers_ctorN)
r   r   r   rD  rF  rG  rH  rI  rJ  rK  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   s   t jd d S r   r   re   r.   r.   r/   r   f	  s    zTestPoisson.setup_methodc                 C   s@   t d}tjg d|}d|d |d d g}t|| d S )NrW   r   r   rW   rh   r   )rZ   rI  r2   r;  r  r   )rb   Zln2r  rK   r.   r.   r/   test_pmf_basici	  s    
zTestPoisson.test_pmf_basicc                 C   s@   t jg dd}g d}t|| t jdd}t|d d S )NrM  r   )r   r   r   ffffff?r   r   )r2   r;  r  r   intervalr   )rb   r  rK   rQ  r.   r.   r/   test_mu0p	  s
    
zTestPoisson.test_mu0c                 C   s   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 )Nrh   r   r   r   r   r   )r2   r;  r   r   r   r  r  r   r  r   r  r  r  r  r.   r.   r/   r	  y	  s    zTestPoisson.test_rvsc                 C   s   d}t jj |dd}t|||td| d| g tg d}t jj |dd}||tjddtd gtjddgf}t|| d S )	Ng      0@r  r  r  )rm   r  rl   r   rW   rh   )r2   r;  r   rZ   r  r   r   )rb   r  r  rK   r.   r.   r/   r  	  s     &zTestPoisson.test_statsN)r   r   r   r   rN  rR  r	  r  r.   r.   r.   r/   rL  e	  s
   	rL  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d Zdd Zdd Zdd ZdS )	TestKSTwoc                 C   s   t jd d S r   r   re   r.   r.   r/   r   	  s    zTestKSTwo.setup_methodc                 C   s   dD ]}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   rW   r   rR   rS   rv   r   rh   r   r  rW   rm   )rZ   r   r1   r   gammalnr   r2   ksonerS  r  kstwor`   r   )rb   r,  rQ   v1lgelgrK   r  r.   r.   r/   r  	  s    &zTestKSTwo.test_cdfc                 C   s   t ddd}dD ]}t dd| d| ddd|  dg}d| | }tj|d }|dkrjt |nd}t ddd||  dtj	d| t
d| ddg}tj	||}t|| qd S )Nr   r   rC  rT  rh   r  rW   )rZ   r  r   r1   r   rU  r   r2   rV  rS  rE  rW  r   )rb   rQ   r,  rX  rY  rZ  rK   r  r.   r.   r/   rV  	  s    &
zTestKSTwo.test_sfc                 C   s\   t ddddd  }g d}|D ]4}|t | }tj||}t |}t|d q"d S )Nr   rW   rC  r   )r   rS   r  i  rv   rw   r  )rZ   r  r  r2   rW  r`   diffr
   )rb   rQ   ns_xxnprobsZdiffsr.   r.   r/   test_cdf_sqrtn	  s    
zTestKSTwo.test_cdf_sqrtnc                 C   sF   t ddd}dD ].}tj||}tj||}t|d|  qd S Nr   r   rC  rT  )rZ   r  r2   rW  r`   rS  r   )rb   rQ   r,  r  r  r.   r.   r/   r  	  s
    zTestKSTwo.test_cdf_sfc                 C   sT   t ddd}dD ]<}|t | }tj||}tj||}t|d|  qd S ra  )rZ   r  r  r2   rW  r`   rS  r   )rb   rQ   r,  r^  r  r  r.   r.   r/   test_cdf_sf_sqrtn	  s    zTestKSTwo.test_cdf_sf_sqrtnc                 C   sn   t ddd}dD ]V}||d| k }tj||}d|k |dk @ }tj||}t|| || dd qd S )	Nr   r   rC  rT  rh   r  r_  rp   )rZ   r  r2   rW  r`   r7  r   rb   rQ   r,  r^  r  condr  r.   r.   r/   test_ppf_of_cdf	  s    zTestKSTwo.test_ppf_of_cdfc                 C   sn   t ddd}dD ]V}||d| k }tj||}d|k |dk @ }tj||}t|| || dd qd S )	Nr   r   rC  rT  rh   r  r_  rp   )rZ   r  r2   rW  rW  rS  r   )rb   rQ   r,  r^  Zvals_isfrd  r  r.   r.   r/   test_isf_of_sf	  s    zTestKSTwo.test_isf_of_sfc                 C   st   t ddd}dD ]\}|t | |d| k }tj||}d|k |dk @ }tj||}t|| ||  qd S )Nr   r   rC  rT  rh   r  )rZ   r  r  r2   rW  r`   r7  r   rc  r.   r.   r/   test_ppf_of_cdf_sqrtn	  s    zTestKSTwo.test_ppf_of_cdf_sqrtnc                 C   st   t ddd}dD ]\}|t | |d| k }tj||}d|k |dk @ }tj||}t|| ||  qd S )Nr   r   rC  rT  rh   rO  )rZ   r  r  r2   rW  rS  rW  r   )rb   rQ   r,  r^  r  rd  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 ra  )rZ   r  r2   rW  r7  r`   r   )rb   r_  r,  r^  r  r.   r.   r/   r  	  s
    zTestKSTwo.test_ppfc              	   C   s   g d}t g d}t g dg dg dg dg dg dg}t|D ]J\}}|t d	 t t jd	 |  }tj||}t	||| d
d qLd S )N)rR   r   rS   r  r  rv   )r   gUUUUUU?rh   r   rW   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$?g qO?)g}+: >gwQ9>gH{?g]qv(?g)~/v?gmJ?)gV27J=gGk(>gWX?gY?g{0`?gZ
H?)g_R=g4>g̪?gT_@?g<e?g2?rW   h㈵>rp   )
rZ   r   	enumeraterI  r  r[   r2   rW  r`   r   )rb   r\  ZratiosrK   idxr,  rQ   r  r.   r.   r/   test_simard_lecuyer_table1	  s    "z$TestKSTwo.test_simard_lecuyer_table1N)r   r   r   r   r  rV  r`  r  rb  re  rf  rg  rh  r  rl  r.   r.   r.   r/   rS  	  s   
		
rS  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestZipfc                 C   s   t jd d S r   r   re   r.   r.   r/   r   "
  s    zTestZipf.setup_methodc                 C   s   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 )Nrn  r   r   r   r   r   )r2   zipfr   r   r   r  r  r   r  r   r  r  r  r  r.   r.   r/   r	  %
  s    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,   rh  skr,   r  )r2   rn  r   rZ   r  r   r   r  r  r.   r.   r/   rq  0
  s
    zTestZipf.test_momentsN)r   r   r   r   r	  rq  r.   r.   r.   r/   rm  !
  s   rm  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestDLaplacec                 C   s   t jd d S r   r   re   r.   r.   r/   r   ;
  s    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 )Nrn  r   r   r   r   r*  )r2   dlaplacer   r   r   r  r   r  r   r  r  r  r  r.   r.   r/   r	  >
  s    zTestDLaplace.test_rvsc                 C   s   d}t |}| d\}}}}d}t| |d }||}	t|	|d  t|	|d   }
}t||fd t||f|
||
d  d fd	d
d d S )Nr  r  r  r   rW   r   rP  r  r  r  r   )r2   rt  rZ   r   r  r%  r   r   )rb   r,   dlro  rp  rD   rN   r  rO  ppm2m4r.   r.   r/   r  I
  s    

&zTestDLaplace.test_statsc                 C   sF   t d}t|}|d\}}}}t||fd t||fd d S )Nrl   r  )rm   rm   )r        
@)rZ   rI  r2   rt  r   r   )rb   r,   ru  ro  rp  rD   rN   r.   r.   r/   test_stats2V
  s
    

zTestDLaplace.test_stats2N)r   r   r   r   r	  r  rz  r.   r.   r.   r/   rs  :
  s   rs  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   s   t jd d S r   r   re   r.   r.   r/   r   _
  s    zTestInvgauss.setup_methodzrvs_mu,rvs_loc,rvs_scale)rW   r   r   )g
ףp=@g r@gʡE6@c                 C   sF  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r<d	ksBn J d S )NrS   r   r  rU   rV   r   r   ro   r   r   r  r  )fmur   )Zfix_mur   )
r2   r   r   r   rZ   r2  r   r%  r   r   )rb   rvs_mur   r  r   r  rU   rV   Zmu_temp	scale_mleZmu_mleZ
shape_mle1Z
shape_mle2Z
shape_mle3r.   r.   r/   r  b
  s.    



zTestInvgauss.test_fit)gX9v>@g	@gGz@c                    s   t jjd|||d}ttt jt jj}||}t j|}t|| ||ddd}t jj|ddd}t|| tt j||d t	||d  dksJ tt j||d d tt j|dd tt j||tj
dd d d S )	NrS   r|  r   rW   )r   r}  r   r   r  )r2   r   r   r   r   r   r   r   rZ   r  r   rand)rb   r  r   r  r   Z	super_fitZsuper_fittedZinvgauss_fit	__class__r.   r/   r   
  s"    



z(TestInvgauss.test_fit_MLE_comp_optimizerc                 C   sL   t tj tt$ tjjg ddd W d    n1 s>0    Y  d S )Nr   rW   r   )r   r2   r   r   r   r    r   re   r.   r.   r/   test_fit_raise_errors
  s    
z"TestInvgauss.test_fit_raise_errorsc                 C   s   g d}g d}t jjd|d}t|| t jjddd}t|d t jjddd}t|d	 t jd
d}t|d t jdd}t|d d S )N)g4wT;?gjdV&}?g{i\0>gDV_h?gqacX?)r   r   r   r   r   皙?r  r  ?gfFn   gr^:g9̗?r_  gx_;:g!?gٷ
??)r2   r   r`   r   r   rS  )rb   r  rK   rI   Z
cdf_actualZ	sf_actualr.   r.   r/   r  
  s    



zTestInvgauss.test_cdf_sfc                 C   sh   t jjddd}t|d t jdd}t|d t jjddd}t|d t jdd}t|d	 d S )
Nr_  r  r  giJ.r  gr^ߺr  gpgFgpQ^L)r2   r   rj  r   r  )rb   rj  r  r.   r.   r/   r  
  s    	


zTestInvgauss.test_logcdf_logsfzmu, ref))g:0yU>g,9)r  g%!)rj   g40)r   gK'
@)rc  g`p
@c                 C   s   t tj||dd d S r  )r   r2   r   r>   )rb   r  r<  r.   r.   r/   r)  
  s    zTestInvgauss.test_entropy)r   r   r   r   r   r   r   r  r   r  r  r  r)  __classcell__r.   r.   r  r/   r{  ^
  s   
!#r{  c                       sz   e Zd Zejdg dejdg ddd Zejdg d fd	d
Zdd Zdd Z	dd Z
dd Z  ZS )TestLaplacer   )r  r   r   rW   r  )r   rW   r   rR   c                 C   sL  t jjd||d}t|}tt|| t| }t j|\}}t	||ddd t	||ddd t jj||d\}}t	||ddd t jj||d\}}t	|| |d }tt|| t| }t jj||d\}}t
|| t jj||d\}}t
|| ttt jj|||d ttt jjtjg ttt jjtjg d S )	NrS   r  ro   r   r   r  rW   r  )r2   r  r   rZ   r  r%  r   r   r   r   r   r  r   r   r   r   )rb   r   r  r   Zloc_mler  rU   rV   r.   r.   r/   r  
  s*    



zTestLaplace.test_fitrvs_loc,rvs_scale))r  rR   rR   ru   )rh   ry  c                    s   t jjd||d}dd }t j|\}}ttt jt j|\}}||||}	||||}
|	|
k s|tj|	|
ddds|J d S )Nrv   r  c              	   S   s8   dt | td|  d| tt||     S )Nr   rW   r   )r   rZ   rI  r%  r   )rU   rV   r   r.   r.   r/   ll"  s    z3TestLaplace.test_fit_MLE_comp_optimizer.<locals>.llro   r   )r2   r  r   r   r   r   rZ   r   )rb   r   r  r   r  rU   rV   Zloc_optZ	scale_optZll_mleZll_optr  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)r  r  r  r         @re  r  r   r   ro   r   r  )rZ   r   r2   r  r   r   )rb   r   rU   rV   r.   r.   r/   test_fit_simple_non_random_data0  s
    z+TestLaplace.test_fit_simple_non_random_datac                 C   sl   d}t j| }|dksJ t j|}|dks6J t j|}|dksNJ t j| }|dkshJ d S )Nrv   rm   r  )r2   r  r`   rS  )rb   rQ   Zp0p1r.   r.   r/   test_sf_cdf_extremes9  s    z TestLaplace.test_sf_cdf_extremesc                 C   s.   d}t j|}t|t| d dd d S )Nr  rW   ry   rp   )r2   r  rS  r   rZ   r   )rb   rQ   r-  r.   r.   r/   rV  N  s    zTestLaplace.test_sfc                 C   s.   d}t j|}t|td|  dd d S )Ng}:rW   ry   rp   )r2   r  rW  r   rZ   rI  )rb   r-  rQ   r.   r.   r/   rY  S  s    zTestLaplace.test_isf)r   r   r   r   r   r   r  r   r  r  rV  rY  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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)r   rl   g      ?)g     ?g      p?gSQ>c                 C   s   t tj|||dd d S rn   )r   r2   powerlawrS  )rb   rQ   r,   rS  r.   r.   r/   rV  \  s    zTestPowerlaw.test_sfr  r  c                 C   s   t jdS r   r  re   r.   r.   r/   r   b  s    zTestPowerlaw.rngr   )rO   rh   r  r   rW   r   r  r  r  r  c                 C   s   g | ]}d |v r|qS r  r.   r  r.   r.   r/   r9   j  s   zTestPowerlaw.<listcomp>TFr   r  c           
      C   sh   t jjd||||d}t }	|r(||	d< |rDt| tj |	d< |rP||	d< tt j|fi |	 d S )Nr  )r   r,   rU   rV   r|   r   r   r   )	r2   r  r   r   rZ   	nextafterrE  r   r   r	  r.   r.   r/   r   f  s    z(TestPowerlaw.test_fit_MLE_comp_optimizerc                 C   sR   d}d}d}t jj|||dtjdd}d| d i}tt j|fi | d S )	Ng`- @rm   grߟA@rS   ru   )r,   rU   rV   r   r|   r   rW   )r2   r  r   rZ   r   r   ptpr   )rb   r,   r
  rV   r   r   r.   r.   r/   test_problem_casez  s    
zTestPowerlaw.test_problem_casec                 C   sh  t tj d}tt|d& tjjg dddd W d    n1 sF0    Y  d}tt|d$ tjjg ddd W d    n1 s0    Y  d}tt|d$ tjjg dd	d W d    n1 s0    Y  d
}tt|d$ tjjg ddd W d    n1 s0    Y  d}tt|d$ tjjg ddd W d    n1 sZ0    Y  d S )Nz7 Maximum likelihood estimation with 'powerlaw' requiresr   r   rW   r   r   r   r  rW   r   r   z$Negative or zero `fscale` is outsiderN  r  z0`fscale` must be greater than the range of data.)r   r2   r  r  r    r   r   )rb   r*   r.   r.   r/   r    s     
4224zTestPowerlaw.test_fit_warningsc                 C   sH   g d}t j}tjdd t|| W d    n1 s:0    Y  d S )N)r   r   rW   rW   r   r   r   r   r   r   ru   r  r  Zover)r2   r  rZ   r  r   )rb   r   r8   r.   r.   r/   test_minimum_data_zero_gh17801  s    z+TestPowerlaw.test_minimum_data_zero_gh17801N)r   r   r   r   r   r   rV  r  r   r$   r   r  r  r  r.   r.   r.   r/   r  Y  s$   


r  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))rS   r  r   ga!R()r  r  r   g;?)r  r  r   gE?)MDr  r   g=c                 C   s   t tj||||dd d S rx   )r   r2   r   rS  rb   rQ   rN  rD   r<  r.   r.   r/   rV    s    zTestPowerLogNorm.test_sfzq, c, s, ref)g?r  r   rj   )gR4-r  r   rv   c                 C   s   t tj||||dd d S )Ng|=rp   )r   r2   r   rW  )rb   r6  rN  rD   r<  r.   r.   r/   rY    s    zTestPowerLogNorm.test_isf))(,* Er  r   g?)r  r  r   gv6)r  r  r   g+	94|7)r5  r  r   g?c                 C   s   t tj||||dd d S )Ngt =rp   )r   r2   r   r`   r  r.   r.   r/   r    s    zTestPowerLogNorm.test_cdf))r  r  r   gS^Ռe9)@xDr  r   g0g;)g\)c=Hr  r   g7H7c                 C   s   t tj||||dd d S )NgAfc=rp   )r   r2   r   rY   r  r.   r.   r/   r    s    zTestPowerLogNorm.test_pdfN)
r   r   r   r   r   r   rV  rY  r  r  r.   r.   r.   r/   r    s$   


r  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 )TestPowerNormr  ))rz  r   g| <)r  rW   ge()rS   r  g%!@6)r  rj   gT;-c                 C   s   t tj|||dd d S rx   )r   r2   	powernormrS  r  r.   r.   r/   rV    s    zTestPowerNorm.test_sfr  ))ri  r  gĿ)gwJ?rS   g!X)r<  r  g缂U)r   r  gͫ1@)r  rW   gD@)Jz5ru   gU!zYr@c                 C   s   t tj|||dd d S Nr  rp   )r   r2   r  rW  r  r.   r.   r/   rY     s    zTestPowerNorm.test_isf))irz  g.u	T9)rW   rz  ?)rK  rz  gsK-)r  r  gk8>)rK  r  g^u1-c                 C   s   t tj|||dd d S r  )r   r2   r  r`   r  r.   r.   r/   r    s    zTestPowerNorm.test_cdfN)	r   r   r   r   r   r   rV  rY  r  r.   r.   r.   r/   r    s   


r  c                   @   s>   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	dS )TestInvGammac                 C   s   t   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|| qW d    n1 s0    Y  d S )Nr*  g(\O3@r  rr  )g~?gCX&?g*7gS?gBqFq @)皙?@gffffff@)r  gEy?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@)r.  r/  r0  r1  r2   r   r   rZ   r   r   r   r   )rb   r  rK   r,   rQ   r  r.   r.   r/   test_invgamma_inf_gh_1866  s    



z&TestInvGamma.test_invgamma_inf_gh_1866c                 C   s6   t dd}tj|d}tj|d}t|| d S )Ngr   r   )rZ   rM  r2   r   r`   r7  r   r  r.   r.   r/   rP  /  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        rW   rS      r   r  rp   )	sysmaxsizerZ   rM  r2   r   rS  rW  r   r  r.   r.   r/   r  6  s    
zTestInvGamma.test_sf_isfa, ref)r   g70K6:)rc  gVMOuc                 C   s   t tj||dd d S rn   )r   r2   r   r>   rb   r,   r<  r.   r.   r/   test_large_entropyC  s    zTestInvGamma.test_large_entropyN)
r   r   r   r  rP  r  r   r   r   r  r.   r.   r.   r/   r    s   r  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
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)rW   r   r  c                 S   s&   g | ]\}}}|j |jg|R  qS r.   rY   r,   r7   _f_argsr   r.   r.   r/   r9   Y  r:   z(TestF.test_endpoints.<locals>.<listcomp>c                 S   s   g | ]\}}}|qS r.   r.   r7   r  r  Z	_correct_r.   r.   r/   r9   Z  r:   )r2   frY   r,   r   )rb   r   r  r  Z_correctanscorrectr.   r.   r/   rE  S  s    zTestF.test_endpointsc                 C   sX   t jj dddd\}}}}tt| tt| tt| tt|  d S )NrC        @r  r  )r2   r  r   rZ   r  r  r.   r.   r/   test_f_moments]  s
    zTestF.test_f_momentsc                 C   sT   t  8 t dt tjjdgd g ddd W d    n1 sF0    Y  d S )Nr*  rC  r   )rW   r   r  r  r  dfndfdr  )r.  r/  r0  r1  r2   r  re   r.   r.   r/   test_moments_warningse  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   rC  r  r  r  rW   r   r  r  ru      )rZ   r   r2   r  r   r  )rb   r  r  ro  rp  rD   rN   rw  Zv2s2Zk2numZk2denZk2r.   r.   r/   test_stats_broadcastk  s"    
0
 
 zTestF.test_stats_broadcastN)r   r   r   rE  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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 )Nru   r  g?g?)r   r2   r  r3  re   r.   r.   r/   test_rvgeneric_std~  s    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  )rZ  r  )\(?rm   rW   gGz @g     i@r   rq  gGz@r   g
ףp=
@)rm   gq    @)r   r2   r  rZ   r   r   re   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   rW   r  rS   )g?@gTM]?ggY?U?ry   rp   r   r2   r  r>   )rb   rZ  rK   r.   r.   r/   test_t_entropy  s    zTestStudentT.test_t_entropyzv, ref)rS   r  )rc  r9  c                 C   s   t tj||dd d S r	  r  )rb   rp  r<  r.   r.   r/   test_t_extreme_entropy  s    z#TestStudentT.test_t_extreme_entropymethname)rY   r   r`   r7  rS  rW  
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   rR   r   r   r   rZ  rU   rV   rT   )rZ   r   r   r   boolr  r  randnr   r2   r  r  r   r   )rb   r  r  rZ  rQ   Zt_distZ
t_dist_refZ	norm_distZt_methZ
t_meth_refZ	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 ]2}t|| | ||  t|| |  ||  qtj	j|ddd}tj
jddd}tj	j||  ddd}t|| | t||  | d S )Nr   r  rR   r   r   r   r  )rZ  rU   rV   r  rU   rV   r  r   r  rT   )rZ   r   r   r   r  r  r  r   r2   r  r  r  r   r>   )rb   r  rZ  r   Z
res_ex_infZ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   ra  rR   r   )rc  d~QJr  r   )gZ_2g9g!ǟuIgdg)g73?r   gմFhAW;gm0_?ro   rp   r  )r   r2   r  r   rY   )rb   rQ   rZ  Z
logpdf_refZ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  }  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d Zdd Zdd Zdd ZdS )TestRvDiscretec                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    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  qL| }tt|tjsJ d S )N)r   r   r   rW   r   r   )rm   r5  r  rm   r5  rm   rv   sample)namevaluesr   r   )r2   r;   r   r   r  r   r  r   r   r%  r   rZ   r   r   integer)rb   ZstatesZprobabilitysamplesr>  rQ   rD   r-  r.   r.   r/   r	    s    &zTestRvDiscrete.test_rvsc                 C   sr   t g d}tjg d|fd}tt|| }| }t|| tjg dg dfd}| }t|d d S )N)r   ri  r5  rM  r  )r  r   r   rm   )	rZ   r   r2   r;   r%  r   r>   r   r   )rb   r\  r-  r'  r(  r.   r.   r/   r)    s    
zTestRvDiscrete.test_entropyc                 C   sT   g d}g d}t j||fd}ddgddgg}t||dd	gd
dggdd d S )Nr  rh   r5  ry  r  r  r  r  rW   rh   ry  rm   r5  r  r}   )r2   r;   r   r  )rb   xkpkr  rQ   r.   r.   r/   r$    s    
zTestRvDiscrete.test_pmfc                    sd   g d}g d}t j||fd g d}g d}t ||dd t fdd	|D |dd d S )
Nr  r  r  )r   r  r  rn  rl   r  r   ru   )r   rh   rh   rh   r*  r*  r   r   r  r}   c                    s   g | ]}  |qS r.   )r`   )r7   rO  r  r.   r/   r9     r:   z+TestRvDiscrete.test_cdf.<locals>.<listcomp>)r2   r;   r   r`   )rb   r  r  Zx_valuesrK   r.   r  r/   r    s    zTestRvDiscrete.test_cdfc                    sd   g d}g d}t j||fd g d}g d}t ||dd t fdd	|D |dd d S )
Nr  r  r  )rO   rh   r1  r*  rw  r  )r   r   rW   rW   r   r   r  r}   c                    s   g | ]}  |qS r.   )r7  )r7   r6  r  r.   r/   r9   $  r:   z+TestRvDiscrete.test_ppf.<locals>.<listcomp>)r2   r;   r   r7  )rb   r  r  Zq_valuesrK   r.   r  r/   r    s    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   rW   r   r>  r  )rO   ry  r5  r5  rO   r  r   r  r   )r2   r;   r   r7  r`   r  )rb   r  r  r.   r.   r/   test_cdf_ppf_next'  s
    z TestRvDiscrete.test_cdf_ppf_nextc                 C   s`   t dd}t g dg dg dg}tj||fd}t| t |j	|j
 dd d S )Nr  )r   r   )rO   rO   r  r   )rO   rO   r   r   r  r  r}   )rZ   r   r  r   r2   r;   r   r   r%  r  r  rb   r  r  r  r.   r.   r/   test_multidimension/  s    
z"TestRvDiscrete.test_multidimensionc                 C   s   g d}ddg}t ttjfi t||fd g d}t ttjfi t||fd g d}g d}t ttjfi t||fd g d}g d}t ttjfi t||fd d S )Nr   rh   r  )rh   333333?gffffff濩r   rW   r   r   ru   )r5  r5  r5  r5  r?  )r  r   r2   r;   r   rb   r  r  r.   r.   r/   test_bad_input8  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   rW   rW   )rW   r   gUUUUUU?r  r  r   rW   r   )rZ   r   r  r  r  r   r2   r;   r   r   r  r  r.   r.   r/   test_shape_rv_sampleH  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   rW   r   r  r>  rC  )rO   ry  ry  ry  ry  rO   r  r  r}   )r2   r;   r   r   rZ   r%  r  r  r  r.   r.   r/   test_expect1W  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      @ra  g     0@g     @g     P@g     @g     p@g      @g     @g      @g     @r  g     h@g     0@g     @g     @g     @g     P@g     @g     @g     @r  g     8@g      @g     ȩ@g     @g     X@g      @g     @g     @g     x@g     @@g     @g     h@g     ̰@g     0@g     @g     @g     \@g     @)/g-C6:?rm   gF%uk?g:vz?rm   rm   g.nr?g|гY?rm   rm   rm   g @6*? 4U0*C?g@+?gC6z?g nr?g ?gOjM?g n?g1w-!?g:pΈ?gףp=
?g _Le?rm   g^)p?g~jtx?gJ4q?gGzt?g J4q?g Mb@?g@Psׂ?g@^)ˀ?rm   rm   g N@s?g 1w-!_?r  gൄ|г?rm   gH}}?rm   g
F%u?rm   rm   g ^)ˀ?g v?rm   r  r  r}   c                 s   s   | ]\}}|| V  qd S rd   r.   r7   rp  wr.   r.   r/   	<genexpr>}  r:   z.TestRvDiscrete.test_expect2.<locals>.<genexpr>c                 S   s   | d S NrW   r.   r   r.   r.   r/   rE     r:   z-TestRvDiscrete.test_expect2.<locals>.<lambda>c                 s   s   | ]\}}|d  | V  qdS )rW   Nr.   r  r.   r.   r/   r    r:   )r2   r;   r   r   r2  r%  r   )rb   r  pyr  r.   r.   r/   test_expect2^  s    zTestRvDiscrete.test_expect2N)r   r   r   r   r	  r)  r$  r  r  r  r  r  r  r  r  r.   r.   r.   r/   r    s   	r  c                   @   s   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  ru   rS   r   rp  )	rZ   r  r   r2   
skewcauchyrY   r  r`   r7  rX  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   rR   rW   r   ru   )
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?)
rZ   r   r   r  r   r2   r  rY   r`   r7  )rb   r,   rQ   rY   r`   r.   r.   r/   test_skewcauchy_R  s    z TestSkewCauchy.test_skewcauchy_RN)r   r   r   r  r  r.   r.   r.   r/   r    s   	r  rW   ru   g@r   gףp=
1@r   gRZ@i   gS㥛Ԋ@rO   rP   g&@iQ i'  i0ybi l   HO1Z i3rN  irR   irS   ikr  i1rw   i  i4i N  i(  lEI. @ i c                   @   sZ   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Ze	j
dedd Zdd ZdS )TestSkewNormc                 C   s   t d| _d S r   )r   r   re   r.   r.   r/   r     s    zTestSkewNorm.setup_methodc                 C   s0   t ddd}ttjj|ddtj| d S r  )rZ   r  r   r2   skewnormrY   r  rX  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   ru   r  )r,   r   r|   rN  )r2   r  r   r   r   r  )rb   r  rQ   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  ru   rW   )r,   r   rU   rV   r|   r  )r,   rU   rV   r  r  rL  )r2   r  r   r  r   rZ   r2  r  r  Zkurtosisr   )rb   XrK   r  r.   r.   r/   rq    s    $$zTestSkewNorm.test_momentsc                 C   sF   t jg dd}t|tddd t jdd}t|ddd d S )	N)rR   r  r   r   r   r  rp   r  r  r  )r2   r  r`   r   rZ   onesrD  r.   r.   r/   test_cdf_large_x  s    zTestSkewNorm.test_cdf_large_xc                 C   sr   g dg dg dg dg dg}|D ]F\}}}t j||}t||dd t j| | }t||dd q&d S )N)rx  r   gzbLe9)rL  rW   gn'/2;)r   ru   g::)rj  r   g|<)r  rL  r  r  rp   )r2   r  r`   r   rS  )rb   ZcdfvalsrQ   r,   Zcdfvalr-  r.   r.   r/   test_cdf_sf_small_values  s    z%TestSkewNorm.test_cdf_sf_small_valuesz
a, momentsc                 C   s6   t |ddD ]$\}}tj||}t||dd qd S )Nr   )startr  rp   )rj  r2   r  r  r   )rb   r,   r  orderrK   Zmomr.   r.   r/   test_noncentral_moments  s    z$TestSkewNorm.test_noncentral_momentsc                 C   s  t jd}d\}}}t|||}|jd|d}tjj|ddd\}}}	tjj|ddd\}
}}||  krvdks|n J ||
ksJ tjj|ddd	d
\}}}|dksJ t|||}|jdd}t |t|f}t	|| tj
jdd|d}tj|}t t |sJ tjj|d	d\}}}t |s@J t |t | }}t	|||t dt j    t	||d ddt j    d S )Nl   #ke )r   r  rh   rS   rp  r}  r   r   gmmr   methodmsr  r   r  rW   )rZ   r   r   r2   r  r   r   r2  r  r   r  r  r  isinfr  r  r[   )rb   r   r,   rU   rV   r8   r   a2loc2scale2a3loc3scale3Za4loc4scale4dist4r   r<  Za5Zloc5Zscale5ro  rp  r.   r.   r/   r    s,    

zTestSkewNorm.test_fitN)r   r   r   r   r  r	  rq  r  r  r   r   r   _skewnorm_noncentral_momentsr  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	S )
	TestExponc                 C   s   t tjdd d S rC  )r   r2   r"  rY   re   r.   r.   r/   	test_zeroE  s    zTestExpon.test_zeroc                 C   s0   t tjdd t tjtjdd d S )Nr  r  )r   r2   r"  r`   rW  rS  re   r.   r.   r/   	test_tailH  s    zTestExpon.test_tailc                 C   s,   t dddddt jg}tttjj| d S No_?46@yX5ͻ@j+?UX@)rZ   r   r   r  r   r2   r"  r   rX  r.   r.   r/   test_nan_raises_errorL  s    zTestExpon.test_nan_raises_errorc                 C   s,   t dddddt jg}tttjj| d S r  )rZ   r   r   r  r   r2   r"  r   rX  r.   r.   r/   test_inf_raises_errorQ  s    zTestExpon.test_inf_raises_errorN)r   r   r   r  r  r  r  r.   r.   r.   r/   r  D  s   r  c                   @   s>   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	dS )TestNormc                 C   s,   t dddddt jg}tttjj| d S r  )rZ   r   r   r  r   r2   r  r   rX  r.   r.   r/   r  X  s    zTestNorm.test_nan_raises_errorc                 C   s,   t dddddt jg}tttjj| d S r  )rZ   r   r   r  r   r2   r  r   rX  r.   r.   r/   r  ]  s    zTestNorm.test_inf_raises_errorc                 C   s    g d}t ttjj|dd d S )Nr   shrimp)plate)r  r   r2   r  r   rX  r.   r.   r/   test_bad_keyword_argb  s    zTestNorm.test_bad_keyword_argrU   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.:rC  r  rU   ry   rp   )r2   r  
_delta_cdfr   )rb   rU   rK   r  r.   r.   r/   test_delta_cdff  s
     zTestNorm.test_delta_cdfN)
r   r   r   r  r  r!  r   r   r   r$  r.   r.   r.   r/   r  W  s
   r  c                   @   s    e Zd ZdZdd Zdd ZdS )TestUniformgh-10300c                 C   s,   t dddddt jg}tttjj| d S r  )rZ   r   r   r  r   r2   r  r   rX  r.   r.   r/   r  v  s    z!TestUniform.test_nan_raises_errorc                 C   s,   t dddddt jg}tttjj| d S r  )rZ   r   r   r  r   r2   r  r   rX  r.   r.   r/   r  {  s    z!TestUniform.test_inf_raises_errorN)r   r   r   __doc__r  r  r.   r.   r.   r/   r%  t  s   r%  c                
   @   s   e Zd Zdd Zdd Zdd Zdd Zej	d	g d
dd Z
ej	dg dg dg dg dg dgdd Zej	dg dg dg dg dg dg dgdd ZdS )TestExponNormc                 C   s   dd }d\}}}d||  }t jj |||dd}t||||| d\}}}d||  }t jj |||dd}t||||| d\}}}d||  }t jj |||dd}t||||| d	\}}}d||  }t jj |||dd}t||||| d S )
Nc                 S   sh   dd| | d   }d| | d  |d  }dd| | d  d  }|d|   || d| |    ||gS )Nr  r   rW   r   r}        @r   r.   )lamsigr  ZopK2Zexp_skewZexp_kurtr.   r.   r/   get_moms  s    z,TestExponNorm.test_moments.<locals>.get_moms)r   r   r   r  r  r  )rN  rW   rO   )r   r   r   )r  rC  r  )r2   	exponnormr   )rb   r,  r  r+  r*  Kstsr.   r.   r/   rq    s"    



zTestExponNorm.test_momentsc                 C   s2   t dddddt jg}tttjj|ddd d S 	Nr  r  r  r  r  r   r   r  )rZ   r   r   r  r   r2   r-  r   rX  r.   r.   r/   r    s    z#TestExponNorm.test_nan_raises_errorc                 C   s2   t dddddt jg}tttjj|ddd d S r0  )rZ   r   r   r  r   r2   r-  r   rX  r.   r.   r/   r    s    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   rm     rj   )r   r2   r-  rY   re   r.   r.   r/   test_extremes_x  s    zTestExponNorm.test_extremes_xzx, K, expected))r  rj   g6
N-)r   rj   g՜n+H?)r   rj   gi?)rK  rj   gbJI-)rR   r   gI8?)rR   rK  gQ3|-0?c                 C   s   t tj|||dd d S r  )r   r2   r-  rY   )rb   rQ   r.  rK   r.   r.   r/   test_std_pdf  s    zTestExponNorm.test_std_pdfzx, K, scale, expected)r   rj   r   gVAҤ?)r  {Gzt?r   g'^>)r  rj   rS   rm   )r  rj   rv   gbr ;)ru   r  r   gVMe?c                 C   s:   t jj|||d}|dkr(|dks6J nt||dd d S )Nr  rm   ry   rp   )r2   r-  r`   r   rb   rQ   r.  rV   rK   r-  r.   r.   r/   test_cdf_small_K  s    zTestExponNorm.test_cdf_small_K)rR   rj   r   ghG}$;)rW   r4  r   g]fJ?)ru   r4  rh   g31"g#;)rR   r4  rh   gf
+-)r  r4  rh   rm   )rN  r  r   ga9S?c                 C   s:   t jj|||d}|dkr(|dks6J nt||dd d S )Nr  rm   -a=rp   )r2   r-  rS  r   r5  r.   r.   r/   test_sf_small_K  s    zTestExponNorm.test_sf_small_KN)r   r   r   rq  r  r  r2  r   r   r   r3  r6  r8  r.   r.   r.   r/   r(    s6   

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   )simpsrR   rj   rh   rl   )Zdxr   )scipy.integrater:  r2   genexponrY   r   r   r   )rb   r:  r-  r.   r.   r/   test_pdf_unity_area  s    z TestGenExpon.test_pdf_unity_areac                 C   s:   t jtdddddd}ttd|k|dk@  d S )Nr   rR   rj   rh   rl   r   )r2   r<  r`   r   r   r   r  )rb   r`   r.   r.   r/   test_cdf_bounds  s    zTestGenExpon.test_cdf_boundszx, p, a, b, c))r   gM <r   rW   rn  )r   g%DYY?rh   rW   r   )r   gS4z?      #@rW   rh   )rj   ga^5?r  r   rh   )ry  gs%)?r  r   rh   )r  gdm?r   ru   rh   c                 C   sD   t j||||}t||dd t j||||}t||dd d S r	  )r2   r<  rS  r   rW  )rb   rQ   r-  r,   r-   rN  rS  rW  r.   r.   r/   r    s    zTestGenExpon.test_sf_isf))r   g;\i?rh   rW   r   )r   gu0?r?  rW   rh   )rj   g-%I?r  r   rh   )ry  g]d?r  r   rh   )r  g泩'?r   ru   rh   c                 C   sD   t j||||}t||dd t j||||}t||dd d S r	  )r2   r<  r`   r   r7  )rb   rQ   r-  r,   r-   rN  r`   r7  r.   r.   r/   rP    s    zTestGenExpon.test_cdf_ppfN)
r   r   r   r=  r>  r   r   r   r  rP  r.   r.   r.   r/   r9    s   
r9  c                   @   s   e Zd Zdd ZdS )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  rS   g_93@gBX@g,M<gǃ@֫5r4  rp   r[  )r   r2   
truncexponrS  rW  )rb   r-   rQ   r<  r.   r.   r/   r  *  s
    zTestTruncexpon.test_sf_isfN)r   r   r   r  r.   r.   r.   r/   r@  (  s   r@  c                   @   s   e Zd Zdd ZdS )TestExponpowc                 C   s6   t tjddd t tjtjdddd d S )Nr4  rl   r  ru   r*  )r   r2   exponpowr`   rW  rS  re   r.   r.   r/   r  5  s    zTestExponpow.test_tailN)r   r   r   r  r.   r.   r.   r/   rB  4  s   rB  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )TestSkellamc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )Nr  r   r  )gYjP'?g$S?gQ`s2?gC/qF?gD<]Y?g/Xj?g86y?g]a¨?g:?g?gQ>?g?g:?g]a¨?g96?g0X?gA<]?gB/q?gQ`s?g$S?gYjP'?gX_?g+rx?gfSr?gJXx~?r  )r   r   r   r   r2   skellamr  )rb   rN   mu1mu2ZskpmfRr.   r.   r/   r$  <  s    zTestSkellam.test_pmfc                 C   s@   t dd}d\}}t g d}ttj||||dd d S )Nr  r   r  )gƃQ?gS`X'?gVy)>?g:	 S?gei.f?gȼJ]x?g)?g{^'+i?gLIg>?gnZ?g?rvͪ?gA?g0?g#J?gqSm
.?g~B?gd?gFBD?gQ9?gmF^?gcMy?gGJq?gC^c?g.){?gñݸ?ru   r  )r   r   r   r   r2   rE  r`   )rb   rN   rF  rG  ZskcdfRr.   r.   r/   r  Q  s    zTestSkellam.test_cdfc                 C   sB   d\}}}t tj|||ddd t tj|||ddd d S )N)r   r   gs1Cr   r:  r}   r   )r   r2   rE  r  r`   )rb   rQ   rF  rG  r.   r.   r/   test_extreme_mu2f  s    
zTestSkellam.test_extreme_mu2N)r   r   r   r$  r  rH  r.   r.   r.   r/   rD  ;  s   rD  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S )TestLognormc                 C   sX   t  < t dt tjg dd}t|g d W d    n1 sJ0    Y  d S )Nr*  r   rh   r   r   )rm   g~r?g e3E?)r.  r/  r0  r1  r2   r   rY   r   rb   rY   r.   r.   r/   r  n  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?rC   )r   r2   r   rS  r  rZ   rI  r  )rb   r  r  sigmar.   r.   r/   r  v  s    
zTestLognorm.test_logcdfr  r  c                 C   s   t jdS r   r  re   r.   r.   r/   r   ~  s    zTestLognorm.rngr   rO   rW   r   )r   r   rW   r  )ry  r   ru   r  c                 C   s   g | ]}d |v r|qS r  r.   )r7   er.   r.   r/   r9     s   zTestLognorm.<listcomp>)FTr   r  r  r  c           
      C   sV   t jjd||||d}i }	|r&||	d< |r2||	d< |r>||	d< tt j|fi |	 d S )NrS   )r   rD   rV   rU   r|   r   r   r   )r2   r   r   r   r	  r.   r.   r/   r     s    	z'TestLognorm.test_fit_MLE_comp_optimizerN)r   r   r   r  r  r   r  r   r   r   r$   rZ   r  r   r.   r.   r.   r/   rI  m  s   


rI  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zejj	e
d	d
dd Zejj	e
d	d
dd Zejj	e
d	d
dd Zdd Zejjedd
dd Zejdejjejjgejdddgdd Zejdg ddd Zd S )!TestBetac                 C   s:   t jddd}t|d t jddd}t|tj d S )Nr   r   rh   g;B.)r2   r  r   r   rZ   r   rb   r   r.   r.   r/   r    s    
zTestBeta.test_logpdfc                 C   sV   d\}}t g d}t||}t|| d t||t || d S )Ni  i  ry  rh   r1  gƒ)	rZ   r   r2   r  r   r   r%  rY   r   rb   r   r  rQ   r-   r.   r.   r/   test_logpdf_ticket_1866  s
    z TestBeta.test_logpdf_ticket_1866c                 C   s$   g d}t ttjj|dddd d S )NrO   rh   r1  r   r   r  )r   r   r   )r  r   r2   r  r   rX  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 )NrU  rh   )fafix_a)r  r   r2   r  r   rX  r.   r.   r/   #test_fit_duplicated_fixed_parameter  s    z,TestBeta.test_fit_duplicated_fixed_parameterzOverflow, see gh-14901reasonc                 C   s$   d\}}}t tj|||d d S )N)g?g     R@g   0xAgx)>)r   r2   r  r7  )rb   r-  r,   r-   r.   r.   r/   test_issue_12635  s    	
zTestBeta.test_issue_12635c                 C   sh   t g d}t g d}d}tj||d d| }t|| tj||d d| }t|| d S )N)g@3@?g^?gNC?)rR   rS   rv   r  r   r   )rZ   r   r2   r  rW  r   rS  )rb   Zinv_RZ
count_listr-  invr   r.   r.   r/   test_issue_12794  s    
zTestBeta.test_issue_12794c           	      C   sb   d}t dd}d}d| |d ||   }}}tj|||}tj|||}t|d|  d S )Nh㈵>r   r  r   )rZ   r   r2   r  r7  r`   r   )	rb   Zalpha_2Zcount_Znobsr6  r,   r-   r]  r   r.   r.   r/   test_issue_12796  s    zTestBeta.test_issue_12796c                 C   s   d\}}t tjd||tj d\}}t tjd||tj d\}}t tjd||d t tjd||d d\}}t tjd||d t tjd	||d d S )
Nr  r   )ry  r   r   )r   ru   ru   +ph  )ru   r   r  )r   r2   r  rY   rZ   r   )rb   r,   r-   r.   r.   r/   rE    s    zTestBeta.test_endpointszDoes not convert boost warningc                 C   sH   d\}}}t t  tj||| W d    n1 s:0    Y  d S )N)gףp=
?g   vH7B  @0B)r   warnsr1  r2   r  r7  )rb   r6  r,   r-   r.   r.   r/   test_boost_eval_issue_14606  s    
z$TestBeta.test_boost_eval_issue_14606r  a, b)ra        )@)rf  ra  c                 C   s,   d}z|||| W n t y&   Y n0 d S )Nrw  )OverflowError)rb   r  r,   r-   r-  r.   r.   r/    test_beta_ppf_with_subnormal_a_b  s
    z)TestBeta.test_beta_ppf_with_subnormal_a_br0  ))rh   rh   gο)r  r   g )r   rK  g&׾k )r   r   g*)Mc                 C   s   t t|| | d S rd   )r   r2   r  r>   r7  r.   r.   r/   r)    s    zTestBeta.test_entropyN)r   r   r   r  rT  rV  rY  r   r   skipifMACOS_INTELr\  r^  r`  rE  xfailr   rd  r   r2   r  r7  rW  rh  r)  r.   r.   r.   r/   rO    s(   



 rO  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))r  r   r   D>?)rb  r   r   m嗽?)r   r   rO   gPK?)r   r   r   g%p?)r4  r   rO   g#|/?)r4  rn  rn  gsM
<)r4  r   r   $5Є*?)^ 9^;r   rO   gompP?)rp  rn  rn  g7j"!9)rp  r   r   z^J?)r  r   rO   gܷ"+>)r  rn  rn  grNs: )r  r   r   gK>c                 C   sZ   d\}}t g d}t||}tt ||  t|	|t 
|| d S )NrQ  rR  )rZ   r   r2   r   r   r  r   r  r   rY   r   rS  r.   r.   r/   r  B  s
    zTestBetaPrime.test_logpdfc                    s   t jddd}t|d d\ tg d}t j| }tt|  t j	j
 fdd|D }t||dd	d
 d S )Nr   ry  r5  rm   rQ  rR  c                    s   g | ]}t j| qS r.   )r2   r   )r7   r  r   r  Zgen_cdfr.   r/   r9   V  r:   z*TestBetaPrime.test_cdf.<locals>.<listcomp>-=r   )r2   r   r`   r   rZ   r   r   r  r  r<   Z_cdf_singler   )rb   rQ   rV  Zcdfs_gr.   rr  r/   r  I  s    
zTestBetaPrime.test_cdfzp, a, b, expected))rj         ?r  gV)?)r[  rt  r  gWJB9*=)r  rt  r  gOG J<)rl  r         @gΣ01)      ?r   ru  g8ǘ`?)>q?r   rO   gMDc                 C   s"   t j|||}t||dd d S r	  )r2   r   r7  r   )rb   r-  r,   r-   rK   rQ   r.   r.   r/   r  h  s    
zTestBetaPrime.test_ppfz
x, a, b, pc                 C   s   t tj||||dd d S r	  )r   r2   r   r7  )rb   rQ   r,   r-   r-  r.   r.   r/   test_ppf_gh_17631u  s    zTestBetaPrime.test_ppf_gh_17631zx, a, b, expected))rb  rn  rn  r  )rb  r   rO   gV[?)r  r   rO   rw  c                 C   s   t tj||||dd d S r	  )r   r2   r   r`   )rb   rQ   r,   r-   rK   r.   r.   r/   test_cdf_gh_17631y  s    zTestBetaPrime.test_cdf_gh_17631)r  r   rO   g%?)r  r   r   goXr?c                 C   s.   t j|||}|dk sJ t||dd d S )Nr  gh㈵>rp   )r2   r   r`   r   )rb   rQ   r,   r-   rK   r  r.   r.   r/   test_cdf_extreme_tails  s    z$TestBetaPrime.test_cdf_extreme_tailsc                 C   sB   g d}g d}g d}g d}t j|||}t||dd d S )N)ru   r   rW   r   r   r   r   r   r   r   r   r   rn  rn  )r   rW   r   rO   rO   rO   rO   r   r   r   r   r   rn  rn  )rb  r  ꌠ9Y>)Fr  r4  rp  r  r  rb  r4  rp  r  rb  r4  )g/:g  U/7gKH9g<![a?gw 4?g)J?g5?rq  ro  rn  rm  g%?gsM
<r  r[  rp   )r2   r   rS  r   )rb   r,   r-   rQ   r<  Z	sf_valuesr.   r.   r/   rV    s    zTestBetaPrime.test_sfc                 C   s.   t jjg dddd t jddd d d S )N)rO   r   r5  r  皙?r   r   r  r  r  )r2   r   r   re   r.   r.   r/   test_fit_stats_gh18274  s    z$TestBetaPrime.test_fit_stats_gh18274c                 C   s.   t jdg}tdddgd}t|| d S )NgooB?rW   r  gffffff@ru   )rZ   r   r2   r   r  r   )rb   r<  r   r.   r.   r/   test_moment_gh18634  s    
z!TestBetaPrime.test_moment_gh18634N)r   r   r   Zcdf_valsr  r  r   r   r   r  rx  ry  rz  rV  r}  r~  r.   r.   r.   r/   rl  %  s2   	




rl  c                   @   s`   e Zd Zdd Zdd Zdd Zdd Zej	d	d
dgdd Z
ej	dg ddd ZdS )	TestGammac                 C   s<   t jjdddd}t|d t jjdddd}t|d d S )	NZ   i  ry  r  g
CTb?r   rR   gBΖ?)r2   r  rY   r   rK  r.   r.   r/   r    s    
zTestGamma.test_pdfc                 C   s   t jdd}t|d d S rC  )r2   r  r   r   rP  r.   r.   r/   r    s    zTestGamma.test_logpdfc                 C   s"   g d}t ttjj|ddd d S )NrU  r   r  )r   r   )r  r   r2   r  r   rX  r.   r.   r/   rV    s    z#TestGamma.test_fit_bad_keyword_argsc                 C   s@   t jtjdddddsJ t jtjdddd	ds<J d S )
Nrl  r   gplC@r  r}   r  rS   g1}t@ry   )rZ   iscloser2   r  rW  re   r.   r.   r/   rY    s    
zTestGamma.test_isfrV   r  r  c                 C   s.   t jj|d |d d|d}t|ddd d S )N   r  r   r  g>S*ry   rp   )r2   r  r#  r   rb   rV   r  r.   r.   r/   r$    s    zTestGamma.test_delta_cdfza, ref, rtol))r_  gt.ro   )rW   r  ro   )rS   gX>k-־@ry   )r  gwM7@ro   )g NgmCg%og$6@ro   )rc  oܘ#]@ro   c                 C   s   t tj|||d d S r  )r   r2   r  r>   )rb   r,   r<  rq   r.   r.   r/   r)    s    zTestGamma.test_entropyN)r   r   r   r  r  rV  rY  r   r   r   r$  r)  r.   r.   r.   r/   r    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   sz   t jd}d}|jd|d}|jd|d}tj||}tjt 	||d }t
|| t|}t||| d S )Nl   OP($ rR   r  )rH  r   rW   )rZ   r   r   normalr  r2   dgammarY   r  r   r   r   )rb   r   r   rQ   r,   r   r<  r8   r.   r.   r/   r     s    

zTestDgamma.test_pdfzx, a, expected))rK  r   ggrU>)ra  r   g$IC<)iru   g2Wj<)r  g~)A.=)ru   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  )r2   r  r`   r   r7  rS  rW  )rb   rQ   r,   rK   r`   r7  rS  rW  r.   r.   r/   test_cdf_ppf_sf_isf_tail  s    z#TestDgamma.test_cdf_ppf_sf_isf_tailr  ))rn  gmqn @)?g?)r  gx?c                 C   s   t tj||dd d S r	  r   r2   r  r>   r  r.   r.   r/   r)  %  s    zTestDgamma.test_entropy))r  r8  )r4  g>_)ri  g5i)r  go@)  4&kCg4Fa3@)rc  grO]@c                 C   s   t tj||dd d S r3  r  r  r.   r.   r/   test_entropy_entreme_values7  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   ru   r  ri  )rZ   r   r2   r  r>   r  r   )rb   rQ   r  r  r.   r.   r/   test_entropy_array_inputJ  s    z#TestDgamma.test_entropy_array_inputN)r   r   r   r  r   r   r   r  r)  r  r  r.   r.   r.   r/   r    s   



r  c                   @   s6   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 )Nrv   gޞw1D?r  r  rS   g6:֜?r   r2   chi2rY   re   r.   r.   r/   r  S  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 )Nrh  gλm:=6g'bd5 <r4  rp   rh   gQ8@   gܐ؆0guu[9=rO   g8-*@)r2   r  r7  r   )rb   rZ  rQ   r.   r.   r/   r  Y  s    zTestChi2.test_ppfr^  ))r_  gܫ>)r   gƯʉ?)rS   gn>@)   g͔v0@)r  g9:3@c                 C   s   t t| |dd d S rx   )r   r2   r  r>   rd  r.   r.   r/   r)  q  s    zTestChi2.test_entropyN)	r   r   r   r  r  r   r   r   r)  r.   r.   r.   r/   r  Q  s   r  c                   @   s>   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	dS )TestGumbelLc                 C   s2   t dd}tj|}tj|}t|| d S Nr  rL  )rZ   r  r2   r  r`   r7  r   r  r.   r.   r/   rP  }  s    zTestGumbelL.test_cdf_ppfc                 C   sH   t dd}tj|}tj|}t |}t| }t	|| d S r  )
rZ   r  r2   r  rj  r  r   r   expm1r   )rb   rQ   r  r  urp  r.   r.   r/   r    s    
zTestGumbelL.test_logcdf_logsfc                 C   s2   t dd}tj|}tj|}t|| d S )NrK  ru   )rZ   r  r2   r  rS  rW  r   r  r.   r.   r/   r    s    zTestGumbelL.test_sf_isfrU   r   r   c                 C   s2   t jjd|d}t jj||d\}}t|| d S )NrS   )r   rU   r   )r2   r  r   r   r   )rb   rU   r   Z
fitted_locr   r.   r.   r/   test_fit_fixed_param  s    z TestGumbelL.test_fit_fixed_paramN)
r   r   r   rP  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S )TestGumbelRc                 C   s   t tjdddd d S )Nr   ?~T}%m;r  rp   )r   r2   r  rS  re   r.   r.   r/   rV    s    zTestGumbelR.test_sfc                 C   s   t tjdddd d S )Nrl  r  r  rp   )r   r2   r  rW  re   r.   r.   r/   rY    s    zTestGumbelR.test_isfN)r   r   r   rV  rY  r.   r.   r.   r/   r    s   	r  c                   @   s  e Zd Zejdd Zejdd Zejdd Zej	de
dej
d	ejjd
gej	dddgej	dg dej	dddgdd Zejjej	dddgdd Zdd Zejjddej	ddd gej	d!ddgd"d# Zd$d% Zd&d' Zd(d) Zej	d*e
g d+g d,g d-ej
g d.g d/g d0ejjd
ej
g d1ed2d3d4ed5dd6ejjd
gd7d8 Zej	d*e
g d+g d,g d-ej
g d.g d/g d0ejjd
ej
g d1ed2d3d4ed5dd6ejjd
gd9d: Zej	d;d<dgej	d=d>d?gd@dA Zej	dBdCdDgdEdDggdFdG Zej	dHdId<ejejejfgdJdKggdLdM Zej	dNg dOej	dPejj dQedRd<dSdTfejj!dQedRd<dSdTfejj dUed<dVdSdQfejj!dUed<dVdSdTfgdWdX Z"dYS )ZTestLevyStablec                 C   s,   t ttjd }t jjj|jdd}|S )a  Sample data points for pdf computed with Nolan's stablec

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

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

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

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

        Typically inputs for stablec:

            stablec.exe <<
            1 # pdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-pdf-sample-data.npyx,p,alpha,beta,pctnames	rZ   loadr   __file__parentcorerecordsZ
fromarraysTr  r.   r.   r/   nolan_pdf_sample_data  s    z$TestLevyStable.nolan_pdf_sample_datac                 C   s,   t ttjd }t jjj|jdd}|S )a#  Sample data points for cdf computed with Nolan's stablec

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

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

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

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

        and the equivalent for the right tail

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

        Typically inputs for stablec:

            stablec.exe <<
            2 # cdf
            1 # Nolan S equivalent to S0 in scipy
            .25,2,.25 # alpha
            -1,-1,0 # beta
            -10,10,1 # x
            1,0 # gamma, delta
            2 # output file
        z.data/levy_stable/stable-Z1-cdf-sample-data.npyr  r  r  r  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)rZ   r  r   r  r  r  r.   r.   r/   nolan_loc_scale_sample_data  s    	z*TestLevyStable.nolan_loc_scale_sample_datasample_sizer   ro  ZmarksparameterizationZS0ZS1z
alpha,beta))r  r   )r  r   )rn  r   )rA  rh   zgamma,deltar   r   r  c           
      C   sF   |t j_t j||||d}t |j|dd|j\}}	|	dksBJ d S )N)r   r  rV   rU   r   rp  r   )r2   levy_stabler  rs  r   r`   )
rb   r  r   r  r  r  r  lsr   r-  r.   r.   r/   r	    s    zTestLevyStable.test_rvsr  rh   r   c                 C   sZ   t jd d}d}d}tjj||||dd}tj|d||||fd\}}|d	ksVJ d
S )z3Additional test cases for rvs for alpha equal to 1.h:r  rh   rn  r   rU   rV   r   r  r  rj   N)rZ   r   r   r2   r  r   rs  )rb   r  r   rU   rV   rQ   statr-  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  rm   rm   rm   rm   羼 u?r  r  r  r  67',?r  r  r  r  tA}˜.?r  r  r  r  Gz?r   rj   r   )\(̿rW   gۧ1?r   g9]c?)r  r  r  r  r  r   gv?r  )r2   r  r  r   r   r   rb   rQ   alpha1beta1loc1scale1r  alpha2beta2r
  r  r.   r.   r/   r  7  s    

zTestLevyStable.test_fitzUnknown problem with fitstart.rZ  zalpha,beta,delta,gamma)rn  r  rW   r   )r  r  rW   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.rK  r   rU   rV   r   r|   rj   rp   N)r2   r  r  r   r  r   )rb   r   r  r  r  r  r   r   Z	alpha_obsZbeta_obsZ	delta_obsZ	gamma_obsr.   r.   r/   test_fit_rvsO  s    

zTestLevyStable.test_fit_rvsc           
      C   s~   t g d}tj|\}}}}tj| \}}}}	t|d |dksNJ t|| t||  t||  t|	| d S )Nr   r   r   r   rR   rR   rR   r   r   rS   rS   r   r   )rZ   r   r2   r  r  r   r   )
rb   rQ   r  r  r  r  r  r  r
  r  r.   r.   r/   test_fit_beta_fliph  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  )rZ   r   r2   r  r  r   )rb   SHIFTrQ   r  r  r  r  r  r  r
  r  r.   r.   r/   test_fit_delta_shiftt  s    

z#TestLevyStable.test_fit_delta_shiftc                 C   s   g d}t j|\}}}}|dk s2J d| |t|k sVJ dt| d| g d}t j|\}}}	}
|dksJ d| |	t|ksJ dt| d|	 d S )	N)r   r   r   r   rR   rR   rR   r   r      r  r   zExpected alpha < 1, got zExpected loc < z, got )r   r   r   r   rR   rR   rR   r   r      r  zExpected alpha > 1, got zExpected loc > )r2   r  r  rE  r  r  r.   r.   r/   test_fit_loc_extrap  s    $z"TestLevyStable.test_fit_loc_extrapz pct_range,alpha_range,beta_range)rj   rh   r  )rO   r   rW   )r   r   r*  )rj   r   rh   rO  r  )rO   rh   r   rn  rW   )r   r   r   r5  r1  r   )rj   r   rO   r   ffffff?rh   ?r  rw  rO  r  rO   rW   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 ]4\}	\}
}}|
tj_	|dur||| n|}t
 }|td tjj|d |d |d ddd}tjddP t|g d|t||d  t||d  t|d  g}W d   n1 s0    Y  ||d |kt|B  }t||d |d |	|
||jj|f d!d" W d   q1 s0    Y  qd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   rh   rw  r|  r  rj   r  r5  r   rO  ry  rO   r   r  )rh   r1  r2  r  r  )gٿ333333ӿr5  r  rh   r  r  rO   ry  r5  r  )r*  rw  r  r@  r  )rZ   isinr   r>  alpha_range
beta_range	pct_ranger.   r/   rE     s    










 
%


*


/


4
9
>
C
z7TestLevyStable.test_pdf_nolan_samples.<locals>.<lambda>	piecewiser  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr  r   r  ry  r  rZ   r  r  r  r.   r/   rE     s    

c                    s:   | d dk @ t | d @ d v @ t | d @ S )Nr   r  r  r  r  r  r  r  is_linux_32r  r.   r/   rE     s    
g&.=c                    s<   t | d t | d  @ t | d @ | d dk@ S )Nr  r   r  ry  r  r  r  r.   r/   rE     s    
fft-simpsonri  c                    s<   | d dkt | d @ t | d  @ t | d @ S )Nr   rA  r  r  r  r  r  r.   r/   rE     s    
r  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk @ S )Nr  r   r  r   rA  r  r  r  r.   r/   rE   '  s    

Nz2Density calculations experimental for FFT method.*rQ   r   r  r   r   rV   rU   r  r  ZcalcZabserrrelerrr-  r  z8pdf test %s failed with method '%s' [platform: %s]
%s
%sFerr_msgverbose)platformunamesystemmachinejoin	processorrj  r2   r  pdf_default_methodr   recordr1  rY   rZ   r  r   r   isnanr   r   r  )rb   r  r  r  r  r   r  Zplatform_desctestsixdefault_methodrq   filter_funcsubdatasupr-  subdata2failuresr.   r  r/   test_pdf_nolan_samples  s    
O
	 $	
z%TestLevyStable.test_pdf_nolan_samplesc                    s  |}dd fddgdd fddgdd fd	dgdd
 fddgdd fddgdd fddgg}t |D ]2\}\}}	}
|tj_|
dur||
| n|}t }|td tjj|d |d |d ddd}tj	ddP t
|g d|t||d  t||d  t|d  g}W d   n1 sR0    Y  ||d |	kt|B  }t||d |	d|||jj|f dd W d   q1 s0    Y  qdS ) z4 Test cdf values against Nolan's stablec.exe output.r  rs  c                    s   t | d t | d  @ t | d @ | d dkt | d g d@ | d dk@ | d dkt | d g d@ | d dk@ B  @ S 	Nr  r   r  r  )r  r?  r@  rj   rO   ry  r5  r  r  r  r  r.   r/   rE   ~  s$    



z7TestLevyStable.test_cdf_nolan_samples.<locals>.<lambda>r   c                    s   t | d t | d  @ t | d @ | d dkt | d g d@ | d dk@ @ | d dkt | d g d@ | d dk@ B S r  r  r  r  r.   r/   rE     s"    

	

r  ri  c                    s<   t | d t | d  @ t | d @ | d dk@ S )Nr  r   r  333333?r  r  r  r.   r/   rE     s    
r_  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr  r   r  rn  r  r  r  r  r.   r/   rE     s    

r  c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr  r   r  r  rn  r  r  r  r.   r/   rE     s    

rj   c                    sH   t | d t | d  @ t | d @ | d dk@ | d dk@ S )Nr  r   r  r  r  r  r  r  r.   r/   rE     s    

Nz[Cumulative density calculations experimental for FFT method. Use piecewise method instead.*rQ   r   r  r   r   r  r  r  r  r-  r  z)cdf test %s failed with method '%s'
%s
%sFr  )rj  r2   r  cdf_default_methodr   r  r1  r`   rZ   r  r   r   r  r   r   r  )rb   r  r  r  r  r   r  r  r  rq   r  r  r  r-  r  r  r.   r  r/   test_cdf_nolan_samplesa  sr    	

N$	
z%TestLevyStable.test_cdf_nolan_samplesr   r   rk  rY   r`   c           
      C   s   t  }|jdko dt  d v }|r8|dkr8td |}dtj_dtj_	||d |k }d| tj_
|d	v svJ |dkrtjjntjj}||d
 |d |d ddd}	t|	|| d dS )zGTests for pdf and cdf where loc, scale are different from 0, 1
        r  32bitr   rY   z4Test unstable on some platforms; see gh-17839, 17859r  r   S)rY   r`   rQ   r   r  rW   r   r  ri  N)r  r  r  architecturer   r   r2   r  r  r  r  rY   r`   r   )
rb   r  r   rk  r  r  r   r  r  rX  r.   r.   r/   test_location_scale  s     
z"TestLevyStable.test_location_scalezmethod,decimal_placesr  r   r  c              	   C   s   t g d}t g d}t g d}t jddp t J}|jtdd |tj_tjj	|d|dd	d
}t
|||| W d   n1 s0    Y  W d   n1 s0    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   rW   rW   rW   rW   r   r   r   r   r   r   r   r   )gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g?gDioɴ?g r?gH?g+?gHPs?gX ?g&?g0*?gv/?ga2U0*?)r   r   rh   r   r   r   rh   r   r   r   rh   r   r   r   rh   r   r   r   rh   r   r  r  zDensity calculation unstable.*)categorymessager   r   r  N)rZ   r   r  r   rH   r1  r2   r  r  rY   r   )rb   r  Zdecimal_placesxsdensityZbetasr  rY   r.   r.   r/   'test_pdf_alpha_equals_one_beta_non_zero  s&    z6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerozparams,expected)r  r  r   r   )rW   rw  rR   rn  )rR   r  r   r   c                 C   s4   t jj |d |d |d |d dd}t|| d S )Nr   r   rW   r   r  r  )r2   r  r   )rb   paramsrK   Zobservedr.   r.   r/   r  :  s
    zTestLevyStable.test_statsr   )r   rh   r  zfunction,beta,points,expectedr  r  rR   rm   r=  r  c                 C   s>   d|  k rdk sn 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   rZ   r  r   )rb   r   r  r  r  rK   r.   r.   r/   !test_distribution_outside_supportH  s
    (z0TestLevyStable.test_distribution_outside_supportN)#r   r   r   r   r  r  r  r  r   r   r   r  r	  r  r  rk  r  r  r  r  rZ   r  r   r  r  r   r  r   r   r  r2   r  r`   rY   r  r.   r.   r.   r/   r    s   
!
+

 B
{ 
 
r  c                   @   s   e Zd Zdd Zdd ZdS )TestArrayArgumentc                 C   s   t jd d S r   r   re   r.   r.   r/   r   x  s    zTestArrayArgument.setup_methodc                 C   s.   t jjtdtddd}t|jd d S )Nru   r  r  )r2   r  r   rZ   r   r  r   r  rb   r   r.   r.   r/   test_noexception{  s    z"TestArrayArgument.test_noexceptionN)r   r   r   r   r  r.   r.   r.   r/   r	  w  s   r	  c                   @   s   e Zd Zdd Zdd ZdS )TestDocstringc                 C   sD   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 )Nr   rG  )r2   r   r'  r   lowerrG  re   r.   r.   r/   test_docstrings  s    zTestDocstring.test_docstringsc                 C   s   t   t   d S rd   )r2   r<   r;   re   r.   r.   r/   test_no_name_arg  s    zTestDocstring.test_no_name_argN)r   r   r   r  r  r.   r.   r.   r/   r    s   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   rW   r   rW   r   r   r   rW   )r   rW   rW   r   r   r   )r   r   r   rZ   r   r,   r-   rN  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)ncfrV  rW  c                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestFitMethod.setup_method)r"  r  r  z	dist,argsc                 C   sz   || j v rtd|  tdddddtjg}tdddddtjg}tt|}t	t
|j|dd t	t
|j|dd d	S )
r&  z"%s fit known to fail or deprecatedr  r  r  r  r  r   r  N)fitSkipNonFiniter   r   rZ   r   r   r   r   r2   r  r   r   )rb   r8   r   rQ   r  Z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n 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    n1 s0    Y  d S )Ni90  r  r  r   rm         4@r  r   rW   r   r  r  r}   )rZ   r   r   r  r2   r   r   r  rI  r2  r   r   r   )rb   rQ   Zexpected_shaper.   r.   r/   test_fix_fit_2args_lognorm  s    "
z(TestFitMethod.test_fix_fit_2args_lognormc                 C   s   t dd}tj|\}}t|d t|t d tjj|dd\}}t|d t|t d tjj|dd\}}t|d t|d d S )Nr   r  r   rW   r   r  )rZ   r   r2   r  r   r   r  r   rb   rQ   rU   rV   r.   r.   r/   test_fix_fit_norm  s    


zTestFitMethod.test_fix_fit_normc                 C   sn  t dd}t | }d}tjj||d\}}}t | | }tt |t	| |dd t
|| t|| | dd d}d}tjj|||d\}}}t
|| t
|| t|| | dd d	}d}tjj|||d\}}}t
|| t
|| t|| | dd d}d	}	tjj|||	d
\}}}t
|| t
||	 |t |	 }
tt	||
 d S )Nr   r  r   r   ru   r  r  r   r   rW   r  )rZ   r   rI  r2  r2   r  r   r   r   Zdigammar   )rb   rQ   Zmeanlogr   r,   rU   rV   rD   r   r   rN  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   rZ   rI  r%  r   psi)r,   r-   rQ   r,  s1r  Zpsiabr   r.   r.   r/   mlefunc  s    z0TestFitMethod.test_fix_fit_beta.<locals>.mlefunc)r  r   rh   r   r   r  r  r}   rW   )r   r   r   ri  )r   r   r   rh   rJ  )r   r   r   )r   r   r   r   )r   r   r   r   )
rZ   r   r2   r  r   r   r   r   r  r   )rb   r  rQ   r,   r-   rU   rV   dadbr  r	  b2r
  r  r  r.   r.   r/   test_fix_fit_beta  s:    








zTestFitMethod.test_fix_fit_betac                 C   s   t g d}tj|\}}t|d t|d tjj|dd\}}t|d t|d tjj|dd\}}t|d t|d d S )N)rW   rW   r   r   r   r   r   r  rW   r   r  r   r   r   )rZ   r   r2   r"  r   r   r  r.   r.   r/   test_expon_fit(  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)rn  r   rR   r      r  r   r   r[  rp   r  r  rW   r  )r   Zfix_s)rZ   r   rI  r2   r   r   r   r3  r   r   r2  r  )rb   rQ   Zlnxm1r  rU   rV   r.   r.   r/   test_lognorm_fit7  s     




zTestFitMethod.test_lognorm_fitc                 C   s   t g d}tj|\}}t||  t||  tjj|dd\}}t|d t||  tjj|dd\}}t|d t|d t	t
tjj|dd t	t
tjj|dd d S )N)r  r  r        "@r   r   rR   r  rl   r  )rZ   r   r2   r  r   r   rE  r  r  r  r   r  r.   r.   r/   test_uniform_fitK  s    


zTestFitMethod.test_uniform_fitr  ZMLEZ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  rS   r   rp  r  )r   r  )rW  r  r[  r   )rX  r  r  )r   r  )r  r  )r  r  r   rW   )rW  r   r  r   r   )rW  r   r   r   r  )rW  r   r   r  )r  r   r   r   )	r2   r  r   r   r   r  r   r   r  )rb   r  r,   r-   rQ   Zres_1Zres_2Zres_3Zres_4Zres_5ZaaZ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 )NrW   rS   )r.  r   i)Zenikibenikir  )r2   r-  r   r   r  r   r   )rb   r  r8   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                   @   sT   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 )
TestFrozenc                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    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  rT   r  r   rW   )r2   r  rY   r   r`   r7  rW  rS  r  r2  r  r3  r>   r  r,   r-   )rb   r8   frozenresult_fr  r.   r.   r/   r    sJ    
















zTestFrozen.test_normc                 C   s  d}t j}t |}|d}|d|}t|| |d}|d|}t|| |d}|d|}t|| |d}|d|}t|| |d}|d|}t|| | }||}t|| |	 }|	|}t|| |
 }|
|}t|| | }||}t|| | }||}t|| |d}|d|}t|| t|j|jj t|j|jj d S )Nrl   r  r   r  rW   )r2   r  rY   r   r`   r7  rW  rS  r  r2  r  r3  r>   r  r,   r8   r-   )rb   r,   r8   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   rW   r  r  )r2   r   r  r   )rb   r,  m1rw  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 ]l}t|}t j|d}|j|j	 }}t|d t
t| td}t j|\}}t||gdd	g qd S )
Nr@  r  rm   r  rO   r   r  r  rh   )r2   r  r8   r  r   rY   rZ   r   r,   r-   r   r   r  r   )rb   rN  r  r,   r-   Zrv1r.   r.   r/   r    s2    



zTestFrozen.test_abc                 C   s   t ttjd d S )NZ	rv_frozen)r   r+   r2   r3   re   r.   r.   r/   test_rv_frozen_in_namespace9  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  rp  )r2   r  r   r+   r|   r   Z	get_staterZ   r   ZRandomStater   )rb   r,  Zrndmr.   r.   r/   test_random_state=  s    
zTestFrozen.test_random_statec           
      C   s   t dd}t d}t jg dg dfd}|||fD ]}d|_|jdd	 t|}|jdd	}t|}|jdd	}t	|| |
d
|
d
g}	t	|	d |	d  t	||	d ||	d  q8d S )Ngdsz@g@e?r  )r   r   rW   r   r  r  r   r  r   rh   r   r   )r2   r  r;  r;   r|   r   pickledumpsloadsr   r7  r`   )
rb   r  Zpoissr  distfnrD   Zr0Z	unpickledZr1Zmediansr.   r.   r/   test_picklingK  s$    




zTestFrozen.test_picklingc              
   C   s   dd }t jdddd}tjddd< |j|d	dd
d}t jj|dddd	dd
d}W d    n1 sh0    Y  t|| t jddd}||}t jj|ddd}t|| d S )Nc                 S   s   | S rd   r.   r   r.   r.   r/   r   f  s    z$TestFrozen.test_expect.<locals>.funcrW   r   r   )r,   rU   rV   r  )r  divider   T)r   ubconditionalrW   r   rU   rV   r   r:  r;  r"  )r   r   rU   )r2   r  rZ   r  r   r   r;  )rb   r   ZgmZgm_valZ	gamma_valr-  Zp_valZpoisson_valr.   r.   r/   test_expectc  s    $

zTestFrozen.test_expectN)r   r   r   r   r  r.  r0  r  r1  r3  r8  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   s   | d | d  S )Nru   r.   r   r.   r.   r/   rE   |  r:   z&TestExpect.test_norm.<locals>.<lambda>ru   rW   rT   r   r  r  c                 S   s   | S rd   r.   r   r.   r.   r/   rE     r:   r   rO  c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   rU   rV   r   r:  rw  c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   TrU   rV   r   r:  r;  r  )r2   r  r   r   r7  )rb   rp  ro  r   r:  prob90prob90cr.   r.   r/   r  {  s    zTestExpect.test_normc              	   C   s   t jjdd dddd}t|ddd	 t jjd
d dddd}t|ddd	 t jjdddddd}t jjdddddd}t jjdd ddd||dd}t|ddd	 t jjdd ddd||dd}t|ddd	 d S )Nc                 S   s   | d | d  S )NUUUUUU@r.   r   r.   r.   r/   rE     r:   z&TestExpect.test_beta.<locals>.<lambda>r  ru   rW   )r   rU   rV   qq?r  r  c                 S   s   | S rd   r.   r   r.   r.   r/   rE     r:   r  rl   rE  rO  rR   rT   r   c                 S   s   dS )Nr  r.   r   r.   r.   r/   rE     r:   )rR   rR   Fr=  rw  c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   Tr  )r2   r  r   r   r7  )rb   rp  ro  r:  r   rC  rD  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  rR   r  r  r"  c                 S   s   | S rd   r.   r   r.   r.   r/   rE     r:   z+TestExpect.test_hypergeom.<locals>.<lambda>)r  rR   r  r>  r  r  c                 S   s   | d d S Nr&  rW   r.   r   r.   r.   r/   rE     r:   r  c                 S   s   | d d S rH  r.   r   r.   r.   r/   rE     r:   ru   )r   rU   r   r:  r   c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   r  r  c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   T)r   rU   r   r:  r;  c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   r   )r   r   r:  )r2   r  r   r   r  r%  )
rb   Zm_trueZv_truero  rp  Zv_boundsZ	prob_trueprob_boundsZprob_bcZ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   s   dS r   r.   r   r.   r.   r/   rE     r:   z)TestExpect.test_poisson.<locals>.<lambda>r<  r   F)r   r   r;  r   rW   r  r  c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   T)r2   r;  r   r`   r   )rb   rI  Zprob_b_trueZ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)rn  r  )rh   r  r  )r2   Zgenhalflogisticr   r   )rb   Z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   s   dS r   r.   r   r.   r.   r/   rE     r:   z/TestExpect.test_rice_overflow.<locals>.<lambda>)rN  r  c                 S   s   dS r  r.   r   r.   r.   r/   rE     r:   c                 S   s   dS Nr   r.   r   r.   r.   r/   rE     r:   )r   rZ   r  r2   ricerY   r   re   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)r5  r   c                 S   s   | S rd   r.   rN   r.   r.   r/   rE     r:   z(TestExpect.test_logser.<locals>.<lambda>r  r  ro   r}   c                 S   s   | S rd   r.   rR  r.   r.   r/   rE     r:   r>  )r2   r  r   r   rZ   rI  )rb   r-  rU   Zres_0Z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   s   | S rd   r.   r   r.   r.   r/   rE     r:   z)TestExpect.test_skellam.<locals>.<lambda>r  c                 S   s   | d S r  r.   r   r.   r.   r/   rE     r:   r[  r}   rW   )r2   rE  r   r   )rb   r  p2r/  rw  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   s   | S rd   r.   r   r.   r.   r/   rE     r:   z)TestExpect.test_randint.<locals>.<lambda>c                 s   s   | ]
}|V  qd S rd   r.   r7   r   r.   r.   r/   r    r:   z*TestExpect.test_randint.<locals>.<genexpr>ro   r}   )r2   r   r   r   r%  r  )rb   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   s   | d S r  r.   r   r.   r.   r/   rE     r:   z&TestExpect.test_zipf.<locals>.<lambda>r<  )r	   r1  r2   rn  r   re   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   s   dS r   r.   r   r.   r.   r/   rE     r:   z/TestExpect.test_discrete_kwds.<locals>.<lambda>r<  r  c                 S   s   dS r   r.   r   r.   r.   r/   rE     r:   rJ      r  )r   Zmaxcount	chunksizeZ	tolerancer  r  )r2   r;  r   r   )rb   Zn0Zn1r.   r.   r/   test_discrete_kwds   s
    zTestExpect.test_discrete_kwdsc                 C   s6   dd }dD ]$}t jd|}t|||dd qd S )Nc                 S   s0   | d d| d   d| d   d| d   |  S )Nru   rR   r   r  r   r   rW   r.   r  r.   r.   r/   poiss_moment5
  s    z-TestExpect.test_moment.<locals>.poiss_moment5)ru   r>  ru   r4  rp   )r2   r;  r  r   )rb   r_  r  Zm5r.   r.   r/   test_moment  s    zTestExpect.test_momentc                 C   sn   t tjjdddd t tjjdddd t tjjdddd t tjjddd	 t tjjd
dd
 d S )Nr
  r  rT   r  rR   rO   )   r  ra  U   r"  )r   r2   r  r   r  r  re   r.   r.   r/   test_challenging_cases_gh8928  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 )NrR   ru   rT   rz  r)  rA  rC  r  r1  TrB  r  g433333@g433333r  )r2   r  r2  r   r   )rb   r8   r<  r.   r.   r/   test_lb_ub_gh15855  s"    zTestExpect.test_lb_ub_gh15855N)r   r   r   r  rG  rJ  rK  rM  rQ  rS  rU  rZ  r[  r^  r`  rc  rd  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S )TestNctc                 C   s@   t dd}t|dd t dd}t|dddd d S )Nru   r   rh   r   g K?rR   r  )r2   nctr   r`   r   r   r.   r.   r/   test_nc_parameter1  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 )Nru   r   r>  rO   r   )gMp^j?g6].ftv?gȳ'ς?gu?)g!Y<a?g]d1p?go|?g?)gHdY?g2Ԥg?g}o/u?g .mr?ri  rp   )r2   rf  rY   rZ   r   r  r   r   )rb   r   rK   r.   r.   r/   test_broadcasting9  s    zTestNct.test_broadcastingc                 C   s   t dd}t| d d S )Nr   r   rl   )r2   rf  r   r  r   r.   r.   r/   test_variance_gh_issue_2401A  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 )Nrw  r5  r  )rZ  ncr  rA  r  )r2   rf  r   rZ   r   r   r  r  r  r.   r.   r/   test_nct_inf_momentsI  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 )Nrv   rW   g@ @g*dn?r   r4  rp   r   gqI  @gL) ?r  )r2   rf  r2  r   )rb   Znct_mean_df_1000Znct_stats_df_1000Zexpected_stats_df_1000Znct_meanZ	nct_statsr0  r.   r.   r/   test_nct_stats_large_df_valuesV  s    
z&TestNct.test_nct_stats_large_df_valuesc                 C   s   t tjddtdd d S )NrW   i   r   )r   r2   rf  r`   r   re   r.   r.   r/   test_cdf_large_ncl  s    zTestNct.test_cdf_large_ncN)	r   r   r   rg  rh  ri  rk  rl  rm  r.   r.   r.   r/   re  0  s   re  c                   @   s,   e Zd Zdd Zdd Zdd Zdd Zd	S )
TestRecipInvGaussc                 C   s   t jdd}|dksJ d S )Nr   r1  rm   )r2   recipinvgaussrY   rD  r.   r.   r/   test_pdf_endpoints  s    z#TestRecipInvGauss.test_pdf_endpointc                 C   s"   t jdd}|tj ksJ d S )Nr   r1  )r2   ro  r   rZ   r   r  r.   r.   r/   test_logpdf_endpointw  s    z&TestRecipInvGauss.test_logpdf_endpointc                 C   s$   t jdd}d}t||dd d S )Nr   rh   g9V9s;r  rp   )r2   ro  r`   r   rb   r-  rK   r.   r.   r/   test_cdf_small_x{  s    z"TestRecipInvGauss.test_cdf_small_xc                 C   s"   t jdd}d}t||d d S )NP   rh   glH<r  )r2   ro  rS  r   rr  r.   r.   r/   test_sf_large_x  s    z!TestRecipInvGauss.test_sf_large_xN)r   r   r   rp  rq  rs  ru  r.   r.   r.   r/   rn  q  s   rn  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )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)ry  r  r  rm   r-   )rO   rO   rh   rw  r   r  r  r  r   )r   rZ   r  r2   rP  rY   r  r   r`   rj  r7  r   )rb   rQ   r6  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  rw  r   )r   ru   )r-   r   )r2   rP  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 )NrR      )g/Ƹ?g[jǊ\?g 	?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?rO   r   g     @_@r   r  )	g<~@gwd
@gC?@gb
0@g` A@@g'NxP@g33-a@g4pv@g$F@rh      )gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g<
uQ@giff T@g9r[V@g3bXQ Y@gqxJ[@g`*DD ^@g@`@gdAa@)r2   rP  r`   rZ   r   r   r7  r1   )rb   r`   Zcdf_expZprobabilitiesr7  Zppf_expr.   r.   r/   test_rice_gh9836  s    "

zTestRice.test_rice_gh9836N)r   r   r   rx  ry  r|  r.   r.   r.   r/   rv    s   rv  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )
TestErlangc                 C   s   t jd d S r   r   re   r.   r.   r/   r     s    zTestErlang.setup_methodc              	   C   s   t  j 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    n1 sx0    Y  d S )Nr*  r  r   r   r   r  )rh   r  rl   r  r~  r  rp   )r.  r/  r0  r1  r  r2   erlangr   r   r  r   )rb   r   Zresult_erlangZ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 )Nrh   r   r   rp  )r   r2   r~  rY   r  re   r.   r.   r/   test_gh_pr_10949_argcheck  s    z$TestErlang.test_gh_pr_10949_argcheckN)r   r   r   r   r  r  r.   r.   r.   r/   r}    s   r}  c                   @   sp   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	ejdddgddggdd Z
dd Zdd ZdS )TestRayleighc                 C   s   t jd d S )Nr  r   re   r.   r.   r/   r     s    zTestRayleigh.setup_methodc                 C   s   t jd}t|d d S )Nr   g)Zx)r2   r   r   r   rb   r  r.   r.   r/   r    s    zTestRayleigh.test_logpdfc                 C   s   t jd}t|d d S )Nr   i)r2   r   r  r   r  r.   r.   r/   r     s    zTestRayleigh.test_logsfr  )gB)Q?got|?)gS2P?g3?c                 C   s   t jjd||d}dd }|||}t jj||d\}}t|| t|| t jj|dd\}}t|d t j|\}}t|||| d S )Nr  r  c                 S   s"   t | | d dt|   d S )NrW   rh   )rZ   r%  r   )r   r   r.   r.   r/   r  	  s    z(TestRayleigh.test_fit.<locals>.scale_mler   r1  r  )r2   r   r   r   r   )rb   r   r  r   r  Zscale_expectrU   rV   r.   r.   r/   r    s    



zTestRayleigh.test_fitrN  rj   g̡=E?g@1d?c                 C   s"   t jjd||d}tt j| d S )Nr  r  )r2   r   r   r   )rb   r   r  r   r.   r.   r/    test_fit_comparison_super_method  s    z-TestRayleigh.test_fit_comparison_super_methodc                 C   s   t tj d S rd   )r   r2   r   re   r.   r.   r/   r  %  s    zTestRayleigh.test_fit_warningsc           	      C   s   t jd}d\}}}tjj||||d}tj|\}}|t |k sLJ tjj||d\}}|t |k srJ ||ks~J d S )Ni  )r   r  r  rp  r  )rZ   r   r   r2   r   r   r   rE  )	rb   r   rU   rV   r   r   r   r   r   r.   r.   r/   test_fit_gh17088(  s    
zTestRayleigh.test_fit_gh17088N)r   r   r   r   r  r  r   r   r   r  r  r  r  r.   r.   r.   r/   r    s   


r  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 )NrO   r  r   g:23W+g~`9k)r2   	exponweibrY   r   r   )rb   rQ   r,   rN  r-  r  r.   r.   r/   test_pdf_logpdf7  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 )NrL  r   r   r   rS   )rZ   rM  r2   r  rY   weibull_minr   r   rb   rQ   r,   rN  r-  rK   r  r.   r.   r/   test_a_is_1B  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 )Nrx  r   rR   )rZ   rM  r2   r  rY   r"  r   r   r  r.   r.   r/   test_a_is_1_c_is_1R  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   r  r  g'vR0=)g_QPr  r  gQ:<c                 C   s"   t j|||}t||dd d S r	  )r2   r  rS  r   )rb   rQ   r,   rN  r<  rS  r.   r.   r/   rV  q  s    zTestExponWeib.test_sfzp, a, c, ref))r   r  r  g;y$(@)gMg<r  r  gdbq^@)r[  r   rW   gE@)gvIh%L=r  r   g/7@)r  r  r  gTWTOc                 C   s"   t j|||}t||dd d S r  )r2   r  rW  r   )rb   r-  r,   rN  r<  rW  r.   r.   r/   rY    s    	zTestExponWeib.test_isfN)r   r   r   r  r  r  r   r   r   rV  rY  r.   r.   r.   r/   r  5  s   

r  c                   @   s   e Zd Zdd Zdd ZdS )TestFatigueLifec                 C   s    t jdd}t|ddd d S )Nr  r  X9ry   rp   )r2   r   rS  r   rU  r.   r.   r/   test_sf_tail  s    zTestFatigueLife.test_sf_tailc                 C   s$   d}t j|d}t|ddd d S )Nr  r  r  ry   rp   )r2   r   rW  r   )rb   r-  r6  r.   r.   r/   test_isf_tail  s    zTestFatigueLife.test_isf_tailN)r   r   r   r  r  r.   r.   r.   r/   r    s   r  c                   @   sX   e Zd Zdd Zdd Zejdddgdd	 Zd
d Z	ejdddgdd Z
dS )TestWeibullc                 C   s   t jdd}t|d d S rC  )r2   r  r   r   r  r.   r.   r/   r    s    zTestWeibull.test_logpdfc           
      C   sP  d}d}d}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|t	
d  t jj|||d}t|tt	
d  t jj|||d}t|td t jj|||d}	t|	d t jjdddd}t|td	 t jjdddd}	t|	d	 d
}t jj|||d}t|tdd  t jj|||d}t|dtd  t jj|||d}t|td t jj|||d}t|d t jj|||d}t|t	
d  t jj|||d}	t|	tt	
d  t jjdddd}t|t	
d  t jjdddd}	t|	tt	
d  d S )Nrn  rl   r  r  rH  r   r   rW   r  r}  g&.gCe )r2   r  rY   r   rZ   r   r   rI  r`   r   r  rj  rS  r  Zweibull_max)
rb   rQ   r,   r-   r-  r  rN  lcrD   r  r.   r.   r/   test_with_maxima_distrib  sH    


z$TestWeibull.test_with_maxima_distribrV   r  rO   c                 C   s*   t jj|d |d d|d}t|d d S )Nry  r  r   r  g>)r2   r  r#  r   r  r.   r.   r/   r$    s    zTestWeibull.test_delta_cdfc                 C   s   t jd}d\}}}t|||}|jd|d}tjj|ddd\}}}	tjj|ddd\}
}}||  krvdks|n J ||
ksJ tjj|ddd	d
\}}}|dksJ t|||}|jdd}t |t|f}t	|| d S )Nl   > )rW   r  rh   rS   rp  rn  r   r   r|  r  r  r  r  )
rZ   r   r   r2   r  r   r   r2  r  r   )rb   r   rN  rU   rV   r8   r   c2r
  r  c3r  r  Zc4r  r  r  r   r<  r.   r.   r/   test_fit_min$  s    
zTestWeibull.test_fit_minr  )r   r   r  )rv   r*  gq뮕qH)c                 C   s4   t tj|||dd t tj|||dd d S r  )r   r2   r  rS  rW  r  r.   r.   r/   r  B  s    zTestWeibull.test_sf_isfN)r   r   r   r  r  r   r   r   r$  r  r  r.   r.   r.   r/   r    s   T

r  c                   @   s   e Zd Zdd Zdd ZdS )TestDweibullc                 C   sR   t jd}d|jddd }tj|}tj|t d }t	||dd d S )N   q>~). rR   rS   r  rh   ro   rp   )
rZ   r   r   r  r2   dweibullr>   r  rI  r   )rb   r   rN  r   r<  r.   r.   r/   r)  K  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  rR   r   r  rh   ro   rp   )
rZ   r   r   r  r  r2   r  rS  r  r   )rb   r   rN  rQ   r   r<  r.   r.   r/   rV  X  s    zTestDweibull.test_sfN)r   r   r   r)  rV  r.   r.   r.   r/   r  J  s   r  c                   @   sT   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 )TestTruncWeibullc                 C   s(   t jddgddd}t|ddg d S )NrO   rl   g)\(?gףp=
?rm   )r2   truncweibull_minrY   r   r  r.   r.   r/   test_pdf_boundse  s    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 )Nrl   r  rm   r  g~?)r2   r  r   rZ   r   r   r   r  r.   r.   r/   r  j  s    
zTestTruncWeibull.test_logpdfc                 C   s(   t jddgddd}t|ddg d S )Nrm   r  rl   rO   )r2   r  r7  r   r  r.   r.   r/   test_ppf_boundsr  s    z TestTruncWeibull.test_ppf_boundsc                 C   s:   g d}t j|ddd}t j|ddd}t|| d S N)rm   rO   r   rh   r  rw  r  rl   rm   r  )r2   r  r7  r`   r   rb   r6  rQ   Zq_outr.   r.   r/   test_cdf_to_ppfw  s    z TestTruncWeibull.test_cdf_to_ppfc                 C   s:   g d}t j|ddd}t j|ddd}t|| d S r  )r2   r  rW  rS  r   r  r.   r.   r/   test_sf_to_isf}  s    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 )Nrl   r  r  c                    s   | | t j|   S rd   )r2   r  rY   )rQ   r,  r  r.   r/   xnpdf  s    z)TestTruncWeibull.test_munp.<locals>.xnpdfr   r   c                    s
    | dS r   r.   r   r  r.   r/   rE     r:   z,TestTruncWeibull.test_munp.<locals>.<lambda>rW   c                    s
    | dS r  r.   r   r  r.   r/   rE     r:   r   c                    s
    | dS rO  r.   r   r  r.   r/   rE     r:   r   c                    s
    | dS )Nr   r.   r   r  r.   r/   rE     r:   )r2   r  r  r   r   r   )rb   rm  r/  Zm1_expectedr   rw  Zm2_expectedZm3Zm3_expectedrx  Zm4_expectedr.   )r,   r-   rN  r  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 )Nr  r  rl   r   rh   r  )rZ   r  rI  r   r2   r  r`   r   rj  r7  rS  r  rW  )rb   r,   r-   rN  Zx_medr`   r  r7  rS  r  rW  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 )
Nrn  rl   rm   r  r  r   rW   r   r  )rZ   r   r2   r  rY   r  r   r   r`   rj  rS  r  r   )rb   rQ   rN  r,   r-   rV   r-  Zp_truncr  Zlp_truncr`   Z	cdf_truncr  Zlc_truncrD   Zs_truncr  Zls_truncr.   r.   r/   test_compare_weibull_min  s6    





z)TestTruncWeibull.test_compare_weibull_minc           
      C   s   d\}}}t ||d}tj||||}tj||||}tj||tj|| }tj||| }tj||tj|| | }	t j|| t j||	 d S )N)r  r   rt  rS   )	rZ   r  r2   r  rY   r`   r  testingr   )
rb   rN  r,   r-   rQ   r  r,  r  r  r-  r.   r.   r/   test_compare_weibull_min2  s    
 z*TestTruncWeibull.test_compare_weibull_min2N)r   r   r   r  r  r  r  r  r  r  r  r  r.   r.   r.   r/   r  c  s   )r  c                   @   s   e Zd Zdd Zdd ZdS )	TestRdistc                 C   s0   t j}g d}t|||dd|dd d S )Nr  g     @ru   r  )r2   rdistr   r`   r7  )rb   r7  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  rR   g@rh   rW   r   )rZ   r  r   r2   r  rY   r  )rb   rQ   rN  r.   r.   r/   test_rdist_beta  s
    &zTestRdist.test_rdist_betaN)r   r   r   r  r  r.   r.   r.   r/   r    s   r  c                   @   s<   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestTrapezoidc                 C   s`   g d}|D ]N}d|dg}t tj|||tj|| t tj|||tj|| qd S )N)r   r5  rh   r   r   r   )r   r2   r   rY   triangr`   )rb   modesmoderQ   r.   r.   r/   test_reduces_to_triang  s    
z$TestTrapezoid.test_reduces_to_triangc                 C   sN   t ddd}ttj|ddtj| ttj|ddtj| d S Nr   r   rR   )rZ   r  r   r2   r   rY   r  r`   rX  r.   r.   r/   test_reduces_to_uniform
  s    z%TestTrapezoid.test_reduces_to_uniformc                 C   s  t tjdddd t tjdddd t tjdddd t tjdddd t tjd	ddd
 t tjdddd t tjdddd
 t tjd	ddd t tjdddd t tjdddd t tjdddd t tjdddd d S )Nr   rW   r   rh   r*  r-  ry  r  rO   g      ?rt  rw  r  r  g      ?)r   r2   r   rY   r`   re   r.   r.   r/   
test_cases  s     zTestTrapezoid.test_casesc           	         sf  d\              f\}}}}d      fdd}|d}|d|d  }d          t d      }ttj|||||dd ttj|||||dd ttj|||||dd ttjd	d	d
dddd ttjd	dd
dd	dd ttjd	dd
dddd d S )N)rN  r   rW   r   rW   c                    sT   | d  | d     | d   | d        | d  | d  S )NrW   r   r.   )r,  r,   r-   rN  dr(  r.   r/   r  *  s     z6TestTrapezoid.test_moments_and_entropy.<locals>.momentr   rh   r  r  r   rN  r  r   r   )rZ   rI  r   r2   r   r2  r  r>   )	rb   r  rT  rU   rV   r  r2  r  r>   r.   r  r/   test_moments_and_entropy#  s&    0>z&TestTrapezoid.test_moments_and_entropyc                 C   sb  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|||||
< qt|||jdd t tjj||dd	}t ||\}}t |jd
f}t 	|j}	t
|	| | D ]"\}
}}tjj||dd	||
< q"t||j|jdd d S )Nr  rh   r1  )r  r   rw  r  ro   r}   r  r  r   )rZ   r   r2   r   rY   Zbroadcast_arraysemptyr   r   r   r   ravelr   r  r  r   r  )rb   rN  r  rQ   rp  ccddrO  r   indr  r  c1d1r.   r.   r/   test_trapezoid_vect>  s"    &z!TestTrapezoid.test_trapezoid_vectc                 C   s0   t ddd}ttj|ddtj| d S r  )rZ   r  r   r2   r?   rY   r  rX  r.   r.   r/   
test_trapzX  s    zTestTrapezoid.test_trapzN)	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S )
TestTriangc                 C   s$  t jdd  ttjddd ttjddd ttjddd ttjddd ttjddd ttjddd	 ttjddd ttjddd
 ttjddd ttjddd ttjddd ttjddd W d    n1 s0    Y  d S )Nraiser  r   rl   rh   r  r   rm   rW   r  r   )rZ   r  r   r2   r  rY   r`   re   r.   r.   r/   test_edge_cases_  s    zTestTriang.test_edge_casesN)r   r   r   r  r.   r.   r.   r/   r  ^  s   r  c                   @   s@   e Zd Zejdddgdd Zejdg ddd	 Zd
S )TestMaxwellr  )r  gCR5&.)rj   g7q?c                 C   s   t tj||dd d S r	  )r   r2   maxwellrS  r  r.   r.   r/   rV  w  s    zTestMaxwell.test_sfr  ))r  g1!@)g    ?g?)g      <gCuJ!@c                 C   s   t tj||dd d S rn   )r   r2   r  rW  r  r.   r.   r/   rY    s    zTestMaxwell.test_isfNr  r.   r.   r.   r/   r  r  s   
r  c                   @   s   e Zd Zdd Zdd ZdS )
TestMielkec                 C   s\   d\}}t t||dtj t t|ddtj ttt|dd d S )N)g rh@gv?r   r  r  )r   r2   mielker  rZ   r   r   r  )rb   rN   rD   r.   r.   r/   rq    s    zTestMielke.test_momentsc                 C   s@   t ddd}d\}}ttj|||| tj||| d S )Nrj   rS   r   )g@gHzG@)rZ   r  r   r2   burrrY   r  )rb   rQ   rN   rD   r.   r.   r/   test_burr_equivalence  s    z TestMielke.test_burr_equivalenceN)r   r   r   rq  r  r.   r.   r.   r/   r    s   r  c                   @   s$   e Zd Zdd Zdd Zdd ZdS )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   )rh   rW   )r   r   )rW   rh   r  rh   r  )r   rW   rl   c                 S   s&   g | ]\}}}|j |jg|R  qS r.   r  r  r.   r.   r/   r9     r:   z0TestBurr.test_endpoints_7491.<locals>.<listcomp>c                 S   s   g | ]\}}}|qS r.   r.   r  r.   r.   r/   r9     r:   c                 S   s&   g | ]\}}}|j |jg|R  qS r.   )r   r,   r  r.   r.   r/   r9     r:   c                 S   s   g | ]\}}}t |qS r.   )rZ   rI  r  r.   r.   r/   r9     r:   )r2   Zfiskr  burr12r   )rb   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)r  r   )g4U?g&MI?)r2   r  r   )rb   rN  r  r2  varianceZmean_hcZ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)rh   r   )rn  r   )r   rW   r   r   )r  r   )r  r   )r  r   )r2   r  r   rZ   r  r  _munpr   )	rb   rN  r  r2  r  e1e2Ze3Ze4r.   r.   r/   test_burr_nan_mean_var_9544  sL    "z$TestBurr.test_burr_nan_mean_var_9544N)r   r   r   r  r  r  r.   r.   r.   r/   r    s   r  c                   @   s&   e Zd Zejdddgdd ZdS )
TestBurr12zscale, expected)r  gd~)r  gR톇T c                 C   s(   t jjdddd|d}t||dd d S )Ng     jAg     jAr   r  r  ry   rp   )r2   r  r#  r   )rb   rV   rK   r  r.   r.   r/   r$    s    zTestBurr12.test_delta_cdfN)r   r   r   r   r   r   r$  r.   r.   r.   r/   r    s   r  c                   @   s  e Zd Zg dZg dZg dZeeeefZg dZ	ddddd	ej
gZg d
Zeeee	eeeZddddej
dfddej
dfddej
dfgZdd Zejjdd ZejeZdZeejeeZe !eZ"W d   n1 s0    Y  ej#de"d dd Z$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$@g{Gz&@gh|?5	@gQ8@g&1@g|?5@g@gOn@g!rhm@gB`"@ro  gʡEs@g|?5^@g/$@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@)rO  r  r@  r   r   rR   r  x   )rW   r  r  r  )rO   r   i)#  gupm1f?)r   rR   rv   g?<-=A?gv"?r   gd暕?ga-A?c                 C   s<   | j D ]0\}}|\}}}tj|||}t||dd qd S )Nr_  rp   )r   r2   studentized_ranger`   r   )rb   pvkr6  Z
p_expectedrp  rN   Zres_pr.   r.   r/   test_cdf_against_tables&  s    
z,TestStudentizedRange.test_cdf_against_tablesc                 C   s<   | j D ]0\}}|\}}}tj|||}t||dd qd S )NMb@?rp   )r   r2   r  r7  r   )rb   r  Z
q_expectedr-  rp  rN   Zres_qr.   r.   r/   test_ppf_against_tables,  s    
z,TestStudentizedRange.test_ppf_against_tablesz&data/studentized_range_mpmath_ref.jsonNcase_resultZcdf_datac                 C   sN   |d }|d }|d |d |d f}t jj| }t|||d |d d d S 	Nsrc_case	mp_resultr6  rN   rp  expected_atolexpected_rtolr   )r2   r  r`   r   rb   r  r  r  Zqkvr   r.   r.   r/   test_cdf_against_mp8  s    z(TestStudentizedRange.test_cdf_against_mpZpdf_datac                 C   sN   |d }|d }|d |d |d f}t jj| }t|||d |d d d S r  )r2   r  rY   r   r  r.   r.   r/   test_pdf_against_mpC  s    z(TestStudentizedRange.test_pdf_against_mpz+intermittent RuntimeWarning: invalid value.Zmoment_datac                 C   sz   |d }|d }|d |d |d f}t jdd tjj| }W d    n1 sT0    Y  t|||d |d	 d
 d S )Nr  r  ro  rN   rp  r  r  r  r  r   )rZ   r  r2   r  r  r   )rb   r  r  r  Zmkvr   r.   r.   r/   test_moment_against_mpN  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   rR   r   r  r   )r   r2   r  rY   rZ   r   r   )rb   rN   rp  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   rR   rj   )stepr   r_  rp   )rZ   r   r2   r  r`   rY   r   r   )rb   rN   rp  rQ   Zy_cdfZ	y_pdf_rawZy_pdf_cumulativer.   r.   r/   test_pdf_against_cdfe  s    
z)TestStudentizedRange.test_pdf_against_cdfr_case_resultc                 C   sV   |\}}}}t jdd  tj|||}W d    n1 s>0    Y  t|| d S )Nr  r  )rZ   r  r2   r  r`   r   )rb   r  r6  rN   rp  Zr_resr   r.   r.   r/   test_cdf_against_ru  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>0    Y  t|jd	 tjt	d
d( tjdddgg d W d    n1 s0    Y  d S )Nr  r  r   rW   r   ru   rR   rC  r<  z...could not be broadcast...r   )rR   rC  r  )
rZ   r  r2   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2 |t tjg d\}}}}W d    n1 sL0    Y  W d    n1 sj0    Y  ttj	|| d S )Nr  r  r   )
r   rZ   r  rH   r   r2   r  r  r   Z	_argcheck)rb   r  rN   rZ  r   r.   r.   r/   test_fitstart_valid  s    
T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   rR   韆 r_  r   )r2   r  rY   rZ   r   r   r`   )rb   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   rR   r   r  i r  r   )r2   r  rY   r  AssertionErrorr   r`   )rb   r   r  Z
res_sanityr.   r.   r/   test_df_cutoff  s    

z#TestStudentizedRange.test_df_cutoffc                 C   s8   d\}}}t j|||}t|ddd |dks4J d S )N)gaRA@r   iS  r   r4  r}   )r2   r  rS  r   )rb   r6  rN   rp  r-  r.   r.   r/   test_clipping  s    
z"TestStudentizedRange.test_clipping)1r   r   r   Zq05Zq01Zq001rZ   r+  qsZpsr   vskslistr   r$   r   Zr_datar  r   r   r  r  ospathdirnamer  Zpath_prefixrelative_pathopenr  filejsonr  Zpregenerated_datar   r  r  Zxfail_on_32bitr  r  r   r  r  r  r  r  r  r  r.   r.   r.   r/   r    sT   
(








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?rR   test_540_567)r  r  g2gk?g;B.?gͣh?gHŎ*?rT   g.y?)r   r2   r  r`   r.   r.   r.   r/   r    s    r  c                   C   s   t tjdddd d S )Nrm   rW   rh   r  r  r.   r.   r.   r/   test_regression_ticket_1326  s    r  c               	   C   s  t ddd} t jdd dddt dgdgdggfD ]6}tj| |}t|dk  tt 	|   q:t dgdgd	gg}tj| |}W d    n1 s0    Y  tt 	|   t|d
 dk  t|d dk  t|d dk
  t|d dk
  d S )N      r  rP   r  r9  rm   r=  r  rl   r   r   rW   )rZ   r  r  r   r2   r'   rY   r   r  r  any)rQ   r*  r-  r.   r.   r/   test_regression_tukey_lambda  s    ",r  zdocstrings strippedrZ  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   r2   r;  r'  r.   r.   r.   r/   test_regression_ticket_1421  s    r  c                   C   s  t jdd tt tjdt j tt tjdt j tt tj	dt j tt tj
dt j tt tjdt j tt tjdt j tt tjdt j tt tjdt j tt tjt jd tt tjt jd tt tj	t jd tt tj
t jd tt tjt jd tt tjt jd tt tjt jd tt tjt jd W d    n1 s0    Y  d S )Nr  r  r   rh   )rZ   r  r   r  r2   r  rj  r   r`   r  rS  rY   r   r7  rW  rG  r  rg  r.   r.   r.   r/    test_nan_arguments_gh_issue_1362  s"    r  c                  C   sj  t jd t g d} tjj| d | d | d dd}t jdd	& t tjj|d
d}W d    n1 sr0    Y  t	|| dd t tjj|ddd}t	|| dd t tjj|ddd}t	|| dd t tjj|ddd}t	|| dd t jd d}d}tj
j|ddd}t tj
j||d}t |t || d  g}t	||dd d S )Ni.  )r   rm   rh   r   r   rW   rS   r   r  r  rm   r   r  rh   )r   rU   r   )r   rU   r  rw  rl   r   )rZ   r   r   r   r2   r   r   r  r   r   r  r  r2  )truerQ   r  rU   r   rK   r.   r.   r/   test_frozen_fit_ticket_1536   s&     4 r  c                  C   s<   t jd tjjdd} tj| }d}t||dd d S )Ni	 rS   r   )g
ףp=
?gʡE?r   r  )rZ   r   r   r2   r  r   r   r   )r   r  rK   r.   r.   r/   test_regression_ticket_1530  s
    r  c                  C   sV   t jd t jd} dD ]4}tj| | \}}t||dd t|ddd qd S )Nr   r2  )r  g   6Ar  r}   r1  )rZ   r   r   r  r2   r  r   r   )rQ   offsetrU   rV   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  rW   r   r  rR   r  g
ףp=
	@)r   gz5v?r   gRTgQ?)r   gNg @r   gJFٻ)r2   r'   rZ   r[   r   )rr  rK   r.   r.   r/   "test_tukeylambda_stats_ticket_1545/  s    r  c                   C   s   t ttjdd d S )Nro  r  )r   rZ   r  r2   r;  rg  r.   r.   r.   r/   test_poisson_logpmf_ticket_1436C  s    r  c                  C   s4   ddg} | D ]"\}}t jj |dd}t|| qdS )a  Test the powerlaw stats function.

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

    The exact values are:
    mean:
        mu = a / (a + 1)
    variance:
        sigma**2 = a / ((a + 2) * (a + 1) ** 2)
    skewness:
        One formula (see https://en.wikipedia.org/wiki/Skewness) is
            gamma_1 = (E[X**3] - 3*mu*E[X**2] + 2*mu**3) / sigma**3
        A short calculation shows that E[X**k] is a / (a + k), so gamma_1
        can be implemented as
            n = a/(a+3) - 3*(a/(a+1))*a/(a+2) + 2*(a/(a+1))**3
            d = sqrt(a/((a+2)*(a+1)**2)) ** 3
            gamma_1 = n/d
        Either by simplifying, or by a direct calculation of mu_3 / sigma**3,
        one gets the more concise formula:
            gamma_1 = -2.0 * ((a - 1) / (a + 3)) * sqrt((a + 2) / a)
    kurtosis: (See https://en.wikipedia.org/wiki/Kurtosis)
        The excess kurtosis is
            gamma_2 = mu_4 / sigma**4 - 3
        A bit of calculus and algebra (sympy helps) shows that
            mu_4 = 3*a*(3*a**2 - a + 2) / ((a+1)**4 * (a+2) * (a+3) * (a+4))
        so
            gamma_2 = 3*(3*a**2 - a + 2) * (a+2) / (a*(a+3)*(a+4)) - 3
        which can be rearranged to
            gamma_2 = 6 * (a**3 - a**2 - 6*a + 2) / (a*(a+3)*(a+4))
    )r  )rh   r.  rm   r/  )rl   )gUUUUUU?rF  g^cQg333333r  r  N)r2   r  r   )r  r,   Z
exact_mvskr  r.   r.   r/   test_powerlaw_statsG  s    r  c                  C   s   t jdd} t| d d S )Nr   r   rm   )r2   r  r   r   r-  r.   r.   r/   test_powerlaw_edgem  s    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   rm   )r   r  rn  r  )r2   rC  r   r   rY   rZ   r   r  r.   r.   r/   test_exponpow_edges  s    
r  c                  C   s   t jddd} t| d d S )Nr   r   r  )r2   gengammarY   r   r  r.   r.   r/   test_gengamma_edge  s    r  za, c, ref, tol))g    `6Ar   g2j!@ro   )r{  r   ggA@ro   )rc  r   r  ro   )r  r   g #@ry   )g    `FAr8  gI~mro   )gl$W}Lr  g.I#Uro   c                 C   s   t tj| |||d d S r  )r   r2   r  r>   )r,   rN  r<  r   r.   r.   r/   test_gengamma_extreme_entropy  s    r  c                  C   s@   t jddd} | dksJ t jddd}|tj ks<J d S )Nr   r   r   rm   )r2   r  rY   r   rZ   r   )r-  r  r.   r.   r/   !test_gengamma_endpoint_with_neg_c  s    r  c                  C   s8   t jddd} t| d t jddd} t| d d S )Nr   r  r  g>rR   gqq?)r2   r  r  r   r  r.   r.   r/   test_gengamma_munp  s    
r  c               	   C   s   t g d} t jddZ t 4}|td |td tj	|  W d    n1 s\0    Y  W d    n1 sz0    Y  d S )N)0g>X*ȿgPix#?g=?g&^?goϿg뵏˿gO_ZQ?g\?g~?g)/?gRܶ?g핚οgH߃[g?gS"gm_ пg7k?g#BF?gKU=?gT?gZg[Qs?g2?g6Hwƭ8?g*-
?ga]?g'?g޻?g?J_ ?g~sw?g0FfͿgg"@ӿg?%:˿g&zM?g?Gg	F?g~,g HgW2ҿgTzy?gwmǿg @gW=ֿg	't?g".v1glg.Hꮿg,?g*˿r  r  z:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integer)
rZ   r   r  r   rH   r   r1  r2   rV  r   )r  r  r.   r.   r/   test_ksone_fit_freeze  s    r  c                  C   s   t ttddd } g d}tt | |dd tt | d j|dd tj| d d	 j	}t 
tj| tj|  }t||d	d d S )
Nr   r  r   )gDB.g8_$g%`OAgjhwHRgWMB@v`g7VY}igۦx\Arg	xg#g/dg3$gegd)gNq{3gيGǓgr4g37'
gfFg?dJgضg2,
gm%gӅJgz;pgɿ{gk2gij<%giVSͶgBR4g
Q/Mr  r}   y        +=y        |=r4  )rZ   r   r  r  r   r2   r  rj  realimagr   r   )rQ   rK   ZderivZderiv_expectedr.   r.   r/   test_norm_logcdf  s    	r  c                  C   sT   t g d} t g d}tj| }t||dd tj|}t|| dd d S )N)rv   r  rh   rO   rj   r  )g~V1?r  gba"?g܄4ťY?r  g$%+Ir4  rp   ry   )rZ   r   r2   r   r`   r   r7  )rQ   rK   r  rO  r.   r.   r/   test_levy_cdf_ppf  s    r  c                  C   s:   t g d} t g d}tj| }t||dd d S )N)r  r  gMraB3Gr  )gep[>g}XEQ=gѭEG<g?_%~:r  rp   )rZ   r   r2   r   rS  r   rQ   rK   r  r.   r.   r/   test_levy_sf  s    r  zp, expected_isf))r  gj1e2H)r  g6C)rv  gnE@)r  g!^x1?)r@  gZ?)g   ?g:}!Nu?c                 C   s   t j| }t||dd d S )Nr  r}   )r2   r   rW  r   )r-  Zexpected_isfrQ   r.   r.   r/   test_levy_isf	  s    r  c                  C   s:   t g d} t g d}tj| }t||dd d S )N)gMb{Gzg{Gztg~jtX)g#]<gOul2;gޢا6g̅7=!ry   rp   )rZ   r   r2   r   rS  r   r  r.   r.   r/   test_levy_l_sf  s    r  c                  C   s8   t g d} tj| }tj|}t|| dd d S )N)g [n<r   r  r  rp   )rZ   r   r2   r   rW  rS  r   )r-  rQ   r6  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 )NrO  i i  i  )g      c@g     h@g=
ףp=?Gz?)g      c@g     h@r  rS   r  r   )r   r2   r  rQ  r7  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   rO   r2  ru   numrW   r   r  r"  r   rh   rT   rl   rr  r>  r   r  r  )rZ   r   r   r  r  r   r2   r  rY   r   r`   r7  r>   r   r  r  r"  r  r  r   r.   r.   r/   test_distribution_too_many_args8  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  ry  rW   gYZ@r  r   r   )r2   ncx2r`   rZ   r   Z_cdfvecr   r  r.   r.   r/   test_ncx2_tails_ticket_955`  s    r'  c               	   C   s   t  R t dt ttjdt	dddd tj
dt	ddd} W d    n1 s`0    Y  tt|   t  H t dt ttjddd	d ttj
ddd	d
 W d    n1 s0    Y  d S )Nr*  r   iT  i^  rW   r   rK  r   r  gsq6)r.  r/  r0  r1  r   r2   r&  rY   rZ   r   r   r   r  r  r   )Zlogvalr.   r.   r/   test_ncx2_tails_pdfh  s    
6
r(  zmethod, expectedr`   gu%>g	;Q=rY   g<x>gRz\R>r   gʎK$/gԆX1r7  gfHu@ge:@c                 C   s,   t tj| dddgdd}t||dd d S )NrO   r   r   rR   )rj  rZ  ro   r}   )r   r2   r&  r   )r  rK   r  r.   r.   r/   test_ncx2_zero_ncy  s    r)  c                  C   s4   t jjdddd} t jjddd}t| |dd d S )NrR   r   r   )rZ  rj  r|   )rZ  r|   ro   r}   )r2   r&  r   r  r   )r  rK   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 )NrR   ru   r  r   rZ  rj  r   )rZ   r   r   r2   r&  r`   )rj  r.   r.   r/   test_ncx2_gh12731  s    r,  c                  C   sB   t g d} d\}}tjj| ||d}g d}t||dd d S )N)gю]	@gj%@gb	y/7@g H@gIZ@gXl@g'/2?8@gݰmА@gU@gy]`'@g@g*\@g48c@)r  gh ?8@r+  )r  r  r  r  r  g?gy[qD?rm   rm   rm   rm   rm   rm   r[  r}   )rZ   r   r2   r&  rS  r   )rQ   nur*  rS  Zsf_expectedr.   r.   r/   test_ncx2_gh8665  s
    
r.  c               	   C   sx   d} d}t jtjd| |tjd| |dd}tj|| |}tj|| | t d|  d|  }t||d	d
 d S )Ni,  i  r  r@  rK  r#  rW   r   r_  r}   )	rZ   r  r2   r&  r7  rY   r  r  r   )rZ  rj  rQ   Zncx2_pdfZgauss_approxr.   r.   r/   test_ncx2_gh11777  s    &r/  zx, c, expected))rW   r   g|1q?)rW   rW   g~?)rb  r   V<3T1=) 7yQCr   u	lY<)rb  g   vHGBg^b!*1=)r  r  gS?c                 C   s   t j| |}t||d d S Nr  )r2   Z
foldcauchyrS  r   rQ   rN  rK   rS  r.   r.   r/   test_foldcauchy_sf  s    r5  r~  ))rW   g?)rb  r0  )r1  r2  )g6ްPg8R#/c                 C   s   t j| }t||d d S r3  )r2   
halfcauchyrS  r   )rQ   rK   rS  r.   r.   r/   test_halfcauchy_sf  s    r7  zp, expected))g?g*wӄZ>)333333?gN9?)rh   r  )rj   g8<,O@)r  g:B)gl ׶w/gMb}[Pc                 C   s   t j| }t|| d S rd   )r2   r6  rW  r   )r-  rK   rQ   r.   r.   r/   test_halfcauchy_isf  s    r9  c                  C   s"   t jddd} t| dd d S )Nr   r   r  )r2   r  r   r`   r  r.   r.   r/   test_foldnorm_zero  s    r:  ))rW   r   gwo{?)r  r   gGd-P/)rR   r   gof?)r  r   gOul";c                 C   s   t j| |}t||d d S )Nr  )r2   r  rS  r   r4  r.   r.   r/   test_foldnorm_sf  s    r;  c                  C   s   t j g ddd} t j ddgdd}tdd |D }t||  t j g d} t j dd	g}td
d |D }t||  d S )N)rm   rh   r  r   rh   r  c                 s   s   | ]}t jt j|f V  qd S rd   rZ   r  r   rW  r.   r.   r/   r    r:   z-test_stats_shapes_argcheck.<locals>.<genexpr>)rW   r  r   rW   r  c                 s   s   | ]}t j|t jf V  qd S rd   r<  rW  r.   r.   r/   r  "  r:   )r2   r   tupler   r   )Zmv3Zmv2Zmv2_augmentedr.   r.   r/   test_stats_shapes_argcheck  s    
r>  c                   @   s   e Zd Zdd ZdS )
_distr_genc                 C   s   dS Nr2  r.   rb   rQ   r,   r.   r.   r/   _pdf-  s    z_distr_gen._pdfNr   r   r   rB  r.   r.   r.   r/   r?  ,  s   r?  c                   @   s   e Zd Zdd ZdS )_distr2_genc                 C   s   d| | S r@  r.   rA  r.   r.   r/   _cdf2  s    z_distr2_gen._cdfN)r   r   r   rE  r.   r.   r.   r/   rD  1  s   rD  c                   @   s   e Zd Zdd Zdd ZdS )_distr3_genc                 C   s   || S rd   r.   rb   rQ   r,   r-   r.   r.   r/   rB  7  s    z_distr3_gen._pdfc                 C   s   d| | S r@  r.   rA  r.   r.   r/   rE  :  s    z_distr3_gen._cdfNr   r   r   rB  rE  r.   r.   r.   r/   rF  6  s   rF  c                   @   s   e Zd Zdd Zdd ZdS )_distr6_genc                 C   s   || | S rd   r.   rG  r.   r.   r/   rB  B  s    z_distr6_gen._pdfc                 C   s   d| | S r@  r.   rG  r.   r.   r/   rE  E  s    z_distr6_gen._cdfNrH  r.   r.   r.   r/   rI  @  s   rI  c                   @   s   e Zd Zdd Zdd Zdd Zdd Z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   rp  r2  r?  r   rY   rb   dummy_distrr.   r.   r/   test_correct_shapesL  s    z1TestSubclassingExplicitShapes.test_correct_shapesc                 C   s,   t ddd}tt|jdfi tdd d S )NrK  ArL  r   rp  )r?  r  r   rY   r   rN  r.   r.   r/   test_wrong_shapes_1P  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 )NrK  za, b, crL  r   rW   r   r  )r?  r   r  r   rY   )rb   rO  r   r.   r.   r/   test_wrong_shapes_2T  s    z1TestSubclassingExplicitShapes.test_wrong_shapes_2c                 C   s"   t ddd}tttfi | d S )NrK  r2  rL  )r   r  r   r?  rb   r   r.   r.   r/   test_shapes_stringY  s    z0TestSubclassingExplicitShapes.test_shapes_stringc                 C   s"   t ddd}tttfi | d S )NrK  z(!)rL  r   r  SyntaxErrorr?  rT  r.   r.   r/   test_shapes_identifiers_1^  s    z7TestSubclassingExplicitShapes.test_shapes_identifiers_1c                 C   s"   t ddd}tttfi | d S )NrK  Z4chanrL  rV  rT  r.   r.   r/   test_shapes_identifiers_2c  s    z7TestSubclassingExplicitShapes.test_shapes_identifiers_2c                 C   s"   t ddd}tttfi | d S )NrK  zm(fti)rL  rV  rT  r.   r.   r/   test_shapes_identifiers_3g  s    z7TestSubclassingExplicitShapes.test_shapes_identifiers_3c                 C   s"   t ddd}tttfi | d S )NrK  za=2rL  rV  rT  r.   r.   r/   "test_shapes_identifiers_nodefaultsk  s    z@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaultsc                 C   s"   t ddd}tttfi | d S )NrK  z*argsrL  rV  rT  r.   r.   r/   test_shapes_argso  s    z.TestSubclassingExplicitShapes.test_shapes_argsc                 C   s"   t ddd}tttfi | d S )NrK  z**kwargsrL  rV  rT  r.   r.   r/   test_shapes_kwargss  s    z0TestSubclassingExplicitShapes.test_shapes_kwargsc                 C   s"   t ddd}tttfi | d S )NrK  za, b, c, lambdarL  rV  rT  r.   r.   r/   test_shapes_keywordsw  s    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                   @   s   e Zd Zdd ZdS )zFTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_genc                 S   s   t j|| S rd   r2   r  rB  rA  r.   r.   r/   rB    s    zKTestSubclassingExplicitShapes.test_shapes_signature.<locals>._dist_gen._pdfNrC  r.   r.   r.   r/   	_dist_gen~  s   r`  r,   r   rh   rW   rp  r2   r<   r   rY   r  rb   r`  r8   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                   @   s   e Zd Zdd ZdS )zSTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_genc                 S   s   t j|| S rd   r_  rA  r.   r.   r/   rB    s    zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.<locals>._dist_gen._pdfNrC  r.   r.   r.   r/   r`    s   r`  re  ra  rh   r   rW   r  )r2   r<   r  r   rY   r   rc  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                   @   s   e Zd Zdd ZdS )z?TestSubclassingExplicitShapes.test_star_args.<locals>._dist_genc                 W   s   |d }t j|| S Nr   r_  )rb   rQ   r   extra_kwargr.   r.   r/   rB    s    zDTestSubclassingExplicitShapes.test_star_args.<locals>._dist_gen._pdfNrC  r.   r.   r.   r/   r`    s   r`  rg  ra  rh   !   rg  )Zxxx)r2   r<   r   rY   r  r  r   r   rc  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                   @   s   e Zd Zdd ZdS )zATestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_genc                 W   s   |d }t j|| | S rf  r_  )rb   rQ   r	  r   rg  r.   r.   r/   rB    s    zFTestSubclassingExplicitShapes.test_star_args_2.<locals>._dist_gen._pdfNrC  r.   r.   r.   r/   r`    s   r`  zoffset, extra_kwargra  rh   o   rh  )r	  rg  rb  rc  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                   @   s   e Zd Zdd ZdS )zBTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_genc                 _   s   | dd}tj|| S )Nrg  r   )popr2   r  rB  )rb   rQ   r   kwargsrg  r.   r.   r/   rB    s    zGTestSubclassingExplicitShapes.test_extra_kwarg.<locals>._distr_gen._pdfNrC  r.   r.   r.   r/   r?    s   r?  rg  ra  r   r   ri  rb  )rb   r?  r8   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                   @   s   e Zd Zdd ZdS )zITestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_genc                 S   s   t j|S rd   )r2   r  rY   rX  r.   r.   r/   rB    s    zNTestSubclassingExplicitShapes.test_shapes_empty_string.<locals>._dist_gen._pdfNrC  r.   r.   r.   r/   r`    s   r`   ra  rh   rb  rc  r.   r.   r/   test_shapes_empty_string  s    
z6TestSubclassingExplicitShapes.test_shapes_empty_stringN)r   r   r   rP  rR  rS  rU  rX  rY  rZ  r[  r\  r]  r^  rd  re  rj  rl  ro  rq  r.   r.   r.   r/   rJ  I  s"   		rJ  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 )NrK  r  r   rp  r2  rM  rN  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 )NrK  rs  r   rp  )rD  r   rY   rN  r.   r.   r/   test_only__cdf  s    
z&TestSubclassingNoShapes.test_only__cdfdocstring strippedrZ  c                 C   sD   t dd}t|jd t|jd td|j}tt|dk d S )NrK  rs  r   r,   zlogpdf\(x, a, loc=0, scale=1\))	r?  r   numargsr   refindallr'  r   r   rb   rO  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 )NrK  rs  rW   re  z!logpdf\(x, a, b, loc=0, scale=1\)r   )	rI  r   rw  r   rx  ry  r'  r   r   rz  r.   r.   r/   test_signature_inspection_2args  s    
z7TestSubclassingNoShapes.test_signature_inspection_2argsc                 C   s   t ttdd d S )NrK  rs  )r  r   rF  re   r.   r.   r/   0test_signature_inspection_2args_incorrect_shapes  s    zHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapesc                 C   s.   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_genr2  c                 S   s   dS r@  r.   rA  r.   r.   r/   rB    s    zCTestSubclassingNoShapes.test_defaults_raise.<locals>._dist_gen._pdfN)r2  rC  r.   r.   r.   r/   r`    s   r`  rK  rs  r2   r<   r  r   r   rb   r`  r.   r.   r/   test_defaults_raise  s    z+TestSubclassingNoShapes.test_defaults_raisec                 C   s.   G dd dt j}tt|fi tdd d S )Nc                   @   s   e Zd Zdd ZdS )z>TestSubclassingNoShapes.test_starargs_raise.<locals>._dist_genc                 W   s   dS r@  r.   )rb   rQ   r,   r   r.   r.   r/   rB    s    zCTestSubclassingNoShapes.test_starargs_raise.<locals>._dist_gen._pdfNrC  r.   r.   r.   r/   r`    s   r`  rK  rs  r~  r  r.   r.   r/   test_starargs_raise  s    z+TestSubclassingNoShapes.test_starargs_raisec                 C   s.   G dd dt j}tt|fi tdd d S )Nc                   @   s   e Zd Zdd ZdS )z<TestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_genc                 [   s   dS r@  r.   )rb   rQ   r,   rn  r.   r.   r/   rB    s    zATestSubclassingNoShapes.test_kwargs_raise.<locals>._dist_gen._pdfNrC  r.   r.   r.   r/   r`    s   r`  rK  rs  r~  r  r.   r.   r/   test_kwargs_raise  s    z)TestSubclassingNoShapes.test_kwargs_raiseN)r   r   r   rt  ru  r   r   ri  DOCSTRINGS_STRIPPEDr{  r|  r}  r  r  r  r.   r.   r.   r/   rr    s   


	rr  rv  c                  C   sT   g d} t jD ]@}tt |}t|t jt jfr| D ]}tt||j	d u  q2qd S )N)z,\s*,z\(\s*,z^\s*:)
r2   rG   r   r  r;   r<   r   rx  searchr'  )Zbadonesdistnamer8   regexr.   r.   r/   r    s    

r  c                   C   s4   t tjtjddd t tjtjddd d S )NrR   rC  r   r  rO   r   )r   r2   rE  rS  rZ   r   r&  rE  r.   r.   r.   r/   test_infinite_input  s    r  c                  C   s&   t jt jddd} t| d d S r  )r2   Zlomaxr7  r`   r   r  r.   r.   r/   test_lomax_accuracy  s    r  c                  C   s&   t jt jddd} t| d d S r  )r2   rA  r7  r`   r   r  r.   r.   r/   test_truncexpon_accuracy  s    r  c                  C   s*   t jt jddd} t| ddd d S )Nrz  r   r&  r   r  )r2   r   rW  rS  r   r  r.   r.   r/   test_rayleigh_accuracy  s    r  c                  C   s   t jddh} t d tjdd tjdd tjdd tjt	j
 d t| }t|d W d   n1 sz0    Y  dS )zregression test for gh-6219T)r  alwaysrh   r   rm   N)r.  r/  r0  r2   rE  r`   rY   r7  r   rZ   r   r   r   )r  Znumber_of_warnings_thrownr.   r.   r/    test_genextreme_give_no_warnings  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=  rW   r   r  rp   r   r  r  rR   r  r   rj  r  rC  )r2   rE  r>   r   r   rZ   rI  )Zeuler_gammar(  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?)r2   rE  rS  r   rW  )rQ   rD   r  r.   r.   r/   test_genextreme_sf_isfB  s    




r  c                  C   s"   d} t j| dd}t|d d S )Nr:  rW   r   gH&8>)r2   r  r7  r   )Zprobr  r.   r.   r/   test_burr12_ppf_small_argn  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   r  r  Nr   r  rl   )r  ro  )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  rp   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>rh   )r  ro  rU   rV   )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  )rZ   r  r2   crystalballrY   r   r   r`   )r  Z
calculatedrK   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
    )rl   r  r  rl   r  )r  r  rl   r  r&  )r  r  r  r  r  r   r  rp   )gԚh@g[&@gͪ@g2dQ@gn6-@g?ޫV&̿g BgQCRgQF\ jr   g
@gn(@rW   g?Җ)r   gMg'#@r   g('UHru   N)rZ   r   r2   r  r  r   r   )r  ro  Zexpected_0th_momentZcalculated_0th_momentr  r,   Zexpected_1th_momentZcalculated_1th_momentZexpected_2th_momentZcalculated_2th_momentZexpected_3th_momentZcalculated_3th_momentZexpected_4th_momentZcalculated_4th_momentZexpected_5th_momentZ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 )NrW   r   )ir   r  r  rp   )	r2   r  r>   rZ   r  r   r   rY   r   )cbrL  rX  rY  r  rQ   r  r.   r.   r/   test_crystalball_entropy  s    
r  c                  C   s\   ddd} t g d}tjj|d| d\}}}t|ddd	 |dksJJ 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   dispZxtolZftol)r#   )r   x0r   r  r.   r.   r/   	optimizer   s    z&test_invweibull_fit.<locals>.optimizer)r   rt  rW   r  ro  r   r  r   ru   r  rR   r  @   c   )r   r  g`?r_  rp   g [@N)r.   r   )rZ   r   r2   r   r   r   )r  rQ   rN  rU   rV   r.   r.   r/   test_invweibull_fit  s    
r  ))r   rn  g7Ըh?)rw   rn  gz]r>)rw   g     "@goBڱ9)r  rn  g$=cC;c                 C   s    t j| |}t||dd d S rn   )r2   r   rS  r   )rQ   rN  rK   r  r.   r.   r/   test_invweibull_sf   s    r  zp, c, expected)rh   r  g9?)geK<ru   g@c                 C   s    t j| |}t||dd d S rn   )r2   r   rW  r   )r-  rN  rK   r  r.   r.   r/   test_invweibull_isf)   s    r  z	df1,df2,x)r   ry  r  rm  r   rC  r>  r  r  c                 C   sh   d}t j|| |}t j|| ||}t||dd t j|| |}t j|| ||}t||dd d S )Nr   r  rp   r  )r2   r  r`   r  r   rY   )Zdf1Zdf2rQ   rj  Zexpected_cdfZcalculated_cdfrs   Zcalculated_pdfr.   r.   r/   test_ncf_edge_case1   s    
r  c                  C   s"   t jddd} t| ddd d S )NrW   r  r   g     `E@r  rp   )r2   r  r  r   )rp  r.   r.   r/   test_ncf_varianceG   s    r  c                  C   s.   t jdddd} d}t|tj| dd d S )Nr  r  rh  gffffff>@g&4I,)?)Zdecimals)r2   r  r`   r   rZ   round)Z	scipy_valZ	check_valr.   r.   r/   test_ncf_cdf_spotcheckR   s    r  r  z(On some 32-bit the warning is not raisedc                     sx   t ddd} d| d< d tt6 tjj| g R  } fdd| D }W d    n1 s`0    Y  t|| d S )Nr   r   r  r:  )rO   rW   ru   r   r   c                    s    g | ]}t jj|g R  qS r.   )r2   r  r7  )r7   xiparr.   r/   r9   e   r:   z,test_ncf_ppf_issue_17026.<locals>.<listcomp>)	rZ   r  r   rc  r1  r2   r  r7  r   )rQ   r6  Zq0r.   r  r/   test_ncf_ppf_issue_17026\   s    0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S )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   rW   rW   r   r   r   r   r   r   r   ru   ru   ru   ru   ru   r  r  r  r  r>  r>  r>  r  r  rz  r  binsr  r  rK  {   r  r   )
rZ   r   r   	histogramr2   r=   templater  r   norm_template)rb   r  r   Znorm_histogramr.   r.   r/   r   j   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rm   rh   r  rn  rl   r  r  r  r  r  r        @r)  r  ru  ry  r        !@r&  r?  )rm   rm   r  r  {Gz?r  Q?r  {Gz?r  ry  ry  r  r  r  r  r  r  rm   rm   r  r  r  r&  rm   r  r   rW   rR   r  r  rT   rO   rp   )rZ   r   r   r   r  rY   r   r  r  r2   r  )rb   r  Z
pdf_valuesrQ   r.   r.   r/   r  z   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  )rm   rm   rm   r  r  r  r  
ףp=
?Q?{Gz?r  rh   r1  (\?RQ?=
ףp=?)\(?r!  r  r  rW   r   r  r&  rS   rm   r   rR   r  rT   rO   rp   )rZ   r   r   r   r  r`   r7  r  r  r2   r  )rb   r  Z
cdf_valuesrQ   r.   r.   r/   rP     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$kd%| dd	 tt|d&kd| dd	 tt|d&kd| dd	 tt|d&kd d S )'NrK  r  rp  r  rm   rl   r  ry  rp   r  r  r  r  rO   r  r  r  r  r  r  r  r  r   r  rh   r)  r1  r  r  ru  r  ry  r  r  r  r  r!  r&  )r  r   r   rZ   r%  r   )rb   r  r  r.   r.   r/   r	     s(    zTestHistogram.test_rvsc                 C   s6   t dD ](}t| j|tdd|dd qd S )Nr   r  r  r   rp   )r  r   r  r  r2   r  r  r8  r.   r.   r/   r     s    zTestHistogram.test_munpc                 C   s$   t | j tjjddddd d S )Nr  r  rT   r   rp   )r   r  r>   r2   r  re   r.   r.   r/   r)     s    
zTestHistogram.test_entropyN)	r   r   r   r   r  rP  r	  r  r)  r.   r.   r.   r/   r  i   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sPJ t j| |fdd}tj|ddgd	 | d
ksJ d}tt|d. t | |f}| d
ksJ W d    n1 s0    Y  t | g df}| dksJ d S )Nr   )r   r   rJ  F)r  rh   r  r  Tg'^P?g     H@z(Bin widths are not constant. Assuming...r   rM  )	r2   r=   rZ   r  r   rY   r  r	   r1  )countsr  r8   r  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r|   krd	ksn J t t |d
 dksJ d S )N   0o[ r  r   rK  rp  rR   r  r1  iL  rv   )rZ   r   r   r2   
loguniformr   Z
reciprocalr   r  log10rE  r  r   r  )rb   r   r  r   Zrv2r   r  r   r.   r.   r/   
test_alias   s    
,zTestLogUniform.test_aliasr  Zmler  c                 C   sn   t jd}tjjddd|d}tjj||d\}}}}|dksDJ tjj|d|d\}}}}|dksjJ d S )	Nr  rO   r   rv   rp  r  rW   r  )rZ   r   r   r2   r  r   r   )rb   r  r   r   r,   r-   rU   rV   r.   r.   r/   test_fit_override   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   rv   r   r  i8r  r   rR   )rZ   r   r   r2   r  r  r   r`   r7  r   r   rY   rI  r2  )
rb   r   r,   r-   r8   r`   r   rQ   rY   r2  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$d%d& Zejdg d'd(d) Zd*S )+	TestArgusc                 C   s2   t jjdddd}tt d | dd d S )Nr   r  E  rp  r   r  )r2   argusr   r   r2  rX  r.   r.   r/   test_argus_rvs_large_chi!  s    z"TestArgus.test_argus_rvs_large_chizchi, random_staterO   r  r     r     c                 C   s6   t jj|d|d}t |d|f\}}t|dk d S )Nr  rp  r  r   r2   r  r   rs  r   )rb   rR  r|   rQ   r   r-  r.   r.   r/   r	  !  s    zTestArgus.test_rvsrR  r  r  c                 C   s6   t jj|ddd}t |dd \}}t|dk d S )Nr  ie rp  c                 S   s   dd| d  d  S )Nr   rW   rn  r.   r   r.   r.   r/   rE   -!  r:   z.TestArgus.test_rvs_small_chi.<locals>.<lambda>r   r  )rb   rR  r>  r   r-  r.   r.   r/   test_rvs_small_chi'!  s    zTestArgus.test_rvs_small_chizchi, expected_mean))r   g щi?)rR   g.憃?)r  g\paP?)r  g	?)r  g,6?c                 C   s"   t jj|dd}t||dd d S )Nr   r  ry   rp   )r2   r  r2  r   )rb   rR  Zexpected_meanro  r.   r.   r/   r]  1!  s    zTestArgus.test_meanzchi, expected_var, rtol))r   gLH'B?ry   )rR   go$?r  )r  g
=>r  )r  g2W>r  )r  gb~P>r  c                 C   s"   t jj|dd}t|||d d S )Nr   r  rp   )r2   r  r  r   )rb   rR  Zexpected_varrq   rp  r.   r.   r/   r1  <!  s    zTestArgus.test_varzchi, expected, rtol))rw  gwM?r  )rh   gj?r  )rO   gHEA`!?r  )rj   gcف>ro   )r  gF=r  )r_  g߹Q#B=r  )r  g0ޟ<r  )r  g*W%:ro   c                 C   s   t t|||d d S r  )r   r!   )rb   rR  rK   rq   r.   r.   r/   test_argus_phi_small_chiG!  s    
z"TestArgus.test_argus_phi_small_chizchi, expected))rh   )g-\/?g+p7c?g5Ϧ\?)ry  )g
f?gi{?ٸ?gZ@7?)rO   )gB	?g]?gR{?)rj   )glͅw?g,?g[Z=?)r  )gz,?g]?gѪ1?)r_  )g8<?gE-?gI?)r  )g~7?g7B.?g9?)r  )g;?g9B.?g}5?c                 C   s*   t g d}ttj|||dd d S )NrO   rh   rw  ry   rp   )rZ   r   r   r2   r  rY   rb   rR  rK   rQ   r.   r.   r/   test_pdf_small_chiT!  s    zTestArgus.test_pdf_small_chi))rh   )gQ߹?e?grJ,?g򺗄?)ry  )gΎd?g?gh?)rO   )g|
o?gvb?g+@?)rj   )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   s*   t g d}ttj|||dd d S )Nr  r  rp   )rZ   r   r   r2   r  rS  r  r.   r.   r/   test_sf_small_chic!  s    zTestArgus.test_sf_small_chi))rh   )g+&?gk?gμm/?)ry  )g?CL\f?g^N?g]AͭR?)rO   )ga>$?g;Lf?gaW?)rj   )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   s*   t g d}ttj|||dd d S )Nr  r[  rp   )rZ   r   r   r2   r  r`   r  r.   r.   r/   test_cdf_small_chir!  s    zTestArgus.test_cdf_small_chi))rh   )gQ)?g6{?r[  )gB`"۹?)g?g8%?r  )rO   )g388?gV%?ry   )rj   )g*j?gRS%?ry   )r  )g!|?gZ%?ry   )r_  )gy[|?gG%?ry   )r  )g"3|?gW%?ry   )r  )g!3|?gW%?ry   c                 C   s"   t jj |dd}t|||d d S )Nrr  r  rp   )r2   r  r   )rb   rR  rK   rq   r  r.   r.   r/   test_stats_small_chi!  s    zTestArgus.test_stats_small_chiN)r   r   r   r  r   r   r   r	  r  r]  r1  r  r  r  r  r  r.   r.   r.   r/   r  !  sR   

	

	







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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+)r2   nakagamir   r   )rb   r-  rQ   r  r.   r.   r/   r  !  s    zTestNakagami.test_logpdfc                 C   sD   d}d}t j||}t|ddd t j||}t||dd d S )Nr  r  g"S+:ry   rp   )r2   r  rS  r   rW  )rb   r-  r  rS  r  r.   r.   r/   r  !  s    zTestNakagami.test_sf_isfzm, ref))ru   g|Bd븿)rh   r`  )rR   g/ۿc                 C   s   t tj||dd d S )Ng^~z=rp   r   r2   r  r>   rb   ro  r<  r.   r.   r/   r)  !  s    zTestNakagami.test_entropy))r  g}Ô%I)r4  gq_)g    ScAgB4U)g    cAgu1U)rb  gb>%)rc  gWҙ\c                 C   s   t tj|| d S rd   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 )Nrc  r  )rZ   r  r2   r  Z_entropyre   r.   r.   r/   test_entropy_overflow!  s    z"TestNakagami.test_entropy_overflowz+Fit of nakagami not reliable, see gh-10908.rZ  r-  )r|  r  r  rU   )rk   rR   #   rV   )r  ru   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 )NrS   9  r   r-  rU   rV   r|   ry  rp   c                    s<   d|  d t d |   d|  |d  t  |   S )Nr   r   rW   rZ   r%  r-  rU   rV   )r  r.   r/   	dlogl_dnu!  s    z(TestNakagami.test_fit.<locals>.dlogl_dnuc                    sN    dt |  td|   dt t | |   t | | d  S )Nr   r   rW   )rZ   rI  r   r%  r  r  r  r.   r/   
dlogl_dloc!  s
    z)TestNakagami.test_fit.<locals>.dlogl_dlocc                    s2   d  |  | d|  |d  t | d   S )Nr   rW   r   r  r  r  r.   r/   dlogl_dscale!  s     z+TestNakagami.test_fit.<locals>.dlogl_dscaler   r  r}   )r2   r  r   r   r   )
rb   r-  rU   rV   nu_estloc_est	scale_estr  r  r  r.   r  r/   r  !  s    zTestNakagami.test_fitc                 C   s   d}d}t jj||||dd}t jj||d\}}}t|}	tt|| d }
t||dd t||	dd t||
dd d S )	Nrh   rS   r  r  r~  rW   r  rp   )	r2   r  r   r   rZ   rE  r  r2  r   )rb   rU   rV   r-  r,  r  r  r  r  Zloc_theoZ
scale_theor.   r.   r/   test_fit_nu!  s    
zTestNakagami.test_fit_nuN)r   r   r   r  r  r   r   r   r)  r  r  rk  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S )TestWrapCauchyc                 C   sr   t ddgddgg}t dgdgg}tj||}|jdksDJ dd	 t ||fD }t| |d
d d S )NQ?r   rh   r  r  r  r  c                 S   s   g | ]\}}t j||qS r.   )r2   
wrapcauchyr`   )r7   r  r  r.   r.   r/   r9   "  s   z>TestWrapCauchy.test_cdf_shape_broadcasting.<locals>.<listcomp>ry   rp   )	rZ   r   r2   r  r`   r  Znditerr   r  )rb   rN  rQ   r-  Zscalar_valuesr.   r.   r/   test_cdf_shape_broadcasting	"  s    z*TestWrapCauchy.test_cdf_shape_broadcastingc                 C   s"   t jtjd}t|ddd d S )Nr  rh   r  rp   )r2   r  r`   rZ   r[   r   rD  r.   r.   r/   test_cdf_center"  s    zTestWrapCauchy.test_cdf_centerc                 C   s   d}d}d}t j||g|}d| d|  }t|d t|t|d  tj  t|d dt|ttj|d   tj   d S )Nr  r  r  r   r   rW   )r2   r  r`   r   rZ   Zarctantanr[   )rb   r  r  rN  r-  Zcrr.   r.   r/   r  "  s    (zTestWrapCauchy.test_cdfN)r   r   r   r   r  r  r.   r.   r.   r/   r  "  s   r  c                  C   sT   G dd dt j} | dd}ttdd |  W d    n1 sF0    Y  d S )Nc                   @   s   e Zd Zdd ZdS )z/test_rvs_no_size_error.<locals>.rvs_no_size_genc                 S   s   dS r   r.   re   r.   r.   r/   _rvs&"  s    z4test_rvs_no_size_error.<locals>.rvs_no_size_gen._rvsN)r   r   r   r  r.   r.   r.   r/   rvs_no_size_gen%"  s   r  rvs_no_sizers  z_rvs\(\) got (an|\d) unexpectedr   )r2   r<   r  r   r   )r  r  r.   r.   r/   test_rvs_no_size_error#"  s    
r  zdistname, argsc                 C   s   | t v rtd|  d tt| }t|tjrt|dkrb|j| \}}t	|t
j t	|t
j d\}}|jg |||R  \}}t	|t
j t	|t
j n&|j| \}	}
t	|	t
j t	|
t
j d S )Nz6skipping test for the support method for distribution .r   r"  )$skip_test_support_gh13294_regressionr   r   r   r2   r  r<   r   supportr   rZ   r   )r  r   r8   a0b0r  r  a1b1r,   r-   r.   r.   r/   test_support_gh13294_regression/"  s"    

r  c                  C   s\  t jg dg d\} }ttj tj tj tjg}ttjtjtjtjg}t| | t|| | j|jksxJ |j|jksJ t jg g \}}tg tg  }}t|| t|| |j|jksJ |j|jksJ t jg ddg\}}	tdtjg }
tdtjg }t||
 t|	| |j|
jksFJ |	j|jksXJ d S )N)r   r   r   r   )r   r   r   r   r   r   )	r2   r  r	  rZ   r   r   r   r   r  )r
  r  Zex_a0Zex_b0r  r  Zex_a1Zex_b1r	  r!  Zex_a2Zex_b2r.   r.   r/   ,test_support_broadcasting_gh13294_regressionJ"  s(     





r  c                  C   sn   ddg} dgdgdgg}t tj| |ddgddgddgg td} td}tj| |jdksjJ d S )	Nrm   r  rl   r  r  r&  r5   r  )r   r2   r  r  rZ   r  r  rT   r.   r.   r/   *test_stats_broadcasting_gh14953_regressionc"  s    &

r  )gn!	g:I"<)gQ	@gE?c                 C   s*   t tj| | t tj|  | d S rd   )r   r2   cosiner`   rS  )rQ   rK   r.   r.   r/   test_cosine_cdf_sfq"  s    r  ))r  gkM6O)rl  g0ӭ!	)r8  g;'u(@c                 C   s*   t tj| | t tj| |  d S rd   )r   r2   r  r7  rW  )r-  rK   r.   r.   r/   test_cosine_ppf_isfy"  s    r  c                  C   s$   t jtj tjg} t| d d S )NgrB)r2   r  r   rZ   r[   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sPJ d S )Nc                 S   s   h | ]\}}t |tr|qS r.   )r  rA   r7   r  r   r.   r.   r/   	<setcomp>"  s   
z*test_distr_params_lists.<locals>.<setcomp>c                 S   s   h | ]\}}|qS r.   r.   r  r.   r.   r/   r  "  r:   c                 S   s   h | ]\}}|qS r.   r.   r  r.   r.   r/   r  "  r:   c                 S   s   h | ]\}}|qS r.   r.   r  r.   r.   r/   r  "  r:   )r   r   r   r   )Zdiscrete_distnamesZinvdiscrete_distnamesZcont_distnamesZinvcont_distnamesr.   r.   r/   test_distr_params_lists"  s    r  c                   C   sB   t jjddd t jjddddks(J t jdddks>J d S )Nr   rN   rr  r   )r  r,   r  )r2   r  Z_statsr  r  r.   r.   r.   r/   test_moment_order_4"  s    r  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   s,   t ttjd }t jjj|jdd}|S )a&  Sample data points for pdf computed with CERN's ROOT

        See - https://root.cern/

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

        pdf calculated for Z0 Boson, W Boson, and Higgs Boson for
        x in `np.linspace(0, 200, 401)`.
        z-data/rel_breitwigner_pdf_sample_data_ROOT.npyzx,pdf,rho,gammar  r  r  r.   r.   r/   ROOT_pdf_sample_data"  s    z'TestRelativisticBW.ROOT_pdf_sample_datazrho,gamma,rtol))qVEB@gj+@r  )FC@Gz @r  )ND@_LU?r7  c                 C   sN   ||d |k|d |k@  }|d |d  }}t |tjj|||d|d d S )Nrhor  rQ   rY   r  rp   )r   r2   rel_breitwignerrY   )rb   r  r!  r  rq   r   rQ   rY   r.   r.   r/   test_pdf_against_ROOT"  s    

z(TestRelativisticBW.test_pdf_against_ROOTzrho, Gamma, rtol))r  r  r7  )r  r  r7  )r  r   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  )rZ   r  r[   )Er  Gammar  rN   r.   r.   r/   rY   "  s
    zFTestRelativisticBW.test_pdf_against_simple_implementation.<locals>.pdfr   rO  rR   r  rp   )rZ   r  r2   r"  r7  rY   r   )	rb   r!  r%  rq   rY   r-  rQ   r   r<  r.   r.   r/   &test_pdf_against_simple_implementation"  s    z9TestRelativisticBW.test_pdf_against_simple_implementationz	rho,gammar  r  r  r  r  r  r   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sbJ tjj|d|d
}t|d |dd |d	 |d fd|fksJ dS )zpTests fit for cases where floc is set.

        `rel_breitwigner` has special handling for these cases.
        l   s;
rl# rv   )rV   r   r|   r   r   rW   ry  rp   r   r  rj   N)rZ   r   r   r2   r"  r   r   r   )rb   r!  r  r   r   r   r   r.   r.   r/   test_fit_floc"  s    z TestRelativisticBW.test_fit_flocN)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dS )TestJohnsonSUrk  )r  r  r  r_  g={?g?5mV>gn?g\}\1@)g`fo@g$ں_@r   r   gvUgN<fj?gwCg~l
@c                 C   s4   t jj |d d ddi}t||dd  dd d S )Nr   r  r  r  rp   )r2   r  r   )rb   rk  r   r.   r.   r/   test_moment_gh18071#  s    z!TestJohnsonSU.test_moment_gh18071N)r   r   r   r   r   r   r)  r.   r.   r.   r/   r(  #  s
   r(  c                   @   sd   e Zd Zdd Zejdddgejdddgejdddgejdddgd	d
 ZdS )TestTruncParetoc                 C   sT   d\}}t dd}t|||}t||t|| }t|| d S )N)?333333@r+  r,  )rZ   r  r2   truncparetorY   r  r`   r   )rb   r-   rN  rQ   r   r<  r.   r.   r/   r  #  s
     zTestTruncPareto.test_pdfr   TFr  r  fix_cc                 C   s   t jd}d\}}}}	tj||||	d}
|
jd|d}i }|rH||d< |rT|	|d< |r`||d< |rl||d	< |r|r|r|rd
}tjt|d$ tjj	|fi | W d    q1 s0    Y  nt
tj|fi | d S )Nl   Z#Lm )r+  r,  r   r  rT   r  rp  r   r   r   r   r   r   )rZ   r   r   r2   r-  r   r   r   r   r   r   )rb   r   r  r  r.  r   r-   rN  rU   rV   r8   r   r   r  r.   r.   r/   r  #  s$    4zTestTruncPareto.test_fitN)r   r   r   r  r   r   r   r  r.   r.   r.   r/   r*  #  s   r*  )N)N)r'  r.  rx  r  r4  pathlibr   r  r  r  Znumpy.testingr   r   r   r   r   r   r	   r
   r   r   r   r   r  r   rZ   r   r   Znumpy.lib.recfunctionsr   r1   r   Zscipy._lib._utilr   r;  r   r   r   r   Zscipy.statsr2   Z!scipy.stats._distn_infrastructurer   Zscipy.stats.distributionsZscipy.specialr   r   r   Zscipy.stats._distr_paramsr   r   Ztest_discrete_basicr   r   Zscipy.stats._continuous_distnsr    r!   Zscipy.optimizer"   r#   	itertoolsr$   flagsoptimizer  r  rj  r  r0   r4   rL   rM   r   r   r   r   r   r   r  rB  rF  rJ  rQ  re  rl  r  r  r  r  r  r  r  r  r  r  r   r&  r/  r}  r  r  r  r  r  r  r  r  r  r2  r>  rL  rS  rm  rs  r{  r  r  r  r  r  r  r  r  r  r  r[   r  r  r  r  r%  r(  r9  r@  rB  rD  rI  rO  rl  r  r  r  r  r  r  r	  r  r  r  r+  r@  re  rn  rv  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  ri  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/  r5  r7  r9  r:  r;  r>  r<   r?  rD  rF  rI  rJ  rr  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.   r.   r/   <module>   s  0 H
J	
)H KFD**"#  @ JX(% wM?* $ lS<37+g !5		$hv12,  IR*     M
 p i ;A%E>h  ^K E
	
&
	
(





	x;	,G."


a6yw

Y