-ii,ddZddlZddlZddlZddlZddlZddlmZddlZddl Z ddl Z ddl m Z m Z mZmZmZmZmZmZddlZddlmZddlZddlmZmZddlmZddlmZdd lm Z dd l!m"Z"m#Z#m$Z$m%Z%ddl&m'Z'dd l(m)Z)dd l*m+Z+ddl,Zdd l-m.Z.m/Z/m0Z0ddl1m2Z2m3Z3ddl4m5Z5m6Z6ddl7m8Z8m9Z9ddl:m;Z;mm?Z?ej@jAdkZBej dkoe jCdkZDddgZEddZFdZGdZHGddZIddZJdZKejLMd gd!d"ZNGd#d$ZOGd%d&ZPGd'd(ZQGd)d*ZRGd+d,ZSGd-d.ZTGd/d0ZUGd1d2ZVGd3d4ZWGd5d6ZXGd7d8ZYGd9d:ZZGd;d<Z[Gd=d>Z\Gd?d@Z]GdAdBZ^GdCdDZ_GdEdFZ`GdGdHZaGdIdJZbGdKdLZcGdMdNZdGdOdPZeGdQdRZfGdSdTZgGdUdVZhGdWdXZiGdYdZZjGd[d\ZkGd]d^ZlGd_d`ZmGdadbZnGdcddZoGdedfZpGdgdhZqGdidjZrGdkdlZsGdmdnZtGdodpZuGdqdrZvGdsdtZwGdudvZxGdwdxZyGdydzZzGd{d|Z{Gd}d~Z|GddZ}GddZ~GddZGddZGddZGddZGddZGddZddejddejzz zddejddejzz zddejddejzz zddejddejzz zddejddejzz zg fdejddejzz ddejddejzz zddejddejzz zdz ddejddejzz zdz ddejddejzz zdz g fddejdejzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dgfgZGddZGddZGddZGddZGddZGddZGddZGddZGdd¦ZGdÄdĦZGdńdƦZGdDŽdȦZGdɄdʦZd˄ZGd̄dͦZGd΄dϦZGdЄdѦZGd҄dӦZGdԄdզZGdքdצZGd؄d٦ZdڄZGdۄdܦZGd݄dަZGd߄dZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZd ZejLeBd  d Zd ZdZdZdZdZdZdZdZdZejLMdgddZdZdZÐdZĐdZŐdZƐdZǐdZȐd Zɐd!Zʐd"ZejLMd#d$ejd%d&gfd'ejd(d)gfd*ejd+d,gfd-ejd.d/gfgd0Z̐d1Z͐d2Zΐd3Zϐd4ZejLMd5gd6d7ZejLMd8gd9d:ZejLMd;gd<d=ZӐd>ZejLMd5gd?d@ZՐdAZGdBdCe'jZGdDdEe'jZGdFdGe'jZGdHdIe'jZGdJdKZGdLdMZejLeBdN dOZސdPZߐdQZdRZdSZdTZdUZdVZdWZdXZdYZejLMd5gdZd[ZejLMd\d]d^gd_ZejLMd`ddgdafdbdcgdafdddegdffgdgZdhZdiZdjZGdkdlZdmZGdndoZGdpdqZGdrdsZGdtduZdvZejLMdwe6e3zdxZdyZdzZejLMd8d{d|gd}ZejLMd;gd~dZdZdZdZGddZGddZGddZGddZGddZGddZejLMdgddZdS(z! Test functions for stats module N)Path) assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_assert_array_lessassert_array_max_ulp)raises) typecodesarray)rec_append_fields)special)check_random_state)IntegrationWarningquad trapezoidcumulative_trapezoid) argsreduce)_XMAX)xlogy polygammaentr)distcont invdistcont) distdiscreteinvdistdiscrete) FitDataError _argus_phi)rootfmindifferential_evolution)productdarwinx86_64 tukeylambdapearson3cV||d|}tt|||dS)Nz does not have attribute msg)r hasattr)abr,s j/var/www/html/bet.cuttalo.com/ml/venv/lib/python3.11/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattrr15s; {00Q00 GAqMMs######cDttjjddS)Nf_gen)r1scipystats distributionsr2r0test_api_regressionr9;sEK-w77777r2cttjjj}dt D}dt D}gd}||z|z}ttd|}||ksJdS)Ncg|] }|d Srr8.0dists r0 z0test_distributions_submodule..Bs///d$q'///r2cg|] }|d Sr<r8r=s r0r@z0test_distributions_submodule..Cs111DQ111r2) rv_discrete rv_continuous rv_histogramentropycHt|d S)N<)str startswithss r0z.test_distributions_submodule..JsA(9(9#(>(>$>r2)setr5r6r7__all__rrfilter)actual continuousdiscreteotherexpecteds r0test_distributions_submodulerU@s *2 3 3F//h///J11L111H   EH$u,H6>>IIJJH X      r2c |eZdZdZejdgdejdddejddgd Z d Z d Z ejd gd dZ ejdgddZ dZejdgddZdZejjejdddgejdgdejdddgejdddgdZejjd Zejd!d"dgd#Zd$Zd%Zd&Zd'S)( TestVonMisescNtjd|_dS)NlExqnprandom default_rngrngselfs r0 setup_methodzTestVonMises.setup_methodP9((44r2k)皙?rexrr dcd}d}||dd|||dd|||dd|||dd|||dd|||dd|dS)Nctj|||}t||||dtjz|zzdS)Nlocscale)r6vonmisesrpdfrZpirbLrKrevms r0check_vonmises_pdf_periodiczHTestVonMises.test_vonmises_periodic..check_vonmises_pdf_periodicVsSq222B q 266!q25y1}2E+F+F G G G G Gr2ctj|||}t||dz||dtjz|zzdzdS)Nrjrrm)r6rnrcdfrZrprqs r0check_vonmises_cdf_periodiczHTestVonMises.test_vonmises_periodic..check_vonmises_cdf_periodicZslq222B q A "qAIM': ; ;a ? A A A A Ar2rrrfr8)r_rbrertrws r0test_vonmises_periodicz#TestVonMises.test_vonmises_periodicSs H H H A A A $#Aq!Q///##Aq!Q///##Aq"a000##Aq!Q///##Aq!Q///##Aq"a00000r2cttjjtj ttjjtjdSN)rr6 vonmises_liner.rZrpr/r^s r0test_vonmises_line_supportz'TestVonMises.test_vonmises_line_supportgs:U(*RUF333U(*BE22222r2cttjd}t|dddS)N r?)r6rnrrv)r_rss r0test_vonmises_numericalz$TestVonMises.test_vonmises_numericalks1 ^C BFF1IIs+++++r2zx, kappa, expected_pdf))rc{Gz?g|65?)rc9@g?U?)rcr~g"?)@rgDfI?)rrg1<)rr~cjtj||}t||ddSNV瞯<rtol)r6rnror)r_rekappa expected_pdfros r0test_vonmises_pdfzTestVonMises.test_vonmises_pdfys6n  E**\666666r2zkappa, expected_entropy))rgA ?)g,eޞ?)rggBb9d22)g G)g chtj|}t||ddSNvIh%<=r)r6rnrEr)r_rexpected_entropyrEs r0test_vonmises_entropyz"TestVonMises.test_vonmises_entropys5.((//!1>>>>>>r2chd}tj|}tj|}tj|}tjddd|}tjddtjzd|}tjdddtjzt|z dz|}t||dt||ddS) Ni@}rrrj random_statermratol) rZr[r\r6rnrvsrpabsr)r_seedrng1rng2rng3rvs1rvs2rvs3s r0test_vonmises_rvs_gh4598z%TestVonMises.test_vonmises_rvs_gh4598sy$$T**y$$T**y$$T**~aQa00044$4GG~aQruWA666:::MM~aQ%&ruWSYY%6q%8;;;;>3D3;Q;Q d////d//////r2zx, kappa, expected_logpdf))rcrg EJ?)rcrgoι?)rcr~g0,)rrgdty)rrgʹw[A)rr~gcjtj||}t||ddSr)r6rnlogpdfr)r_rerexpected_logpdfrs r0test_vonmises_logpdfz!TestVonMises.test_vonmises_logpdfs6&&q%00e<<<<<.Ar2rrmcdSrr8rs r0rLz3TestVonMises.test_vonmises_expect..rr2c0tjd|zS)Ny?)rZexprs r0rLz3TestVonMises.test_vonmises_expect..sBF2a4LLr2 complex_funcN) rZr[r\r6rnexpectr issubdtypedtypefloatingrpanglecomplexfloating)r_r]rkrlbresboundss r0test_vonmises_expectz!TestVonMises.test_vonmises_expectsi##$788A+UBnE22299++FFQ}SY 44444R!be)^#9enE2229++OOOOQ}SY 44444R!be)^#9enE2229:P:PS;ASSSPQSS sag777}SY(:;;;;;;;r2rvs_locrm rvs_shape)rrgחAfix_locTF fix_shapec.|r|rtjdtjd}t j|d||}ddi}|r||d<|r||d<tt j|t jj fi|dS) NzNothing to fit.rrsizerkrfscalerflocf0) pytestskiprZr[r\r6rnr_assert_less_or_close_loglikennlf)r_rrrrr]datakwdss r0test_fit_MLE_comp_optimizerz(TestVonMises.test_fit_MLE_comp_optimizers  + + K) * * *i##$788~!!)$G/2"44!}  #"DL  #"DJ%end&+n&9 C C=A C C C C Cr2c@gd}tj|}dtjz}tj||\}}}|tjtjksJttj|tjj d|dS)N)g!*Kg4,%OԿgZ۵?g ge_@g-8gPghn?grrmg d?)r5r6rnrrZrpr^s r0test_vonmises_fit_boundsz%TestVonMises.test_vonmises_fit_boundssZ    !WA 666    "%'9"5!6Q ?????r2N)__name__ __module__ __qualname__r`rmark parametrizerZrprxr|rrrrrrxslowrslowrrrrrr8r2r0rWrWOs555 [S---00 [S1aC"89911:9101$333,,, [5///0077007 [6;;;<< ?? << ? 0 0 0  [8BBBCC==CC=<<<4 [ [YA// [[---88 [Yu 66 [[4-88CC9876980/ C$ [ O O O [Vb!W-- ( (.- ( Q Q Q999 @ @ @ @ @r2rWFc ||j}|j|fi|}tt||j|fi|}|st j||ksJ|||}|||}||kst j||dsJd|vr|d|dksJd|vr|d|dksJdSdS)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. Nrrrrr)rrsupertyperZanyallclose) r?rfuncmaybe_identicalrmle_analytical numerical_optll_mle_analyticalll_numerical_opts r0rrs! |yTXd++d++N/E$t**d++/====M 7vn 566666^T22tM400 !1 1 1 K)+;% H H H 2 1 1 ~~b!T&\11114b!T(^333333r2c ddg}|jr6t|jd}|gdd|z }tt |t jt|}gd}tjtd5|j |fi|dddn #1swxYwYtjtd5| t j gdddn #1swxYwYtjtd5| t j gdddn #1swxYwYtjtd 5| |d dddn #1swxYwYtjtd 5|j |gd gt|d z zRddddS#1swxYwYdS)Nrr,)rf1f2rrmr3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:rm) extra_keywordzToo many positional arguments.r)shapeslensplitdictziprZarangerr RuntimeErrorr ValueErrornaninf TypeError)r?paramnshapes all_fixedrs r0assert_fit_warningsr>sL X E {.dk'',,-- ###HWH--S #e** 5 56677I 99D |& ' ' '$$ #####$$$$$$$$$$$$$$$ zB D D D "& zB D D D "& y(D E E E(( Q'''((((((((((((((( y(H I I I..-SZZ!^,----..................sZB88B<?B<!D  DD1!EE"%E"F((F,/F,#G>>HHr?)alpha betaprime fatiguelifeinvgammainvgauss invweibull johnsonsblevylevy_llognormgibrat powerlognormrayleighwaldctt}||}tt|}t |j|jg|Rdt|j|jg|Rtj t |j|j g|Rdt|j|j g|Rtj dS)zgh-6235rN) rrgetattrr6rror.rrrZrr/)r?dctargss r0 test_supportr1Us x..C t9D 5$  D/$///333TV+d+++bfW555/$///333TV+d+++bfW55555r2c&eZdZdZdZdZdZdS) TestRandIntcNtjd|_dS)Nl{2rYr^s r0r`zTestRandInt.setup_methodhrar2ctjddd|j}t t j|dkt j|dkzt t|dktjddd|j}t t j|dkt |j j tdvtjdd|j }t |dk|dkzt t|t j tt| tjddd |j }t |j j tdvdS) Nrrgrrm2 AllInteger.rr+r)r6randintrr]r rZrrshapercharr isinstance ScalarTypereprrr_valsvals r0test_rvszTestRandInt.test_rvsksm}  BStx HHtby!!BF419$5$55666D S !!!}  BW48 LL')*** 9\#::;;;mBTX>>sRx())) 3 ..DcOODDDDmB##'''AA )L"99:::::r2ctjdd}tj|dk|dkzdd}tj|dd}t ||dS)Nr$rr6{Gz?)rZr_wherer6r<pmfr)r_rboutrCs r0test_pdfzTestRandInt.test_pdfxs` E!B$KhQ1r6*J::}  Ar**!$,,,,,r2ctjddd}tj|}tj|dk|dkgd|dz dzd z gd}tj|dd}t||d dS) NrrGrgr6r?@rr decimal)rZlinspacefloorselectr6r<rvr)r_rerbrLrCs r0test_cdfzTestRandInt.test_cdf~s K2s # # HQKKib!q&)C!C%'F1C+DaHH}  Ar**!$R888888r2N)rrrr`rErMrWr8r2r0r3r3gsP555 ; ; ;--- 99999r2r3cDeZdZdZdZdZdZdZdZdZ dZ d Z d S) TestBinomcNtjd|_dS)Ni&8jrYr^s r0r`zTestBinom.setup_methodrar2ctjddd|j}t t j|dkt j|dkzt t j|dkt |jj tdvtjdd|j}t t|ttjddd|j}t t|t j t |jj tdvdS Nrfrr7rrr9rr)r6binomrr]r rZrr=rr>r r?intndarrayrBs r0rEzTestBinom.test_rvss{r4gDHMMtqy!!BF42:$6$66777')*** 9\#::;;;koob$TXo>> 3$$%%%k"d##'''AA 3 ++,,, )L"99:::::r2ctjddd}tjddd}t|dddt|ddddS)NrgrrrOrrrr6r]rKr)r_vals1vals2s r0test_pmfzTestBinom.test_pmfsd S!,, 3**sQ7777sQ777777r2ctjdd}tjgd}t t || }|}t||tjdd}|}t|dtjdd}|}t|ddS)Nrmr)?rrgrrO) r6r]rZrsumrrErr)r_r/ expected_p expected_hhs r0 test_entropyzTestBinom.test_entropys K3  X///00 % J77888 IIKK:&&& K3   IIKKQ K3   IIKKQr2cjtj5tjdtt t jdddt t jdddddddS#1swxYwYdS)Nerrorrmrnp) warningscatch_warnings simplefilterRuntimeWarningrr6r]rstdr^s r0 test_warns_p0zTestBinom.test_warns_p0s  $ & & 9 9  !'> : : : qA...3355q 9 9 9 qA...2244a 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9sBB((B,/B,cZd}tjd|d|ksJdS)Nr333333?rO)qrprq)r6r]rr_rps r0 test_ppf_p1zTestBinom.test_ppf_p1s2 {S11Q666666r2cd}d}tjd}tj|||}tj|||z}t ||ddS)NglyCgq]\ T3r r?r^r_rBs r0rEzTestBernoulli.test_rvss""4gDH"MMtqy!!BF419$5$55666')*** 9\#::;;;o!!$TX!>> 3$$%%%od##'''AA 3 ++,,, )L"99:::::r2ctjd}dtjdzdtjdzz }|}t ||tjd}|}t |dtjd}|}t |ddS)NrgпrrrO)r6rrZlogrErr)r_r/rjrks r0rlzTestBernoulli.test_entropys OD ! !26$<<'$rvd||*;; IIKK:&&& OC  IIKKQ OC  IIKKQr2N)rrrr`rErlr8r2r0rrsA555 ; ; ;     r2rceZdZdZdS) TestBradfordcd}tjdd}tj||}tj||}t ||dS)Nrc)rZlogspacer6bradfordrvrr)r_crerzxxs r0 test_cdf_ppfzTestBradford.test_cdf_ppfs\  KR  N  q! $ $ ^  1 % %2r2N)rrrrr8r2r0rrs#r2rcFeZdZdZejdddddddd d d d ed fg dZejdgdejde j j dfe j j dfgdZ ejdgddZejdgdejde j jdfe j jdfgdZdS) TestCauchycTtjd}|dksJdS)NZbtir)r6cauchyrors r0test_pdf_no_overflow_warningz'TestCauchy.test_pdf_no_overflow_warnings* L  U # #Cxxxxxxr2x, ref)r罡HP)gr)gIL8r)gOd@gHP)Mb@?gP)rcg*6y)?g8@(J)gNgmCg'K@$[U)rgonьgs 32crtj|| g}t|||gddSr)r6rrr)r_rerlogps r0 test_logpdfzTestCauchy.test_logpdf s>|""Ar7++sCju555555r2))g7y1gu lY<)g^?)rrg)rr)rr)rg)nE?)g7y1C?z method, sgnrrcF|||z}t||ddSrr)r_rermethodsgnrqs r0 test_cdf_sfzTestCauchy.test_cdf_sfs0 F3q5MM3U++++++r2))gRyXsg!;v+͋)(,* EgjLҳ)$@g )r9B.)g$gCį )g :@sgg>Z)g 5g*\Bctj|}t||dtj| }t||ddSN+g /)rg)rr)rrO) !?gqmA)g?gqJRBcF|||z}t||ddSrr)r_rqrrrres r0 test_ppf_isfzTestCauchy.test_ppf_isfAs0 q M3U++++++r2N)rrrrrrrrrr6rrvrrrrisfrr8r2r0rrs [ # & % ' $ # # # # $ $ % ' ( (66 ( (6  [ % % %   [ , A  ,/2   ,,   ,  [X;;;<<00<<0 [ / / /   [ , A  , B  !"",, ""  ,,,r2rceZdZdZdZdZdZdZdZe j ddefd gd Z e j dgd d Z d S)TestChignT9;g2 >h?@cttjdd}t||jddS)Nrfrrr)r6chirr CHI_SF_10_4r_rKs r0test_sfzTestChi.test_sf]s5 ILLQ  4+%888888r2cttj|jd}t |dddS)Nrrfrr)r6rrrrr_res r0test_isfzTestChi.test_isfas5 IMM$*A . .2E******r2crd}d}tj||}t|dddS)Nrr:ga rr)r6rrr)r_redfrs r0 test_logcdfzTestChi.test_logcdfes?  !!!R(( 6UCCCCCCr2crd}d}tj||}t|dddS)Nrr:@y`rr)r6rrr)r_rerrs r0 test_logsfzTestChi.test_logsfls=   2&&5EBBBBBBr2df, ref@@)gļBgcAcdttj||ddSN-q=r)rr6rrr_rrs r0 test_meanzTestChi.test_meanys-  r**Ce<<<<<?gG6ƴ?g9b?|^?߈܁r?gT C?rrgm?gFZۤ?g HB?gTXek?g?bȓE?gLZ;x?gJ>+=r@)g2c}`?g>t\f?g˂ q?gg'T){?g mw?g>t\?h'T)?7-h J?u8n?A#?g:Q?rrrrgZrԢ?g߄q?g)aL?gr'Orrrrkrl)g3c}?g>t\?g˂ ?f'T)?#n?5-h J??u8n?vL1??#?||P?g:Q?rrrrrrrr)rZrTr6 crystalballrorrr_X calculatedrTs r0rMzTestCrystalBall.test_pdfs; Kc2 & &ss +&**13#*>> 8 K K K L L *59999&**13#*>> 8 J J J K K *59999&**13#3c*RR 8 G G G H H *5999999r2ctjddddd}tj|dd}tjgd }t ||d tj|dd }tjgd }t ||d tj|dd dd}tjgd}t ||d dS)rrrPrNrrOrr)ghQ| )?gj,,?g d}9?gH6?g|^?gEv?glQ| )?g d}9?g|^?go[?gsX?g& Ռ?g~M+?gZR c?gtE_s?gi?gB?gEg?gvP ?gx훟?rrr)gpr?gt\v?ge}?gݠn^?gCȘU?at\?ݠn^?~[n|D?gS4s/?2s?`qfhG?IgL?荩s?rA?IH?guk?ghi"?gP ?g.q?gs?rr)go?rge?rgPU,?rgjݗ ?rg?rg_!Y?rga?r gR?r g( ?r g܉x?r )rZrTr6rrvrrrs r0rWzTestCrystalBall.test_cdfs; Kc2 & &ss +&**13#*>> 8 E E E F F *59999&**13#*>> 8 E E E F F *59999&**13#3c*RR 8 E E E F F *5999999r2zx, beta, m, rootref))(@rOrgI9)"@@?gy <)rcgjt?g +,)grrgGA*?)g>rrPg^v'?)gd~Qr皙?g眭?cntj|||}t||ddS)Nrrr)r6rrr)r_rerrrootrefrs r0rzTestCrystalBall.test_sfs<  ! !!$! ! 4 4G%000000r2ctjgd}tjgd}tjgd}tjd||}t ||dtjgd}tjdd tjd d g}||z }tjd ||}t ||dtjtjtjtjd dg}||z } tjd||} t | | dtjtjtjtjtjdg}||z } tjd||} t | | dtjtjtjtjtjdg}||z } tjd||}t | |dtjtjtjtjtjdg}||z }tjd||}t ||ddS)zs All values are calculated using the pdf formula and the integrate function of Mathematica )rrOrrr)rrrrr)rOrOrOrOrOrMbP?r)gԚh@g [&@gͪ@g2dQ@gn6-@g?ޫV&̿gBgQCRgQF\jrg @gn(@rmg?Җ)rgMg'#@rg('UHrN)rZrr6r_munprr)r_rrexpected_0th_momentcalculated_0th_momentnormr.expected_1th_momentcalculated_1th_momentexpected_2th_momentcalculated_2th_momentexpected_3th_momentcalculated_3th_momentexpected_4th_momentcalculated_4th_momentexpected_5th_momentcalculated_5th_moments r0 test_momentszTestCrystalBall.test_moments"sg x11122 H... / /!h'@'@'@AA % 1 7 74 C C+-BOOOO xHHHII Hh"&)YG H H$h % 1 7 74 C C+-BOOOO Hbfbfbffh? @ @$h % 1 7 74 C C+-BOOOO HbfbfbfbfjA B B$h % 1 7 74 C C+-BOOOO Hbfbfbfbfg> ? ?$h % 1 7 74 C C+-BOOOO Hbfbfbfbfh? @ @$h % 1 7 74 C C+-BOOOOOOr2ctjdd}|}d\}}}tj|||}t t |||}t||ddS)Nrmr)ir6@ Hz>r) r6rrErZrTrrror)r_cbres1lohiNreres2s r0rlzTestCrystalBall.test_entropyOsy  q! $ $zz||& B KB " "bffQii!,,d......r2N) rrrrMrWrrrrr%rlr8r2r0rrs<:<:<:|<:<:<:D [ 0 0 0111+P+P+PZ/////r2rc&eZdZdZdZdZdZdS) TestNBinomcNtjd|_dS)Nl\:rYr^s r0r`zTestNBinom.setup_method[rar2ctjddd|j}t t j|dkt t j|dkt |jj tdvtjdd|j}t t|ttjddd|j}t t|t j t |jj tdvdSr\)r6nbinomrr]r rZrr=rr>r r?r^r_rBs r0rEzTestNBinom.test_rvs^s |DwTXNNtqy!!"""')*** 9\#::;;;lr4dh?? 3$$%%%l2t$$(((BB 3 ++,,, )L"99:::::r2c 2ttjtjdddtjdddtjjddd}t|ddS)Niigp= ף?rr) rrZrr6r3logpmfrKr5r)r_rDs r0rezTestNBinom.test_pmfisu|223TBBCC ((c488 : : :k ''1a00S!r2ctjgddd}tjtjgddd}t ||dS)N)rrrr333333@?ro)r6r3rrZrrvrr_rCrs r0test_logcdf_gh16159zTestNBinom.test_logcdf_gh16159qsb|""<<<3$"??fU\%%lllcT%BBCCc"""""r2N)rrrr`rErer:r8r2r0r0r0ZsP555 ; ; ;#####r2r0ceZdZdZejjdZejjdZejjdZ ejjdZ dZ dZ dZ d Zd S) TestGenInvGausscNtjd|_dS)NlnrYr^s r0r`zTestGenInvGauss.setup_methodyrar2ctjdd}tj|d|j|j\}}t |dkddS)Nffffff@rr皙?Tr6 geninvgausskstestrr]rvrr_gigrrqs r0test_rvs_with_mode_shiftz(TestGenInvGauss.test_rvs_with_mode_shift|YS))|CGGDHGEEswOO1QXt$$$$$r2ctjdd}tj|d|j|j\}}t |dkddS)Nrrr@rrATrBrEs r0test_rvs_without_mode_shiftz+TestGenInvGauss.test_rvs_without_mode_shiftsYT**|CGGDHGEEswOO1QXt$$$$$r2ctjdd}tj|d|j|j\}}t |dkddS)Nrc皙?r@rrATrBrEs r0test_rvs_new_methodz#TestGenInvGauss.test_rvs_new_methodrHr2cfd}t|dddt|dddt|ddddS)Nctj||}|dj}tj||jddkS)Nr@rrrA)r6rCrr]rDrv)rqr/rFrr_s r0 my_ks_checkz4TestGenInvGauss.test_rvs_p_zero..my_ks_checksJ#Aq))C''t$(';;C<SW--a047 7r2rrLTrr)r)r_rPs` r0test_rvs_p_zerozTestGenInvGauss.test_rvs_p_zerosx 8 8 8 8 8 [[C(($///[[C(($///[[C(($/////r2cttjdddddtjddddz dS)Nrmrfrrr)rr6rCrr^s r0test_rvs_negative_pz#TestGenInvGauss.test_rvs_negative_psn!$**..BT.JJE%c1--11r1MMM O O O O Or2cHtjdddd}ttj|ddgddkd d t jd dd }}tj|dd|z | }t|tj ||tj |dd|z | }t|tj | |dS)Nr@rriFPW)rrqr/rr#r0333333?Trgrrf)rqr/rl) r6rCrrrDrZrTrorr#rv)r_igmurepdf_igcdf_igs r0 test_invgausszTestGenInvGauss.test_invgausss   " " " S SU\"js;;;A>EtLLLR[q"--A"&&qDAF"&EEr 2 2 6 6q 9 9:::"&&qDAF"&EEr 2 2 6 6q 9 9:::::r2ctjgd}tjddd}t|tj|dddS)N) g;g8y8?g\}Z?ghܲ0|?gRq?rrrfrr)rZrrTrr6rCro)r_vals_Rres r0 test_pdf_RzTestGenInvGauss.test_pdf_Rsd,,,-- Ka $ $ 1 5 5aa @ @AAAAAr2cttjddddttjdddddS)Nrrg>Ar8rm)rr6rCror^s r0 test_pdf_zerozTestGenInvGauss.test_pdf_zerosTU&**1c377;;; U&**3A66:::::r2N)rrrr`rrrrGrJrMrQrUr]r`rbr8r2r0r<r<xs555 [%%%  [%%%  [%%%  [000OOO ; ; ; B B B;;;;;r2r<ceZdZdZdZejdgddZejdgddZ dZ d Z d Z d Z d Zd ZdS)TestGenHyperbolicctjgd}d\}}}d\}}|||z||zf}tj|||d}tjddd} t || |dd dS) N) gF^T=g{X'=gNunƢsy>g7!t?gɫzI?g̸?g?gq 6.?gmPZz?g:PgN?rmrmrrrrjrfrrrr)rZrr6 genhyperbolicrTrro r_r_lmbdarrrZdeltar0ghres r0 test_pdf_rzTestGenHyperbolic.test_pdf_rs %ud EuU{DJ/  $Be < < < KR $ $q 6>>>>>>r2ctjgd}d\}}}d\}}|||z||zf}tj|||d}tjddd} t || |dd dS) N) g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?rfrgrjrhrfrư>ri)rZrr6rjrTrrvrks r0 test_cdf_rzTestGenHyperbolic.test_cdf_rs %ud EuU{DJ/  $Be < < < KR $ $q 6======r2zx, p, a, b, loc, scale, ref) )rmrrrrg8ɹvF(;)rsrfrrgrrg[ Ϡ?)rsrfrg?rrg✝`D;)rs?r):?rrg dL;)rrtrrurrgzK^7?)rrrurrgj?)rrvrrrga=vG:)rrvrrwrrg?)(rvrrwrrg1bV?)<rvrrwrrg?cttj||||||}t||ddSNrjdy=r)r6rjrvr) r_rerqr.r/rkrlrrvs r0test_cdf_mpmathz!TestGenHyperbolic.test_cdf_mpmathsB!%%aAqc%GGSu------r2))rrqrQrrrgC!,?)rr@@rrg,Ћf?)rrr~rrrrO)rmrrrrgm"چ >),rfrrgrrg:;)ryrvrrwrrgw=)Krvrrwrrg3Z0&Kir0rmrZs r0r@z4TestGenHyperbolic.test_moments_r..%sI  2U ; ; ; B B1 E Er2rrrrri)ranger) r_r_rlrrvals_usr0rmrZs @@@r0test_moments_rz TestGenHyperbolic.test_moments_rs555%ud EuU{DJ/1a[[ ae<<<<<>>4 [% < < <  ..  . [% @ @ @  --  -===. % % %$"*r2rdceZdZejdddgdZejdddgdZd Zd S) TestHypSecantz x, reference)r6gA0=)r8g!b;chtj|}t||ddSr)r6 hypsecantrr)r_re referencers r0rzTestHypSecant.test_sfs4_   " "IE222222r2z p, reference)rqg9bT*@)rgTW-;@chtj|}t||ddSr)r6rrr)r_rqrres r0rzTestHypSecant.test_isfs4 O   " "95111111r2cd}d}tj|}t||dtj| }t||ddS)NI@g!brr)r6rrrrrs r0rzTestHypSecant.test_logcdf_logsfsh %''**%0000%%qb))s//////r2N) rrrrrrrrrr8r2r0rrs  [^9:<==33==3 [^89;<<22<<200000r2rc~eZdZdZdZejdgddZdZ dZ dZ d Z d S) TestNormInvGaussctjgd}tjgd}tj|dd}t ||ddS)N)gp~٧>g @X>g}e?g{)߳?gwH?irrr:rrr.r/rr)rZrr6rrvr)r_r_cdfx_testvals_cdfs r0 test_cdf_RzTestNormInvGauss.test_cdf_Rsr <<<==,,,--%))&A)==%d333333r2ctjgd}tjgd}tj|dd}t ||ddS)N)gp϶>g\H55$?geСt&?go NiH?g]u>rrrrrr)rZrr6rror)r_r_pdfrvals_pdfs r0r`zTestNormInvGauss.test_pdf_Rsp<<<==,,,--%))&A)==%d333333r2zx, a, b, sf, rtol))rrr!7?r)rrr?=r)rrrSgy5`?r)rfrrSgMLC9rctj|||}t|||tj|||}t|||dSNrr6rrrr)r_rer.r/rrrKrs r0test_sf_isf_mpmathz#TestNormInvGauss.test_sf_isf_mpmathsh   ! !!Q * *2D))))   " "2q! , ,14((((((r2cddg}ddg}d}ddg}tj|||}t||dd tj|||}t||d dS) Nrrrrrrrr~rarqrr)r_rer.r/rrKrs r0test_sf_isf_mpmath_vectorizedz.TestNormInvGauss.test_sf_isf_mpmath_vectorizeds H F  "8 9   ! !!Q * *2E6666   " "2q! , ,14((((((r2ctjdd}tjddd}||}||}t ||dS)Nrrrrm)r6rrZrrrr)r_dstrerrs r0 test_gh8718zTestNormInvGauss.test_gh8718s[ A&& IaQ   VVAYYggbkkQr2c.d\}}tj|dz|dzz }||z |dz|dzz d|z|tj|zz ddd|dzz|dzz zz|z f}t|tj||ddS) Nrrrmrrrrmvskmoments)rZrrr6r)r_r.r/gammav_statss r0 test_statszTestNormInvGauss.test_statss11q!t $$u9adUAXosQw!bgenn:L/M!a!Q$hAo-.68We066q!V6LLMMMMMr2cd\}}tjgd}tj|||}t |tj|||dS)Nrrrr)rZrr6rrrrv)r_r.r/rrCs r0test_ppfzTestNormInvGauss.test_ppfsf1---..!%%fa33 2 6 6tQ B BCCCCCr2N) rrrrr`rrrrrrrrr8r2r0rrs 4 4 4444 [0JJJKK )) KK ) ) ) )   NNNDDDDDr2rcPeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d S) TestGeomcNtjd|_dS)NlyrYr^s r0r`zTestGeom.setup_methodrar2ctjdd|j}t t j|dkt t j|dkt |jj tdvtjd|j}t t|ttjdd|j}t t|t j t |jj tdvdS)Nrr7rrr9rr)r6geomrr]r rZrr=rr>r r?r^r_rBs r0rEzTestGeom.test_rvssz~~dtx~HHtqy!!"""')*** 9\#::;;;jnnTn99 3$$%%%j""148"<< 3 ++,,, )L"99:::::r2ctjtjdd|j}|jtjksJtj|tj tj j ksJdS)Nirr) r6rrrZrr]rint64riinfoint32maxr_rs r0 test_rvs_9313zTestGeom.test_rvs_9313sljnnRVC[[qtxnHHyBH$$$$vcBHRX..223333333r2cntjgdd}t|gddS)Nr r)rrgrt)r6rrKrr_rCs r0rezTestGeom.test_pmfs8z~~iii--!$(:(:(:;;;;;r2c8tjtjgdd}tjgdd}t ||ddtjdd}t|ddS)Nr rrrrarr)rZrr6rrKr5rr)r_rcrdrDs r0 test_logpmfzTestGeom.test_logpmfsuz~~iii5566 !!)))S11u5q9999j1%%S#r2ctjgdd}tjgdd}t gd}t ||t |d|z dS)Nr rrr?r)r6rrvrrrr_rCvals_sfrTs r0rzTestGeom.test_cdf_sfsrz~~iii--*-- 3//+++,,!$111!'1X:66666r2c:tjgdd}tjgdd}t gd}t |t j|t |t j| dS)Nr rr) r6rrrrrrZrlog1prs r0rzTestGeom.test_logcdf_logsfsz  C00*""999c22+++,,!$x(8(8999!'28XI+>+>?????r2ctjgdd}tgd}t ||dS)Nrr)rOrr)r6rrrrr_rCrTs r0rzTestGeom.test_ppfsEz~~000#66))!$11111r2cfttjdddddS)NrrOrr)rr6rrr^s r0test_ppf_underflowzTestGeom.test_ppf_underflow#s- ue44cFFFFFFr2cvtjd}t|dddS)Ng<,Ԛ?g۩@rr)r6rrEr)r_rks r0test_entropy_gh18226zTestGeom.test_entropy_gh18226's; Jv   & & ( (,5999999r2ctjd}tjdd|dksJdS)NiKH9rfrr)rZr[ RandomStater6rrr)r_rs r0test_rvs_gh18372zTestGeom.test_rvs_gh18372-sPy,,Y77  u2LIIAMRRTTTTTTTr2N)rrrr`rErrerrrrrrrr8r2r0rrs555 ; ; ;444<<<777@@@222 GGG::: UUUUUr2rceZdZdZdZdS) TestPlanckctjgdd}tgd}t ||dS)Nr rP)g|dy?g8'\>ggrU!>)r6planckrrrrs r0rzTestPlanck.test_sf7sQ|yyy"--22233 "$11111r2ctjgdd}tgd}t ||dS)N)r@@p@r)gP.gh>gTF)r6rrrrrs r0rzTestPlanck.test_logsf>sJ|!!"7"7"7??:::;;!$11111r2N)rrrrrr8r2r0rr5s222222222r2rc&eZdZdZdZdZdZdS) TestGennormcgd}tj|d}tj|}t ||dSNr r)r6gennormrorrr_pointspdf1pdf2s r0 test_laplacezTestGennorm.test_laplaceEsM}  ++}  ((D$'''''r2cgd}tj|d}tj|d}t ||dSNr rmg;f?rl)r6rrorrrs r0 test_normzTestGennorm.test_normLsO}  ++z~~fF~33D$'''''r2ctjd}tjd}|d|}tj||jjdksJtjd}|d|}tj d|}tj ||jdksJtjd}||_ |d|}tj dd| }tj ||jdksJdS) Nrrrrcrrmg;f?rlrr) r6rrZr[r\rrDrvpvaluerks_2samprr)r_r?r]r rvs_laplacervs_norms r0rEzTestGennorm.test_rvsSs&}S!!i##J//hhDsh33|C**1C7777}QhhDsh33m''T'DD ~c;//6<<<<}QhhDsh33:>>t#>NN~c8,,3c999999r2ctjddgddgg}tjd}|gd|}tj|ddddftjdjd d ksJtj|dddd ftjdjd d ksJtj|ddd dftjdjd d ksJtj|ddd d ftjdjd d ksJdS) NrrOrrPr)rrmrmrrrrc)r6rrZr[r\rrDrv)r_r?r]rs r0test_rvs_broadcastingz!TestGennorm.test_rvs_broadcastingesF}sBi"b233i##J//hhLLLsh;;|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJJJr2N)rrrrrrEr r8r2r0rrDsU((((((:::$KKKKKr2rcZeZdZejdddgdZdS) TestGibratx, sfx)rgD.?)gJ]b>HH>>>r2r ceZdZdZejdgddZdZdZ ejdgdd Z d S) TestGompertzctjtjddd}t |ddSN0.++r)r6gompertzrrvrrs r0test_gompertz_accuracyz#TestGompertz.test_gompertz_accuracysA N  u~11&!<g:0N<?)rrg:?cfttj|||ddSr)rr6foldnormrvr_rerrs r0rWzTestFoldNorm.test_cdfs1 **1a00#EBBBBBBr2N)rrrrrrrWr8r2r0r&r&s[ [[+N+M+OPPCCPPCCCr2r&ceZdZejdddgdZejdgddZejdd d gejd gd ejd ddgejdddgdZdZ dS) TestHalfNormr )r |N?)rf Oul2;cttj||dttj||ddSr)rr6halfnormrrrs r0rzTestHalfNorm.test_sf_isfsT ))!,,c>>>>**3//??????r2r))Ww'&l7g;G<^͛7)C]r2r rvs_scalerrgrrTF fix_scalectjd}tj||d|}|r[|rYd}t jt|5tj |||dddn #1swxYwYdSi}|r||d<|r||d<ttj|fi|d d idS Nrrrkrlrrr r rrrrrT) rZr[r\r6r1rrr r halflogisticrr r_rr7rr9r]r error_msgrs r0rz(TestHalfNorm.test_fit_MLE_comp_optimizers^i##$788~!!gYT/2"44  y %I|9=== M M"&&t')&LLL M M M M M M M M M M M M M M M F  #"DL  '&DN &end < rr5s r0rzTestHalfLogistic.test_sf9s0 *--a00#EBBBBBBr2q, ref))rMrg)rOrN)硏v?g .!>)g?grr_rzrs r0rzTestHalfLogistic.test_isfEs0 *..q113UCCCCCCr2cpd}d}tj|}t||ddS)Ng>@guVJrr)r6r>rrr_rerrs r0rzTestHalfLogistic.test_logcdfLs= $#**1--%000000r2cpd}d}tj|}t||ddS)Nrg+rr)r6r>rrr_rerrs r0rzTestHalfLogistic.test_logsfSs= $"((++s//////r2rr6rr7r8rTFr9ctjd}tj||d|}i}|r[|rYd}t jt|5tj |||dddn #1swxYwYdS|r||d<|r||d<ttj|fi|d d idSr;) rZr[r\r6r>rrr rrr) r_rr7rr9r]rrr@s r0rz,TestHalfLogistic.test_fit_MLE_comp_optimizerZs`i##$788!%%'36&88  y %I|9=== M M"&&t')&LLL M M M M M M M M M M M M M M M F  #"DL  '&DN &e&8$ < <$ < <6: < < < < < rr_r,s r0test_fit_bad_flocz"TestHalfLogistic.test_fit_bad_flocwsL g+cfttj|||ddSN绽|=rrr6 truncnormrEr_r.r/rs r0rlzTestTruncnorm.test_entropys1$ //155sGGGGGGr2))rrghiɮ9?)rrr)g0.+rr)}Ô%IrZ_2?cfttj|||ddSrrrs r0test_extreme_entropyz"TestTruncnorm.test_extreme_entropys1 //155sGGGGGGr2c tjgddddgdzd}tjtjdd dd d tjg}t ||dS) NrrrrH.?rrmrrOrrmrjrfO?l@r)r6rrrZrrrrs r0test_ppf_ticket1131z!TestTruncnorm.test_ppf_ticket1131n""#E#E#EsB()s1uA#778RVQ Az1bfMNN!$11111r2c tjgddddgdzd}tjtjdd dd d tjg}t ||dS) NrrrOrrrmrjrrrr)r6rrrZrrrrs r0test_isf_ticket1131z!TestTruncnorm.test_isf_ticket1131rr2cd\}}tj||ddd|j}t ||cxko|cxko|kncd\}}tj||ddd|j}t ||cxko|cxko|kncdS)N)irhrrrfr)rf r6rrr]r minrr_lowhighres r0test_gh_2477_small_valuesz'TestTruncnorm.test_gh_2477_small_valuess T O  T1abtx  P Paeegg........$..../// T O  T1abtx  P Paeegg........$..../////r2cd\}}tj||ddd|j}t ||cxko|cxko|knct|||gfd\}}tj||ddd|j}t ||cxko|cxko|kncd\}}tj||ddd|j}t ||cxko|cxko|kncd\}}tj||ddd|j}t ||cxko|cxko|kncdS) N)rgrdrrrfr)r)'i')i)r6rrr]r rrrHrs r0test_gh_2477_large_valuesz'TestTruncnorm.test_gh_2477_large_valuess T O  T1abtx  P Pquuww1111!%%''1111T111122CdA4G4GGG T O  T1abtx  P Paeegg........$..../// T O  T1abtx  P Paeegg........$....///" T O  T1abtx  P Paeegg........$..../////r2cddgddgfD]\}}tjtj ||tjg}||zdz }tj|||}tj|||}tj|||}tjgd}tjgd} tjgd} |d krtjgd } t||t|| t|| ttj | d | d z |d ztjgd} tj | ||} tj|tj |dz|g} t| | |d kr_ttj|||dttj|||dn^ttj|||dttj|||dtj|||}ttj || d z |dzd z dS)NrrrrrrrrrOrOrr)rd._MT @BKg?rr)rrrrrrmrrrrOgĖy @gdv*?g,mj%V?rg) rZrrr6rrvrrorrrr)r_rrxvalsxmidcdfssfspdfs expected_cdfs expected_sfs expected_pdfspvalsppfs expected_ppfsros r0test_gh_9403_nontail_valuesz)TestTruncnorm.test_gh_9403_nontail_values sa&2r(+ M MICHrvgsD"&9::EHc>D?&&uc488D/$$UC66C?&&uc488DH\\\22M8$8$8$899LH%A%A%ABBMQww ")E)E)E F F m 4 4 4 \ 2 2 2 m 4 4 4 }Q'7 a8H'H I I #c  + + +H]]]++E?&&uc488DHc273<< +A4%HIIM m 4 4 4Qww#EO$6$6tS$$G$G$6888#EO$7$7c4$H$H$68888$EO$7$7c4$H$H$6888#EO$6$6tS$$G$G$6888/%%dC66C s=+;'; < rgrr) rZrrr6rrvrrorrrrrT)r_rrrrrrrrrrrrrroxvals2s r0test_gh_9403_medium_tail_valuesz-TestTruncnorm.test_gh_9403_medium_tail_values-sr(S#J/, P, PICHrvgsD"&9::EHc>D?&&uc488D/$$UC66C?&&uc488DH\\\22M8$8$8$899LH%K%K%KLLMQww "*=*=*=!>!> m 4 4 4 \ 2 2 2 m 4 4 4 }Q'7 a8H'H I I #c  + + +H]]]++E?&&uc488DHc273<< +CT%JKKM m 4 4 4?&&tS$77D e , , ,Qww#EO$6$6tS$$G$G$6888#EO$7$7c4$H$H$9;;;;$EO$7$7c4$H$H$6888#EO$6$6tS$$G$G$9;;;/%%dC66C s=+;'; < K@casec|\}}}}}}tj||d\}} } } t|| | | g||||gddS)NrrFFgEG fg^K[X)rZrrrr6rrr)r_r.r/rerTs r0test_logcdf_gh17064z!TestTruncnorm.test_logcdf_gh17064s HrvgwRVGR8 9 9 HbfbfaRV4 5 5 H*** + ++++ 1--44Q77BBBQB//55qb998DDDDDr2cztjddd}d}t||dS)Nrrrgl).0S?)r6rrr)r_rrs r0test_moments_gh18634z"TestTruncnorm.test_moments_gh18634s@ob!$$++A.. S!!!!!r2N)rrrr`rrrrlrrrrrrrrrZr_truncnorm_stats_datarr%rrrrrrr8r2r0r}r}su555 [[BBBCCHH CCH  [[DDDEE H H EE H222 222 000000&!M!M!MF-P-P-P^,,,    1 1 1 = = = < < < BF       &!                  ;"F%BH%:;; [V%:;;DD<;D +++ 000 ///HHH E E E"""""r2r}ceZdZejdgddZejdgddZejddd gd Zejd d d gdZ ejd ddgdZ ejdddgdZ dS)TestGenLogistic x, expected))ig4`n)ig4 ncg)rgX =)rggh@ X)rg hr r?r^r_rBs r0rEzTestHypergeom.test_rvss""2r17"RRvdai  26$!)#4#44444x~~((((z)L"99999o!!"a$(!CC#s#####ob!R((,,QTX,FF#rz*****y~eatenorangespearsquantiles r0r@z1TestHypergeom.test_precision2..1sC***!!(GeOWeLL***r2)rgpR(g㘍R2gJޱp9g?Mf= G?rrgƠ>ri)g@rg@g@g@)rr g) 9g"1)rZrrr6rr) r_ fruits_eatenrrT quantilesr. expected2r r r s @@@r0test_precision2zTestHypergeom.test_precision2*sx = = =>>D ******(***8999::XAD99990// !!)Wu_guMM>>> iad;;;;;;r2c`tjddd}|}tjddg}tjt || }t||tjddd}|}t|ddS)Nrrrrgr) r6rrErZrrhrrr)r_hgrkrirjs r0rlzTestHypergeom.test_entropy=s _Q1 % % JJLLXtTl++ fU:z::;;; :&&& _Q1 % % JJLLQr2cd}d}d}d}tj||||}d}t||dd}d }d }d }tj||||}d }t||d dS)NrcA.Aj@gorrRr@Xrg_7 j$r:)r6rrrr_rbrrpr-resultrTs r0rzTestHypergeom.test_logsfIs    &&q!Q22FHa8888    &&q!Q22 FHb999999r2cDd}d}d}d}tj||||}d}t||dd}d }d }d }tj||||}d }t||d d}d }d}d}tj||||}d}t||d t jgd}d }d }d }tj||||}t jdd }t||d dS)Nrrrrg)\UrrRrxrr8rg*@Vr:}rgר)rxrxrx)r6rrrrZrfullrs r0rzTestHypergeom.test_logcdfasM    ''1a33FHa8888    ''1a33&FHb9999    ''1a33 FHb9999 H\\\ " "   ''1a3371122FHb999999r2cd}d}d}tj|||}||z |z}t||dS)NipiPi.)r6rrr)r_rrpr-hmrms r0test_mean_gh18511zTestHypergeom.test_mean_gh18511sO    _ ! !!Q * * UQYBr2cd}d}tjdd}d|z}tj|dz |||}tj|dksJtjtj|dksJdS)Nrfrrr:rrr)rZrr6rrrdiff)r_rpr-rpopulation_sizerqs r0test_sf_gh18506zTestHypergeom.test_sf_gh18506s   Ia  q& O  q1uoq! < <va!e}}vbgajj1n%%%%%%%r2N)rrrr`rErrrrrlrrr"rrrr&r8r2r0rrs555 9 9 9>>>FFFLLL<<<&   :::0,:,:,:\     [ & & & & &r2rc\eZdZdZejdgddZejdgddZdZ d Z d Z d Z ejd d dgdZ ejdgddZdS) TestLoggammacNtjd|_dS)NlLrYr^s r0r`zTestLoggamma.setup_methodrar2z x, c, cdf))rrmg;Y%?)rgRٲa6_<)gHrgi|e?)rg6l ?)i+rcg֬CCf9)irgֺl ctj||}t||dtj||}t||ddSr)r6loggammarvrr)r_rerrvrqys r0rzTestLoggamma.test_cdf_ppfsb N  q! $ $3U++++ N  sA & &15))))))r2zx, c, sf))rrgQOu3;)rgg\Z{0)r+rgeɐ?)ig{Gzd?gr0T?ctj||}t||dtj||}t||ddSr)r6r-rrr)r_rerrrKr.s r0rzTestLoggamma.test_sf_isfsb N  a # #2E**** N  r1 % %15))))))r2cjtjdd}t|dddS)N rmg@rr)r6r-rr)r_lps r0rzTestLoggamma.test_logpdfs6 ^ " "4 + +G%000000r2cvd}d}tj||}d}t||ddS)Nr@gI.rr)r6r-rr)r_rerrrs r0rzTestLoggamma.test_logcdfsC  &&q!,,%%000000r2cvd}d}tj||}d}t||ddS)Ng9 @g!{1+ҷrr)r6r-rr)r_rerrrs r0rzTestLoggamma.test_logsfsC  $$Q**#s//////r2ctjgddd}|D]?\}}}}}tj|d}t |||||gd@dS)N)rg"~jg46<@goŏrrOg h"lxg Q?gZd;333333@r g{/L@g??gгYҿgh|?5?rrmsvkrrrR)rZrreshaper6r-r)r_tablerrvarskewkurtcomputeds r0rzTestLoggamma.test_statss wr1~~  ). 1 1 $AtS$~++Av+>>H %hsD$0G./ 1 1 1 1 1 1 1r2rrcrctj|d|j}t j|sJtj|}tjt j ||kt|}| d}|j dcxkr |j ksnJdS)Nrrr)confidence_levelr)r6r-rr]rZisfinitermedian binomtest count_nonzeror proportion_cirr)r_rremedbtestcis r0rEzTestLoggamma.test_rvss N  qvDH  E E{1~~!!#####n##A&& 0S 9 93q66BB  % 8 8v%%%%bg%%%%%%%%r2r"))r(g3H໱k3@)rr)rg8,[H^} )rg90$)rgtum\cdttj||ddSr)rr6r-rEr$s r0rlzTestLoggamma.test_entropy s/ ..q113UCCCCCCr2N)rrrr`rrrrrrrrrrErlr8r2r0r(r(sg555 [[EEEFF**FF* [ZBBBCC ** CC * 111111000 1 1 1 [S3,// & &0/ & [X<<<== D D == D D Dr2r(c^eZdZgdZejdedZdS) TestJohnsonsu))r2rrg?r()rrrgH';vIh%,=)rrrg?x7rNrc|\}}}}}ttj||||dttj|||||dSNrNr)rr6 johnsonsurrr_rrer.r/rtols r0rzTestJohnsonsu.test_sf_isf# j1aS**1a33ReDDDD++B155qsCCCCCCr2Nrrrcasesrrrrr8r2r0rMrM sX ; ; ;E [VU++DD,+DDDr2rMc^eZdZgdZejdedZdS) TestJohnsonb))rrrrr()rrrg0jA:rN)rrrgQbF5rNrc|\}}}}}ttj||||dttj|||||dS)NrNrr)rr6r%rrrRs r0rzTestJohnsonb.test_sf_isf9 rTr2NrUr8r2r0rXrX* sX = = =E [VU++DD,+DDDr2rXceZdZdZdZdZdZdZdZe j ddd gd Z d Z e j d d dgdZdZdS) TestLogisticcNtjd|_dS)Nl}$NrYr^s r0r`zTestLogistic.setup_methodA rar2ctjdd}tj|}tj|}t ||dSNrr)rZrTr6logisticrvrrr_rer.rs r0rzTestLogistic.test_cdf_ppfE sS KR  N  q ! ! ^   " "2r2ctjdd}tj|}tj|}t ||dSr^)rZrTr6r_rrrr`s r0rzTestLogistic.test_sf_isfK sS KR  N  a  ^   " "2r2cd}d}ttjd|z |ttj||dS)Ng.funcm sDAqD AqA~..RVTAXN33356689A>B$(a&$(a0014&$(a00146788:;>>$(#&(TAX.// &end;;;;;r2N)rrrr`rrrdrfrirrrrvrzrrr8r2r0r[r[@ s555  888444)))  [03J3K3MNNCCNNC.FFF  [\D%=99 1 1:9 1<<<<r r?r^r_rBs r0rEzTestLogser.test_rvs s|7JJvdai     x~~((((z)L"99999lt$(;;#s#####l4  $$QTX$>>#rz*****y~gU5rr)g0gu8?g+?g㳒?g,nq?gYnr)r6rrrZtestingr)r_rqrbrrs r0rzTestLogser.test_sf sUTFXJ '   AAA@@@8889 looa## ""3&"99999r2N)rrrr`rErrrr8r2r0rr s_444 9 9 9 $ $ $((( : : : : :r2rc eZdZejddZejdej ej gejdgdejdgdejd d d gd d gfd Z ejd ej dfej dfgdZ dS)TestGumbel_r_lfunctionscopec@tjdSNrTrZr[r\r^s r0r]zTestGumbel_r_l.rng y$$T***r2r?rrrrrrsrcrrzfix_loc, fix_scaleTFc|d|||}t}|r|dz|d<|r|dz|d<t||fi|dS)Nrgrkrmrr)rrr) r_r?rrrsrr9r]rrs r0rzz&TestGumbel_r_l.test_fit_comp_optimizer s|xxSgY%(**vv  '"Q;DL  +&]DN &dD99D99999r2z dist, sgnrrc|tjgdz}||\}}t||dzt|dddS)N)rrrrrrrgW@g@g3qtw>rqr)rZrrr)r_r?rzrkrls r0rvzTestGumbel_r_l.test_fit sf :::;; ;XXa[[ U S!334445DAAAAAAr2N) rrrrfixturer]rrr6gumbel_rgumbel_lrzrvr8r2r0rr s=V^*%%%++&%+ [Venen%EFF [Y 33 [[***55 [1#UmeT];==::==6543GF :  [[ENA+>,1NB+?+ABBBBBBBBBr2rc eZdZdZdZejdejdddgejdddgejd dd gd Z ejdd dgejdddgejd dd gejd de ddgdDe j ddZ e j ddZdZdZdS) TestParetoc tj5tjdttjdd\}}}}t |tjt |tjt |tj t |tj tjdd\}}}}t |tjt |tjt |tj t |tj tjdd\}}}}t |dt |tjt |tj t |tj tjdd\}}}}t |dt |tjt |tj t |tj tjd d\}}}}t|d t|d t |tj t |tj tjdd\}}}}t|dt|d t |tj t |tj tjd d\}}}}t|dt|dt|dtj dzt |tj tjdd\}}}}t|dt|dt|dtj dzt |tj tjdd\}}}}t|dt|dt|dtj dzt|dddddS#1swxYwYdS)NrnrrrrOrrrr~g?grq@rr7gffffff?gK~?g2@g۶m۶m?rUUUUUU?gqq?rr5g%I$I?gQ?gUUUUUU@grq?g88Nb@) rrrsrtrur6paretorrZrrrrr_rrrKrbs r0rzTestPareto.test_stats sk $ & &7 N7 N  !'> : : :++C+@@JAq!Q BF # # # BF # # # BF # # # BF # # #++C+@@JAq!Q BF # # # BF # # # BF # # # BF # # #++C+@@JAq!Q C BF # # # BF # # # BF # # #++C+@@JAq!Q C BF # # # BF # # # BF # # #++C+@@JAq!Q Ay ) ) ) A2 3 3 3 BF # # # BF # # #++C+@@JAq!Q As # # # At $ $ $ BF # # # BF # # #++C+@@JAq!Q Ay ) ) ) A2 3 3 3 A 277+;+;; < < < BF # # #++C+@@JAq!Q Ay ) ) ) Az * * * A027;3G3GG H H H BF # # #++C+@@JAq!Q Ay ) ) ) A2 3 3 3 A RWW-=-== > > > AL M M Mo7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 N7 NsR8SS Scd}d}d}tj||d|}||z |z}t||dS)NeArmrrrj)r6rrr)r_rer/rlrqrTs r0rzTestPareto.test_sf4 sO   LOOAqauO 5 5!Ga<8$$$$$r2z2ignore:invalid value encountered in double_scalarsrrrmrrr7rc jtjd}tjd||||}tj|ddd}tj|ddd}tj|ddd}||cxkr |cxkrdksnJtjd|||d z|}tj|d \} } } t| d z||d z } | j d} t| | tj tj | | z z t| d dS) NrTrgrr/rlrkrrp= ף?)rr)rfix_b)rfbrmr) rZr[r\r6rrrrrr=rhr)r_rrr7r]rshape_mle_analytical1shape_mle_analytical2shape_mle_analytical3 shape_mle_a loc_mle_a scale_mle_a data_shiftndatas r0rvzTestPareto.test_fit< s i##D))|SIY$+# ??!& 0 0A$ 0 G G J % 0 0AT 0 J J1 M % 0 0A$ 0 G G J%)>....%....)-......|SIY%,q[ EE.3l.>.>t!.>.L.L+ Y [1_dhhjj111AX  #[RVBF:jnn6F6F+F$G$GHHH J J JY"""""r2rcfix_shape, fix_loc, fix_scalecg|]}d|v| SFr8r>rqs r0r@zTestPareto.] (---A!&! !+r2TFrrepeatignoreinvalidctjd}tjd||||}i} |r|| d<|r|| d<|r|| d<t tj|fi| dS)NrTrgrrrr)rZr[r\r6rrr r_rrr7rrr9r]rrs r0rz&TestPareto.test_fit_MLE_comp_optimizerY si##D))|SIY$+# ??  #"DJ  #"DL  '&DN%elDAADAAAAAr2c d\}}}tj|||dtjd}t tj|dS)N)rrrrgið&r)r6rrrZr[r\r)r_r=locationrlrs r0test_fit_known_bad_seedz"TestPareto.test_fit_known_bad_seedp sa ")x|xS-/Y-B-B7-K-K MM%elD99999r2cttjtttjjgddtttjjgddddS)Nr rmr)rrmrrrr=)rr6rr[r rr^s r0test_fit_warningszTestPareto.test_fit_warningsz sgEL)))lEL$4iiiaHHHHlEL$4iiia      r2ctjd}tjddd|}t |dtj|}dS)NrTi~rrg)rkr/rrr)rZr[r\r6rrr r)r_r]rrs r0test_negative_datazTestPareto.test_negative_data s`i##D))|DACcJJ$""" L  T " "r2N)rrrrrrrfilterwarningsrrvr%rZerrstaterrrrr8r2r0rr s:N:N:Nx%%% [!122 [[1a&11 [YA// [[1a&11##210/2122 #0 [[2q'22 [YA// [[1a&11 [<--$q)I)I)I---..R["""BB#"..210/32B R["""::#":   #####r2rc eZdZdZdZdZdZdZdZdZ dZ d Z e j d d gd fd dddejdz ejgfddddejdzdgfdgdfgdZdZdS) TestGenparetocrdD]i}tj|}tj|\}}t |dt tj|jtjd}tj|\}}t||gddgdS)NrOrrr) rZrr6 genpareto _get_supportrr isposinfr)r_rr.r/s r0test_abzTestGenpareto.test_ab s $ $A 1 A?//22DAq B    BKNN # # # # JsOO++A..1AS *****r2ctjd}tjddd}t ||tj|t ||tj|t ||tj|tjddd}t | |tj |dS)Nrrrrr6rOrf) r6rrZrTrrorbrvrrr_rvrerzs r0test_c0zTestGenpareto.test_c0 s_r " " " K3 # #q 5;??1#5#5666q 5;??1#5#5666a%+.."3"3444 KB # #q 5;??1#5#566666r2ctjd}tjddd}t ||tj|t ||tj|t ||tj|tjddd}t | |tj |t | d ddS) Nrrrrr6rrOrfr) r6rrZrTrrouniformrvrrrrs r0test_cm1zTestGenpareto.test_cm1 s _s # # # K3 # #q 5=#4#4Q#7#7888q 5=#4#4Q#7#7888a%-"2"21"5"5666 KB # #q 5=#4#4Q#7#7888  ! a(((((r2ctjd}t|tj|tjgddgtt j| tjtjd}t|tj|tjgddgtt j| tjtjd}t|tj|tjgddgtt j| tjdS)NrcrrrOr) r6rrrorZrrvr isneginfrr_rs r0 test_x_infzTestGenpareto.test_x_inf sC _s # # #82r(CCC BIIbf--../// _r " " "82r(CCC BIIbf--../// _s # # #82r(CCC BIIbf--../////r2ctjddd}dD]}tj||}dD]7}tj|||z}t ||d8tj||}dD]7}tj|||z}t ||d8dS) Nrrfr6rrrg+rr)rr)rZrTr6rrorrv)r_rerpdf0dcpdfccdf0cdfcs r0test_c_continuityzTestGenpareto.test_c_continuity s K2r " " 8 8A?&&q!,,D% 8 8**1a"f55d77777?&&q!,,D$ 8 8**1a"f55d77777 8 8 8r2c ttjtjdddtjddddd tjdddz f}d D]\}tj||}d D]7}tj|||z}t||d 8]dS Nrrrcbaserr6FendpointrO)rrrr)rZrIrrTr6rrr)r_rzrppf0rppfcs r0test_c_continuity_ppfz#TestGenpareto.test_c_continuity_ppf E"+eT444+dArE:::r{5$S9999: ; 8 8A?&&q!,,D% 8 8**1a"f55d77777 8 8 8r2c ttjtjdddtjddddd tjdddz f}d D]\}tj||}d D]7}tj|||z}t||d 8]dSr)rZrIrrTr6rrr)r_rzrisf0risfcs r0test_c_continuity_isfz#TestGenpareto.test_c_continuity_isf rr2c \tjtjdddtjddddd tjdddz f}d D]P}t t jt j||||d QdS) Nrrrcrrr6FrrO)r(gC]r2rgV瞯Ҽrr) rZrIrrTrr6rrvr)r_rzrs r0test_cdf_ppf_roundtripz$TestGenpareto.test_cdf_ppf_roundtrip s E"+eT444+dArE:::r{5$S9999: ;/ + +A EO//0C0CAq0I0I1MME + + + + + + +r2cjtjdddd}t|ddS)NrrrrgpEȜ)r6rrrrhs r0rzTestGenpareto.test_logsf s4$$T3155122222r2zc, expected_statsr)rrrmr/rgrgqq @rfrmgqq?g?g$I$ ?rq?rgll0@r)rUUUUUU?r333333cntj|d}t||dddS)Nrrrrra)r6rr)r_rexpected_statsrs r0rzTestGenpareto.test_stats s;&&q&&99UGGGGGGr2chtjd}t|dddS)Nr(gvǼ ?rr)r6rr=r)r_rs r0test_varzTestGenpareto.test_var s3 O   % %,5999999r2N)rrrrrrrrrrrrrrrrZrrrr r8r2r0rr sA + + + 7 7 7 ) ) ) 0 0 0 8 8 8888888+++333  [ \\\  T2gbgajj="&1 2 ]T7271::$5v> ? """ # %&& HH && H:::::r2rc>eZdZdZdZdZdZdZdZdZ dZ d S) TestPearson3cNtjd|_dS)NlTJrYr^s r0r`zTestPearson3.setup_method rar2c,tjdd|j}t j|dksJ|jjtdvsJtjd|j}t|tsJtjdd|j}t|tj sJ|jjtdvsJt|dksJdS)Nrcr7rAllFloatrrr) r6r)rr]rZr=rr>r r?rr_rrBs r0rEzTestPearson3.test_rvs s~!!#G$(!KKx~~((((z)J"77777n  48 <<#u%%%%%nS!!%%adh%??#rz*****y~:!666663xx1}}}}}}r2ctjdgd}t|t jgddtjdd}t|t jdgdtjgd d}t|t jgd ddS) NrmrrcrL)gtT?g+q?g?rqrrrcND}i?rrrrr)rgj?gdC?gs?g'M?)r6r)rorrZrrs r0rMzTestPearson3.test_pdf s~!!!___55bh'K'K'KLL! # # # #~!!"c**bh |444@@@@~!!"4"4"4c::bh(@(@(@AAGK M M M M M Mr2chtjdgd}t|t jgddtjdd}t|dgdtjgd d}t|gd ddS) Nrmr)grE?gTp]0?g~?rqrrrcgE&"J?r)giZ*J?gh+8w?gcK?g|r>neg_infx_evals r0r@z.. sG'''--17FCCAF'''r2)r6r)rvr)r_skewsrint_pdfsrrs @@r0test_negative_cdf_bug_11186z(TestPearson3.test_negative_cdf_bug_11186' su!  ~!!&%00''''' %'''h'''''r2c6tjdd}t|dt |t jsJtjdd}t|dt |t jsJdS)Nrrmrrq)r6r)rrr?rZnumber)r_rs r0test_return_array_bug_11746z(TestPearson3.test_return_array_bug_117462 s&&q!,,VQ&"),,,,,&&q(33VQ&"),,,,,,,r2cgd}d}tjtj|||}t ||t jdgdgg}t jdd}t tj||tj| | t tj||tj | | t tj||tj ||  dS)Nrrrrrrm) r6r)rrvrrZrrTrorr)r_rrrr>res r0test_ppf_bug_17050zTestPearson3.test_ppf_bug_17050= s?!  n  !3!3FE!B!BEJJV$$$x$#(( KA  **1d33**A2u55 7 7 7**1d33))1"te44 6 6 6**1d33++Au555 7 7 7 7 7r2cgd}gd}gd}ttj|||dttj|dtj|ddS)N)rcrrO皙)rPrrr )g7>g~׼=gp'+7g;rrr)rr6r)rr)r_r>rers r0rzTestPearson3.test_sfP s%$$ " " ">>>))!T22CeDDDD))!Q//q1A1ANNNNNNr2N) rrrr`rErMrWrrr rr8r2r0r r  s555   MMMKKK ( ( ( - - -777& O O O O Or2r c8eZdZdZdZdZdZdZdZdZ dS) TestKappa4cgd}d}dD]T}tj|||}tj|| }t ||UdS)N)rrcrLrrO) gffffffrr皙ɿr"rcrLrrOffffff?)r6kappa4rvrrr_rerkrbrC vals_comps r0test_cdf_genparetozTestKappa4.test_cdf_genpareto] sr   - -A<##Aq!,,D++Ar22I D) , , , ,  - -r2ctjddd}d}tjddd}tj|||}tj||}t ||dS)Nrrrfrrr)rZrTr6r(rv genextremerr)s r0test_cdf_genextremezTestKappa4.test_cdf_genextremeh st KAr " "  KAr " "|1a(($((A.. i(((((r2ctjddd}d}d}tj|||}tj|}t ||dS)NrrfrOr)rZrTr6r(rvrbrr)s r0test_cdf_exponzTestKappa4.test_cdf_exponq sa K2r " "  |1a((KOOA&& i(((((r2ctjddd}d}d}tj|||}tj|}t ||dS)Nrrrfr)rZrTr6r(rvrrr)s r0test_cdf_gumbel_rzTestKappa4.test_cdf_gumbel_rz sc KAr " "  |1a((N&&q)) i(((((r2ctjddd}d}d}tj|||}tj|}t ||dS)Nrrrfrr)rZrTr6r(rvr_rr)s r0test_cdf_logisticzTestKappa4.test_cdf_logistic sc KAr " "  |1a((N&&q)) i(((((r2ctjddd}d}d}tj|||}tj|}t ||dS)NrrrfrO)rZrTr6r(rvrrr)s r0test_cdf_uniformzTestKappa4.test_cdf_uniform sc KAr " "  |1a((M%%a(( i(((((r2c0tjdddSrm)r6r(r^s r0test_integers_ctorzTestKappa4.test_integers_ctor s  Qr2N) rrrr+r.r0r2r4r6r8r8r2r0r$r$\ s} - - -)))))))))))))))r2r$c,eZdZdZdZdZdZdZdS) TestPoissoncNtjd|_dS)Nl, rYr^s r0r`zTestPoisson.setup_method rar2ctjd}tjgd|}d|dz |dzdz g}t ||dS)Nrmrrrmrr)rZrr6rrKr)r_ln2rCrTs r0test_pmf_basiczTestPoisson.test_pmf_basic sXfQii}  C00QQq)h'''''r2ctjgdd}gd}t||tjdd}t |ddS)Nr=r)rrrffffff?rr)r6rrKrintervalr)r_rCrTrCs r0test_mu0zTestPoisson.test_mu0 sc}  A..994***=))$22Xv&&&&&r2c6tjdd|j}t j|dksJt j|dksJ|jjtdvsJtjd|j}t|tsJtjdd|j}t|tj sJ|jjtdvsJdS)Nrr7rrr9rr) r6rrr]rZrr=rr>r r?r^r_rBs r0rEzTestPoisson.test_rvs s}  7 JJvdai     x~~((((z)L"99999m$(;;#s#####mC  $$QTX$>>#rz*****y~>#q#9#9!9!$QrT3!455HknnQ**G GX . . . . / /r2c tjddddd}gd}|D]]}|tj|z }tj||}tj|}t|d^dS)Nrrmrr)r8rgrNirrr()rZrTrr6rMrvr$r )r_rens_xxnprobsdiffss r0test_cdf_sqrtnzTestKSTwo.test_cdf_sqrtn s K1b ! !!"" % , , , + +Bbgbkk!BKOOB++EGENNE eT * * * *  + +r2ctjddd}dD]U}tj||}tj||}t |d|z VdSNrrrrJ)rZrTr6rMrvrr)r_rerprrs r0rzTestKSTwo.test_cdf_sf so K1b ! !) = =A{q!,,HknnQ**G %hG < < < < = =r2ctjddd}dD]l}|tj|z }tj||}tj||}t|d|z mdSrZ)rZrTrr6rMrvrr)r_rerprUrrs r0test_cdf_sf_sqrtnzTestKSTwo.test_cdf_sf_sqrtn s K1b ! !) = =ARWQZZB{r1--HknnR++G %hG < < < <  = =r2c0tjddd}dD]|}||d|z k}tj||}d|k|dkz}tj||}t ||||d}dS) NrrrrJrrrr)rZrTr6rMrvrrr_rerprUrcondrCs r0test_ppf_of_cdfzTestKSTwo.test_ppf_of_cdf s K1b ! !) = =A1s1u9B{r1--HLX_5D;??8Q//D DJ4t < < < < <  = =r2c0tjddd}dD]|}||d|z k}tj||}d|k|dkz}tj||}t ||||d}dS) NrrrrJrrOrr)rZrTr6rMrrr)r_rerprUvals_isfr_rCs r0test_isf_of_sfzTestKSTwo.test_isf_of_sf s K1b ! !) = =A1s1u9B{r1--HLX^4D;>>(A..D DJ4t < < < < <  = =r2cVtjddd}dD]}|tj|z |d|z k}tj||}d|k|dkz}tj||}t||||dS)NrrrrJrrO)rZrTrr6rMrvrrr^s r0test_ppf_of_cdf_sqrtnzTestKSTwo.test_ppf_of_cdf_sqrtn s K1b ! !) 2 2Abgajj.!c!e),B{r1--HLX^4D;??8Q//D DJ4 1 1 1 1  2 2r2cVtjddd}dD]}|tj|z |d|z k}tj||}d|k|dkz}tj||}t||||dS)NrrrrJrrA)rZrTrr6rMrrr)r_rerprUrr_rCs r0test_isf_of_sf_sqrtnzTestKSTwo.test_isf_of_sf_sqrtn" s K1b ! !) 2 2Abgajj.!c!e),BknnR++GKGdN3D;??7A..D DJ4 1 1 1 1  2 2r2ctjddddd}dD]R}tj||}tj||}t ||SdSrZ)rZrTr6rMrrvr)r_rVrprUrs r0rzTestKSTwo.test_ppf, st Aq"%%abb)) - -A**B{r1--H He , , , , - -r2c gd}tjgd}tjgdgdgdgdgdgdg}t|D]y\}}|tjd ztjtjd z |z z}t j||}t|||d zdS) N)rfr8rgrNrr)rggUUUUUU?rrrmr)gRT>gr ?gK5 ?gn "5?gU ?gk?)g&6#>gb E>gI5?g\ ?g;?g%1?)g6>gL>g<?g䓀^?gO|6$?g qO?)g}+:>gwQ9>gH{?g]qv (?g)~/v?gmJ?)gV27J=gGk(>gWX?g Y?g{0`?gZ H?)g_R=g4>g̪?gT_@?g<e?g2?rmr6r) rZr enumeraterrrpr6rMrvr)r_rSratiosrTidxrprers r0test_simard_lecuyer_table1z$TestKSTwo.test_simard_lecuyer_table13 s+ * *888998 - - - - - - - - - - - - - - - - - -     mm @ @FC"RWRU1WQY%7%77A{q!,,H Hhsm$ ? ? ? ? ? @ @r2N)rrrrWrrXrr\r`rcrergrrmr8r2r0rHrH s000( / / / + + +============222222---@@@@@r2rHc eZdZdZdZdZdS)TestZipfcNtjd|_dS)Nlp\#rYr^s r0r`zTestZipf.setup_methodV rar2c6tjdd|j}t j|dksJt j|dksJ|jjtdvsJtjd|j}t|tsJtjdd|j}t|tj sJ|jjtdvsJdS)Nrr7rrr9rr) r6zipfrr]rZrr=rr>r r?r^r_rBs r0rEzTestZipf.test_rvsY sz~~cdh~GGvdai     x~~((((z)L"99999jnnStxn88#s#####joo!!!$(!;;#rz*****y~r r?r^r_rBs r0rEzTestDLaplace.test_rvsr s~!!#G$(!KKx~~((((z)L"99999n  48 <<#s#####nS!!%%adh%??#rz*****y~@g @gGz@cRtjd}tjd||||}t ttjtjj}||}tj|}t||||dd}tj|dd}t||ttj||tj ||dz z dksJttj||dz ttj|dttj|||j dd dS) NrTrgrrrm)rrrrr=) rZr[rr6r#rrrrrrrr]) r_rrr7r]r super_fit super_fitted invgauss_fit __class__s r0rz(TestInvgauss.test_fit_MLE_comp_optimizer si##D))~!!sv&-YS"RR$u~..??C  y ~))$// \<000!yA1555 ~))$QA)>> \<000 &endIIIIvtw{+q011111%end1MMMM &endCCCC &end-1X__Q-?-?-B D D D D D Dr2cttjtjt 5tjgddddddS#1swxYwYdSrC)rr6r#rr r rr^s r0test_fit_raise_errorsz"TestInvgauss.test_fit_raise_errors sEN+++ ]< ( ( 2 2 N  yyyq  1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2s$A$$A(+A(cgd}gd}tjd|}t||tjdd}t |dtjdd}t |d tjd d }t |d tjd d }t |ddS)N)g4wT;?gjdV&}?g{i\0>gDV_h?gqac X?)rrrrr皙?rZr?gfFngr^:g9̗?rgx_;:g!?gٷ ??)r6r#rvrrr)r_rZrTrP cdf_actual sf_actuals r0rzTestInvgauss.test_cdf_sf s..."??##CB#//Xv&&&^''$'77  $9:::N%%cd%33  #7888 ##GV44 3444##Hf55 122222r2ctjdd}t|dtjdd}t|dtjdd}t|dtjdd}t|d dS) NrrrgiJ.rgr^ߺrgpgFgpQ^L)r6r#rrr)r_rrs r0rzTestInvgauss.test_logcdf_logsf s&&v$&77 1222&&sD11 5666$$Ut$445666$$S$//011111r2zmu, ref))rg,9)rg% !)rg40)rgK' @)rg`p @cdttj||ddSrP)rr6r#rE)r_rZrs r0rlzTestInvgauss.test_entropy s/ ..r22CeDDDDDDr2ctjtj}tjdd}d\}}t ||||t ||||t ||||t | || |t | || |t | || |t | || |t | || |dS)Nrrr)rOr)r6r#rZrr"rrrorrvrrrr)r_r?dist0rerqs r0test_mu_inf_gh13666z TestInvgauss.test_mu_inf_gh13666! s[~(((s#...1 A Q888 UYYq\\222 A Q888 UYYq\\222 1 u{{1~~666 EHHQKK000 UYYq\\222 UYYq\\22222r2)rrrr`rrrrvrrrrrlr __classcell__rs@r0rr sF555 [7')>?AA>>AA>: [7')>?AA D D D DAA DD222 !3!3!3F222. [Y)D)D)DEE EE EE E3333333r2rc`eZdZejdgddZdZdS) TestLandauname)rorvrrrc|dvrtjdddf}ntjdddf}ttj|}ttj|}||}|g|ddR}t ||d dS) N>rrrcrrrrfrrr)rZrTr.r6landau levy_stabler)r_rre landau_method levy_methodrrs r0test_landau_levy_agreementz%TestLandau.test_landau_levy_agreement3 s > ! ! Ca(()AA B2&&'A d33 e/66 mQk#1#a####Su------r2cttjdtjfdzttjdtjdS)Nrrrr)rr6rrZrrr^s r0r%zTestLandau.test_momentsC sUU\'''77"&1EEEU\((++RV44444r2N)rrrrrrrr%r8r2r0rr2 sW [V%G%G%GHH . .IH .55555r2rceZdZejdgdejdgddZejdgdfdZd Zd Z d Z d Z d Z xZ S) TestLaplacer)rrrrmr7)rrmrrfctjd}tjd|||}tj|}tjtj||z t|z }tj |\}}t||ddt||ddtj ||\}}t||ddtj ||\}}t|||dz}tjtj||z t|z }tj ||\}}t||tj ||\}}t||tttjj ||| tttjj tjgtttjj tjgdS) NrTrgrkrrirrxrmr=)rZr[rr6rrrDrhrrrrrr[rrrr) r_rr7r]rloc_mlerrkrls r0rvzTestLaplace.test_fitJ s i##D))}  cwi.1!33)D//F26$.1122SYY> ]&&t,, UW5u====yu5AAAA]&&t'&:: Uyu5AAAA]&&tI&>> UW%%%kF26$*--..T: ]&&t#&66 UY&&&]&&tI&>> UWc""" lEM$5t'& ( ( ( ( j%-"3bfX>>>j%-"3bfX>>>>>r2rvs_loc,rvs_scale))rrfrfr)rrLctjd}tjd|||}d}tj|\}}tttjtj|\}} ||||} ||| |} | | kstj | | ddsJdSdS)NrTrrkc dt| tjd|zzd|z tjtj||z zz zS)Nrrmr)rrZrrhr)rkrlrs r0llz3TestLaplace.test_fit_MLE_comp_optimizer..ll sSCII%8E'26"&*<*<#=#==>? ?r2rri) rZr[rr6rrrrrr) r_rr7r]rrrkrlloc_opt scale_optll_mlell_optrs r0rz'TestLaplace.test_fit_MLE_comp_optimizery si##D))}  dy.1!33 ? ? ? ]&&t,, U"4 #6#6#(=2225#d)) C%%GY--"+ff38u#F#F#Fr2ctjgd}tj|d\}}t |dddtj|d\}}t |ddddS)N)rOrOrrPr rr/rrrrirx)rZrr6rrr)r_rrkrls r0test_fit_simple_non_random_dataz+TestLaplace.test_fit_simple_non_random_data sx77788]&&t!&44 Uqu59999]&&tA&66 UQU777777r2cFd}tj| }|dksJtj|}|dksJtj|}|dksJtj| }|dksJdS)NrrrO)r6rrvr)r_rep0p1s r0test_sf_cdf_extremesz TestLaplace.test_sf_cdf_extremes s  ]  r " "Syyyy]  q ! !Syyyy ]  a Syyyy]  qb ! !Syyyyyyr2cd}tj|}t|t j| dz ddS)NrNrmrr)r6rrrrZr)r_rerqs r0rzTestLaplace.test_sf sE  M  Q  261"::a>>6"+e&6&<&:: [WtUm44 [[4-88FF9854;:32FFFr2rc eZdZejdddgdZejddZejdgd ejd gd ejd gd ejdde ddgdDdZ dZ dZ dZ dS) TestPowerlawzx, a, sf)rgrg?)g?gp?gSQ>cfttj|||ddSr)rr6powerlawr)r_rer.rs r0rzTestPowerlaw.test_sf s1 ))!Q//%@@@@@@r2rrc@tjdSrrr^s r0r]zTestPowerlaw.rngrr2r)rcrrrrmrrr7rrcg|]}d|v| Srr8rs r0r@zTestPowerlaw. rr2TFrrc,tjd||||}t} |r|| d<|r5t j|tj | d<|r|| d<ttj|fi| ddidS)Nr)rr.rkrlrrrrrT) r6rrrrZ nextafterrrrrs r0rz(TestPowerlaw.test_fit_MLE_comp_optimizer s~!!siW(1"EEvv  #"DJ  =< RVG<> [Y 33 [[***55 [<--$q)I)I)I---..<<..6543?> <$ D D D444666666r2rc>eZdZejdgddZejdddgdZejdgdd Zejdgd d Z d S) TestPowerLogNormz x, c, s, ref))rgrrga!R()rrrg;?)rrrgE?)MDrrg=chttj||||ddSr)rr6r*rr_rerrKrs r0rzTestPowerLogNorm.test_sfds4 *--aA66%HHHHHHr2z q, c, s, ref)g?rrr)gR4 -rrrchttj||||ddS)Ng|=r)rr6r*r)r_rzrrKrs r0rzTestPowerLogNorm.test_isfns4 *..q!Q775IIIIIIr2))rrrg?)rqrrgv6)rqrNrg+ 94|7)ryrNrg?chttj||||ddS)Ngt =r)rr6r*rvrs r0rWzTestPowerLogNorm.test_cdfts4 *..q!Q775IIIIIIr2))rrrgS^Ռe 9)@xDrrg 0g;)g\)c=Hrrg7H7chttj||||ddS)NgAfc=r)rr6r*rors r0rMzTestPowerLogNorm.test_pdfs4 *..q!Q775IIIIIIr2N) rrrrrrrrrWrMr8r2r0rrSs<" [^EEEFF II FF I  [^ACEFFJJFFJ [^AAABB JJ BB J [^GGGHHJJ HHJJJr2rceZdZejdgddZejdgddZejdgddZd S) TestPowerNormr'))rrg|<)rrmge()rgrg%!@6)rNrgT;-cfttj|||ddSr)rr6 powernormrr+s r0rzTestPowerNorm.test_sfs1 **1a00#EBBBBBBr2r))r6rgĿ)rrgg!X)rrg缂U)rArgͫ1@)r3rmgD@)Jz5rgU!zYr@cfttj|||ddSNr|r)rr6rrrs r0rzTestPowerNorm.test_isfs1 ++Aq113UCCCCCCr2))irg.u T9)rmr?)rrgsK-)rrgk8>)rrg^u1-cfttj|||ddSrP)rr6rrvr+s r0rWzTestPowerNorm.test_cdfs1 ++Aq113UCCCCCCr2N) rrrrrrrrrWr8r2r0rrs [[CCCDD CC DD C [[===>>DD>>D [[BBBCC DD CC DDDr2rcxeZdZdZdZdZdZdZej dddgd Z d S) TestInvGammactj5tjdttjdd}gd}t ||gd}tj|d}gdtjdd gtj d d gtj tj d gf}t||D]\}}t|| ddddS#1swxYwYdS) Nrng(\O3@rrw)g~?gCX&?g*7gS?gBqFq@)r@gffffff@)rg Ey?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@) rrrsrtrur6r"rrZrrrr)r_rrTr.rer.s r0test_invgamma_inf_gh_1866z&TestInvGamma.test_invgamma_inf_gh_1866sU $ & & * *  !'> : : :>''%'@@D%%%H D( + + +A>''!V'<_f_argsrs r0r@z(TestF.test_endpoints..4=== E1vrvbd#U###===r2cg|]\}}}| Sr8r8r>rr _correct_s r0r@z(TestF.test_endpoints..>>>!5UI9>>>r2)r6fror.r)r_rrr_correctanscorrects r0rzTestF.test_endpoints s&#&'#' ' ' Bx"&&&&&CC=====>>>>>!#w/////r2c^tjddd\}}}}ttj|ttj|ttj|ttj| dS)Nr@rr)r6rr rZrCrs r0test_f_momentszTestF.test_f_momentssW]]2sF];; 1a A A ABKNN"#####r2ctj5tjdttjdgdzgddddddS#1swxYwYdS)Nrnrr)rmrr/rrdfndfdr)rrrsrtrur6rr^s r0test_moments_warningszTestF.test_moments_warningss  $ & & H H  !'> : : : GMMrd1f,,,M G G G H H H H H H H H H H H H H H H H H HsAA$$A(+A(ctjdgdgg}tjddg}tj||d\}}}}||dz z gdz}t ||d|dzz||zdz z|z |dz dzz |dz z }t ||d|z|zdz tjd|dz zz|d z tj|||zdz zzz } t || d|d |zd z z||zdz z|dz |dz dzzzz} ||d z z|dz z||zdz z} | | z } t || dS) NrrrQrr"rmrrr/r)rZrr6rrr) r_r#r$rrrKrbrv2s2k2numk2denk2s r0test_stats_broadcastzTestF.test_stats_broadcast"shbT{##hBx  W]]sV]DD 1aS1Wo q 2 aZ39q= )C /37Q, >#' J2us{Q"'!S1W+"6"66a273c A #677792cQsURZ(C#IM:Qw37Q,./0sQw37+sSy1}= U]2r2N)rrrrr r%r-r8r2r0rr sS000$$$HHH r2rc eZdZdZdZdZejdddgdZ ejdgd ejd d d gd d gd d ggd gdgd d gd d ggd gd gggdZ ejd d d gd d gd d ggd gdgd d gd d ggd gd gggdZ dZ ejdgddZ dS) TestStudentTchttjddgddgdS)Nrr/g?g?)rr6rrvr^s r0test_rvgeneric_stdzTestStudentT.test_rvgeneric_std5s/!%'++q!f"5"5 J7OPPPPPr2cfttjddtjtjtjtjfttjdddtjtjtjfttjdddtjtjtjfttjddddtjtjfttjd d tjtjfttjd d dtjfttjd d dtjft tjd d dddS)Nrr)rr)\(?rrmgGz@g i@rrvgGz@rg ףp= @)rgq@rr)rr6rrZrrrr^s r0test_moments_tzTestStudentT.test_moments_t9sUW]]a]88VRVRVRV4 6 6 6UW]]dF];;"&"&"&1 3 3 3UW]]a]88"&"&"&1 3 3 3UW]]dF];;/2626: < < <UW]]a]668HIIIUW]]dD]99C=IIIUW]]a]66bf FFF t <<>U" $ $ $ $ $ $r2ctgd}gd}ttj||ddS)N)rrmrrg)g?@gTM]?ggY?U?rrrr6rrE)r_rrTs r0test_t_entropyzTestStudentT.test_t_entropyIsE __;;;++XEBBBBBBr2zv, ref)rgr6)rrcdttj||ddSrr7)r_rrs r0test_t_extreme_entropyz#TestStudentT.test_t_extreme_entropyPs- **Ce<<<<<r?rrfr@rrr)rrkrlrrkrlrrrArj)rZrrBr[r\rr=rr6rrrrrE)r_r<r]rr res_ex_inf res_ex_noinfrs r0test_t_inf_df_stats_entropyz(TestStudentT.test_t_inf_df_stats_entropyws Z $777 i##J// [[BZ%5[ 6 6:gmmrq6mBBZ%%!1f%EE w}}J;Qa,2%44 q ? ?A Q +Z] ; ; ; Q ,l1o > > > >goo!o44Z''AQ'77 w"j[/qJJ S_j111S*%|44444r2cgd}gd}gd}gd}ttj|||dttj|||ddS)N)rrrfr)rd~QJrr)gZ_2g 9g!ǟuIgdg)g73?rgմFhAW;gm0_?rr)rr6rrro)r_rer logpdf_refpdf_refs r0test_logpdf_pdfzTestStudentT.test_logpdf_pdfs OO # # #@@@ >>>q"--zFFFF Ar**G%@@@@@@r2 x, df, ref))gRr:guSaG)rr:r)R@r:gGn`?ctj||}t||dtj| |}t||ddSr)r6rrrr)r_rerrrrs r0rzTestStudentT.test_logcdf_logsfs` 2&&%0000 qb"%%s//////r2N)rrrr1r4r8rrrr:rJrOrTrr8r2r0r/r/4sQQQ$$$ CCC [X68:;; = =;; = [Z*<*<*<== [\QFQFQF-6YY ,B./VaV,<./S1#J,899CC 99== C  [\QFQFQF-6YY ,B./VaV,<./S1#J,89955 995& A A A [\CCCDD00 DD000r2r/cVeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd S)TestRvDiscretecNtjd|_dS)Ni}rYr^s r0r`zTestRvDiscrete.setup_methodrr2cgd}gd}d}tjd||f}|||j}t |t jsJt||D]>\}}tt||kt|z |z dksJ?||j}t j t|t j sJdS) N)rrrrmrr)rryrrryrrsample)rvaluesrrAr)r6rBrr]r?rZr_rrrhrrrinteger)r_states probabilitysamplesrrerKrqs r0rEzTestRvDiscrete.test_rvss$$$444   8V[4I J J J EEwTXE 6 6!RZ((((( ,, > >DAqs16{{5>>1A566===== EEtxE ( (}T!WWbj1111111r2cftjgd}tjgd|f}t t || }|}t||tjgdgdf}|}t|ddS)N)rgr8ryr=r])rOrrr) rZrr6rBrhrrErr)r_rrqrjrks r0rlzTestRvDiscrete.test_entropys***++  iii%7 8 8 8%u--... IIKK:&&&  iii%= > > > IIKKQr2cgd}gd}tj||f}ddgddgg}t||dd gd d ggd dS)NrrryrLrcrOrrrmrrLrryrr)r6rBrrK)r_xkpkrres r0rezTestRvDiscrete.test_pmfs YY __  r2h / / /"X!W q sc$*/ 1 1 1 1 1 1r2cgd}gd}tj||fgd}gd}t||dtfd|D|ddS) Nrrerc)rrOrrrrrr)rrrrrrrrrrc:g|]}|Sr8)rv)r>rrs r0r@z+TestRvDiscrete.test_cdf..s#777777r2)r6rBrrv)r_rfrgx_valuesrTrs @r0rWzTestRvDiscrete.test_cdfs YY __  r2h / / /555555x(((???? 7777h777 u . . . . . .r2cgd}gd}tj||fgd}gd}t||dtfd|D|ddS) Nrrerc)rcrrrrrO)rrrmrmrrrrc:g|]}|Sr8)r)r>rzrs r0r@z+TestRvDiscrete.test_ppf..s#555q555r2)r6rBrr)r_rfrgq_valuesrTrs @r0rzTestRvDiscrete.test_ppfs YY __  r2h / / /000%%%x(((???? 5555H555 u . . . . . .r2c gdgdf}tj|}t|||jdddz|jdddS)N)rrmrrr)rcrLryryrcrcrr(r)r6rBrrrvrf)r_rCrs r0test_cdf_ppf_nextz TestRvDiscrete.test_cdf_ppf_nexts|!:!:!:;  d + + +266"&&ss"4"4t";<<59 & & & & &r2cBtjdd}tjgdgdgdg}t j||f}t |tj|j |j zddS)NrQ)rr)rcrcrXrA)rcrcrArArcrr) rZrr;rr6rBrrrhrfrgr_rfrgrs r0test_multidimensionz"TestRvDiscrete.test_multidimensions Yr]] " "6 * * X---------/00 r2h / / / RVBEBEM%:%:GGGGGGr2cgd}ddg}tttjfit ||fgd}tttjfit ||fgd}gd}tttjfit ||fgd}gd}tttjfit ||fddg}ddg}tttjfit ||fdS)Nr rrc)r333333?gffffff濩rrmrrr)ryryryryr&r)r[rr6rBrr_rfrgs r0test_bad_inputzTestRvDiscrete.test_bad_inputs/ YY3Zj%"3MMtB87L7L7LMMM YYj%"3MMtB87L7L7LMMM YY   j%"3MMtB87L7L7LMMM __ ' ' 'j%"3MMtB87L7L7LMMMV3Zj%"3MMtB87L7L7LMMMMMr2ctjddtjdd}}t t t jfit||ftjddtjdd}}t t t jfit||ftjddtjdd}}tt j||f dddS) NrrmrmrmrgUUUUUU?rcr/rrmr) rZrr;rr[rr6rBrrrKrvs r0test_shape_rv_samplez#TestRvDiscrete.test_shape_rv_samples1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM1%%f--rwvs/C/CBU&r2h777;;A>>DDDDDr2cgd}gd}tj||f}t|t j|j|jzddS)N)rrmrr/rr)rcrLrLrLrLrcrcrr)r6rBrrrZrhrfrgrqs r0 test_expect1zTestRvDiscrete.test_expect1sd  + + +  r2h / / / RVBEBEM%:%:GGGGGGr2c gd}gd}tj||f}t||dt|t dt ||Ddt|dt dt ||DddS) N)/gi@gr@gy@g@@g@g@@g @rg0@g@gP@g@gp@g@g@g @g@rgh@g0@g@g@g@gP@g@g@g@rg8@g@gȩ@g@gX@g @g@g@gx@g@@g@gh@g̰@g0@g@g@g\@g@)/g-C6:?rgF%uk?g:vz?rrg.nr?g|гY?rrrg@6*?4U0*C?g@ +?gC6z?gnr?g ?gOjM?g n?g1w-!?g:pΈ?gףp= ?g_Le?rg^)p?g~jtx?gJ4q?gGzt?gJ4q?gMb@?g@Psׂ?g@^)ˀ?rrgN@s?g1w-!_?rgൄ|г?rgH}}?rg F%u?rrg^)ˀ?gv?rrcrrc3&K|] \}}||zV dSrzr8r>rws r0 z.TestRvDiscrete.test_expect2..Es*99daAE999999r2c |dzSNrmr8rs r0rLz-TestRvDiscrete.test_expect2..H AqDr2c3,K|]\}}|dz|zVdS)rmNr8rs r0rz.TestRvDiscrete.test_expect2..Is.<<AAqD1H<<<<<">"',"2"21"5"5 7 7 7!%"2"6"6qA"6">">"',"2"21"5"5 7 7 7!%"2"6"6qA"6">">"',"2"21"5"5 7 7 7 7 7r2ctjd}|ddzdz }|ddzdz }gd}gd}t t j|||t t j|||t t j |||dS)Nrrfrmrr) g&45?gQʶ?g-4[u?g a2?g Rn?gѦ}cي?) gN@Q?gPPz@ ?g?g; 7?glg?g!?%?gQҙ?gC"?go?g@Sg?) rZr[rrandrr6rrorvr)r_r]r.rerorvs r0test_skewcauchy_Rz TestSkewCauchy.test_skewcauchy_RVs&i##A&& HHRLL1 q  HHRLL2  !%%%$$$ (,,Q22C888(,,Q22C888(,,S!44a88888r2N)rrrrrr8r2r0rrLs2777 9 9 9 9 9r2rceZdZdZejdZejdgddZ dS) TestJFSkewTc*dx}}|dz}gd}gd}tj||}tj|}t||||t||||t||||t|d|ddS)Nrrm)rrrOr)rrcrgrrrOr)r6 jf_skew_trrrorvr)r_r.r/rrerzjfrs r0test_compare_tzTestJFSkewT.test_compare_tzs A U ! ! ! - - - _Q " " GBKKq 15588,,,q 15588,,,q 15588,,,((!''&//:::::r2ctjttjdz }tj|dS)aSample data points computed using the `ST5` distribution from the GAMLSS package in R. The pdf has been calculated for (a,b)=(2,3), (a,b)=(8,4), and (a,b)=(12,13) for x in `np.linspace(-10, 10, 41)`. N.B. the `ST5` distribution in R uses an alternative parameterization in terms of nu and tau, where: - nu = (a - b) / (a * b * (a + b)) ** 0.5 - tau = 2 / (a + b) z"data/jf_skew_t_gamlss_pdf_data.npyz x,pdf,a,bnames)rZloadr__file__parentrec fromarraysrys r0gamlss_pdf_datazTestJFSkewT.gamlss_pdf_datasDw NN !$H H  v  [ 999r2za,b)rz)rr)rQ c||d|k|d|kz}|d|d}}t|tj|||ddS)zCompare the pdf with a table of reference values. The table of reference values was produced using R, where the Jones and Faddy skew t distribution is available in the GAMLSS package as `ST5`. r.r/rerorrN)rr6rro)r_rr.r/rreros r0test_compare_with_gamlss_rz&TestJFSkewT.test_compare_with_gamlss_rsr  S !Q &?3+?1+D E cDK3U_Q2266q99FFFFFFr2N) rrrrrrrrrrr8r2r0rrys{;;;  ^ : :^ : [U$>$>$>?? G G@? G G Gr2rrmrg@rgףp= 1@r:gRZ@igS㥛Ԋ@rcrdg&@iQi'i0ybilHO1Zi3rirfirgikrNi1rii4i Ni(lEI.r'iceZdZdZdZdZdZdZdZdZ e j de d Zd Zd Zd Zd S) TestSkewNormc.td|_dSr)rr]r^s r0r`zTestSkewNorm.setup_methods%d++r2ctjddd}ttj|dtj|dSr)rZrTrr6skewnormrorrs r0 test_normalzTestSkewNorm.test_normalsY KAs # #!%."4"4Q!"4"<"<"'*.."3"3 5 5 5 5 5r2ctd}d}tjd||}t ||jtjd||}t ||jdS)NrT)rrrr)r.rrr)rr6rrrr=)r_r]r=res r0rEzTestSkewNorm.test_rvssv && N  E  D DUAG$$$ N  %c  B BUAG$$$$$r2ctd}tjdt ddd|}t j|t j|tj|tj |g}tjdddd}t||d tjd t ddd|}t j|t j|tj|tj |g}tjd ddd}t||d dS) NrTrrrrm)r.rrkrlrr)r.rkrlrrRr) rr6rrr^rZrr=r>kurtosisr)r_r]rrTr@s r0r%zTestSkewNorm.test_momentss5 && N  Sq,/  1 1GAJJq 5:a==%.:K:KL>''!!V'LL!(Ha@@@@ N  #c((,/  1 1GAJJq 5:a==%.:K:KL>''"!1f'MM!(Ha@@@@@@r2cgdgdgdgdgdgdgdg}|D]8\}}}tj||}t||d 9dS) N)rxrgEAV)rxrgV|@$a)rxrg0rY)rxrZk)rrr)rrļ)rmgcrr(r)r6rrr)r_ logpdfvalsrer. logpdfvalrs r0test_pdf_large_xzTestSkewNorm.test_pdf_large_xs 2 1 1 3 3 3 0 0 0 2 2 2 4 4 4 5 5 5 5 5 5  * 8 8OAq)>((A..D D)$ 7 7 7 7 7 8 8r2ctjgdd}t|t jddtjdd}t|dddS) N)rfrr6rrrrrr~rO)r6rrvrrZonesrs r0test_cdf_large_xzTestSkewNorm.test_cdf_large_xsn N  |||R 0 0271::E2222 N  r3 ' '3U++++++r2cgdgdgdgdgdg}|D]l\}}}tj||}t||dtj| | }t||dmdS)N)rrgzbLe9)rrmgn'/2;)rrg::)rrg|<)rhrr/r(r)r6rrvrr)r_cdfvalsrer.cdfvalrqs r0test_cdf_sf_small_valuesz%TestSkewNorm.test_cdf_sf_small_values s . - - + + + , , , . . . / / /  $ 2 2LAq&""1a((A AvD 1 1 1 1!!1"qb))A AvD 1 1 1 1 1  2 2r2z a, momentsct|dD]7\}}tj||}t ||d8dS)Nr)startrr)rjr6rrr)r_r.rorderrTrs r0test_noncentral_momentsz$TestSkewNorm.test_noncentral_momentss[(::: 7 7OE8.''q11C C 6 6 6 6 6 7 7r2c ttjd}d\}}}tj|||}|d|}tj|dd\}}} tj|dd\} } } || cxkrdksnJ|| ksJtj|ddd \} }}|dksJtj| ||}|d }tj|tj|f}t||tj d d|}tj|}tj tj |sJtj|d \}}}tj |sJtj|tj|}}t|||tjdtjz zzt||dzd dtjz z ztj|d\}}}tj| d\}}}t|||g| | |gtj|d \}} }!tj| d \}"}#}$t|"|#|$g| | |!gdS)Nl# ke)rr7rrgrrSrrgmmrrmsrrrrmmle)rZr[r\r6rrrrr>rrrrCisinfr=rrp)%r_r]r.rkrlr?ra2loc2scale2a3loc3scale3a4loc4scale4dist4rrra5loc5scale5rra6ploc6pscale6pa6mloc6mscale6ma7ploc7pscale7pa7mloc7mscale7ms% r0rvzTestSkewNorm.test_fit#si##$788$ 3~ae,,hhCch22!>--c4a-@@D& >--c4a-@@D&t    q      Rxxxx!>--c1Qt-LLD&{{{{r400kk$k''gcllEJsOO+S!!!|#>>n  &&vbk#&&'''''!>--d4-@@D&x||wt}}bfTll14&271RU7+;+;";;<<<619AI 6777$n00U0CCUG#n00#e0DDUGeW-ufg/FGGG#n00T0BBUG#n00#d0CCUGeW-ufg/FGGGGGr2cF tjgdddgzzdgz}tj|}tj||}tj|d}tj||}||dz ksJtjd d d d d } fd }tjtj|||}tj ||j ddS)N)rrr6rQrrT)superfitrly ND)rr)rhrf)r~rfr.rkrlc(t||S)N)r])r$)funrr]s r0 optimizerz0TestSkewNorm.test_fit_gh19332..optimizerhs)#v3??? ?r2)rrr) rZrr6rrrr[r\rrparams) r_rerr params_superrrr fit_resultr]s @r0test_fit_gh19332zTestSkewNorm.test_fit_gh19332Ss$ H***R1#X5; < <##A&&n!!&!,, ~))!d);; n!!,22S3Yi##$788y;GG @ @ @ @ @Yu~q&INNN  ""6:+<4"HHHHHr2cfttjdddddS)Nrrgi}#%?rr)rr6rrr^s r0rzTestSkewNorm.test_ppfns2 **4557HuUUUUUUr2N)rrrr`rrEr%rrrrrr_skewnorm_noncentral_momentsrrvrrr8r2r0rrs,,,555 %%% A A A888 ,,,222" [\+GHH77IH7 .H.H.H`III6VVVVVr2rc&eZdZdZdZdZdZdS) TestExponc`ttjdddSr)rr6rbror^s r0 test_zerozTestExpon.test_zerovs&U[__Q''+++++r2cttjddttjtjdddS)Nr3rx)rr6rbrvrrr^s r0 test_tailzTestExpon.test_tailysRU[__U++U333U[__U[^^B%7%788"=====r2ctjdddddtjg}ttt jj|dSNo_?46@yX5ͻ@j+?UX @)rZrrr[rr6rbrrs r0test_nan_raises_errorzTestExpon.test_nan_raises_error}< HfffffbfE F Fj%+/155555r2ctjdddddtjg}ttt jj|dSr)rZrrr[rr6rbrrs r0test_inf_raises_errorzTestExpon.test_inf_raises_errorrr2N)rrrrrrrr8r2r0rrusP,,,>>>666 66666r2rcleZdZdZdZdZejdddgdZ dS) TestNormctjdddddtjg}ttt jj|dSr)rZrrr[rr6rrrs r0rzTestNorm.test_nan_raises_error< HfffffbfE F Fj%*.!44444r2ctjdddddtjg}ttt jj|dSr)rZrrr[rr6rrrs r0rzTestNorm.test_inf_raises_errorrr2c\gd}tttjj|ddS)Nr shrimp)plate)r[rr6rrrs r0test_bad_keyword_argzTestNorm.test_bad_keyword_args, IIi(CCCCCCr2rkrrcd}tjd|zd|z|}t||dtjd|z d|z | }t||ddS)Ngg {F.:rrQrkrr)r6r _delta_cdfr)r_rkrTrms r0test_delta_cdfzTestNorm.test_delta_cdfs) %%bfbf#%>>xe4444 %%3i2c6%EExe444444r2N) rrrrrrrrrr r8r2r0rrsv555 555 DDD [UQF++ 5 5,+ 5 5 5r2rceZdZdZdZdZdS) TestUniformgh-10300ctjdddddtjg}ttt jj|dSr)rZrrr[rr6rrrs r0rz!TestUniform.test_nan_raises_error= HfffffbfE F Fj%-"3Q77777r2ctjdddddtjg}ttt jj|dSr)rZrrr[rr6rrrs r0rz!TestUniform.test_inf_raises_errorrr2N)rrr__doc__rrr8r2r0r r s7N888 88888r2r c DeZdZdZdZdZdZej dgddZ ej dgd gd gd gd gd gdZ ej dgdgdgdgdgdgdgdZ dS) TestExponNormcld}d\}}}d||zz }tj|||d}t|||||d\}}}d||zz }tj|||d}t|||||d\}}}d||zz }tj|||d}t|||||d\}}}d||zz }tj|||d}t|||||dS) Ncdd||zdzz z}d||zdzz |dzz}dd||zdzzdzz}|d|z z||zd||zz z||gS)NrOrrmrrS@rr8)lamsigrZopK2exp_skewexp_kurts r0get_momsz,TestExponNorm.test_moments..get_momsszc#g\))DC#I>)D4L8Ha39q.0B77H3JC#s3w- 78L Lr2)rrrrOrrL)rrmrc)rrr)rrr7)r6 exponnormr)r_rrZrrKstss r0r%zTestExponNorm.test_momentssp M M M C 39 o##A2S&#IIC#sB!7!7888! C 39 o##A2S&#IIC#sB!7!7888 C 39 o##A2S&#IIC#sB!7!7888" C 39 o##A2S&#IIC#sB!7!788888r2ctjdddddtjg}ttt jj|dddS Nrrrrrrrr=)rZrrr[rr6rrrs r0rz#TestExponNorm.test_nan_raises_errorD HfffffbfE F Fj%/"5qqKKKKKKr2ctjdddddtjg}ttt jj|dddSr")rZrrr[rr6rrrs r0rz#TestExponNorm.test_inf_raises_errorr#r2cvttjdddttjdddttjdddttjddddS)Ni|rrr)rr6rror^s r0test_extremes_xzTestExponNorm.test_extremes_xsEO//a88#>>>EO//a88#>>>EO//d;;SAAAEO//d;;SAAAAAr2zx, K, expected))rrg6 N-)rrg՜n+H?)rrgi?)rrgbJI-)rfrgI8?)rfrgQ3|-0?cfttj|||ddSr)rr6rro)r_rerrTs r0 test_std_pdfzTestExponNorm.test_std_pdfs1 ++Aq118%HHHHHHr2zx, K, scale, expected)rrrgVAҤ?)r{Gzt?rg'^ >)r~rrgr)r~rrgbr ;)rrrgVMe?ctj|||}|dkr |dksJdSt||ddS)Nrrrr)r6rrvrr_rerrlrTrqs r0test_cdf_small_KzTestExponNorm.test_cdf_small_KsU O  1E  2 2 s??888888 Axe 4 4 4 4 4 4r2)rfrrgh G}$;)rmr*rg ]fJ?)rr*rg31"g#;)rfr*rgf +-)rr*rr)rrrga9S?ctj|||}|dkr |dksJdSt||ddS)Nrr-a=r)r6rrrr,s r0test_sf_small_KzTestExponNorm.test_sf_small_KsU O  q!5  1 1 s??888888 Axe 4 4 4 4 4 4r2N) rrrr%rrr'rrrr)r-r0r8r2r0rrs9996LLL LLL BBB$ [-BBBCCIICCI [4>>>DDD444GGG??? ABB 55 BB 5& [4BBB@@@DDDFFF333@@@ BCC55CC555r2rceZdZdZdZejdgddZejdgddZ dS) TestGenExponcddlm}tjt jdddddd}t||ddddS) Nr)simpsonrfrrr)dxr)scipy.integrater4r6genexponrorZrr)r_r4rqs r0test_pdf_unity_areaz TestGenExpon.test_pdf_unity_area)sd++++++ N  ryB55sC E EGGA$///A66666r2ctjtjdddddd}tjd|k|dkzsJdS)Nrrfrrrr)r6r7rvrZrr)r_rvs r0test_cdf_boundszTestGenExpon.test_cdf_bounds/sTn  1b$!7!7c3GGvqCxC1H-.......r2z x, p, a, b, c))r:gM(++Aq113WEEEE(,,S!44aeDDDDDDr2N)rrrrr8r2r0r?r?Zs(EEEEEr2r?ceZdZdZdS) TestExponpowcttjdddttjtjdddddS)Nrrrrr)rr6exponpowrvrrr^s r0rzTestExponpow.test_tailgsiEN..ub995AAAEN..u~/@/@B/G/GLL     r2N)rrrrr8r2r0rCrCfs#r2rCc eZdZdZdZdZdS) TestSkellamctjdd}d\}}tjgd}ttj||||ddS)Nrhr:r)gYjP'?g$S?gQ`s2?gC/qF?gD<]Y?g/Xj?g86y?g]a¨?g:?g?gQ>?g?g:?g]a¨?g96?g0X?gA<]?gB/q?gQ`s?g$S?gYjP'?gX_?g+rx?gfSr?gJXx~?rR)rZrrrr6skellamrK)r_rbmu1mu2skpmfRs r0rezTestSkellam.test_pmfnsm Ic2  S - - - . . EM--ac::FBOOOOOOr2ctjdd}d\}}tjgd}ttj||||ddS)Nrhr:r)gƃQ?gS `X'?gVy)>?g: S?gei.f?gȼJ]x?g)?g{^'+i?gLIg>?gnZ ?g?rvͪ?gA?g0?g#J?gqSm . ?g~B?gd?gFBD?gQ9?gmF^?gcMy?gGJq?gC^c?g.){?gñݸ?rrR)rZrrrr6rIrv)r_rbrJrKskcdfRs r0rWzTestSkellam.test_cdfsm Ic2  S - - - . . EM--ac::FANNNNNNr2cd\}}}ttj|||ddttj|||dddS)N)rrgs1Crr~rr)rr6rIrKrv)r_rerJrKs r0test_extreme_mu2zTestSkellam.test_extreme_mu2se. 3 ))!S#66FFFF ))!S#66FFFFFFr2N)rrrrerWrPr8r2r0rGrGmsLPPP*OOO*GGGGGr2rGc eZdZdZdZejddZej dddgej d gd ej d gd ej d de ddDe j ddZ dZdS) TestLognormctj5tjdttjgdd}t|gdddddS#1swxYwYdS)Nrnrrrr)rg~r?ge3E?)rrrsrtrur6r(rorr_ros r0rMzTestLognorm.test_pdfs $ & & J J  !'> : : :-##KKK33C %c+H+H+H I I I J J J J J J J J J J J J J J J J J JsAA00A47A4c d\}}}ttj||z |tjt j||z |z ttj||z |tjt j||z |z dS)N)g(\5i@gOn?rJ)rr6r(rrrZrr)r_rprZsigmas r0rzTestLognorm.test_logcdfs* B ((B%(88 bfRUmmE&9:: < < < ++BrEU+;; ((2u)<== ? ? ? ? ?r2rrc@tjdSrrr^s r0r]zTestLognorm.rngrr2rrcrmr)rrrmr7)rLrrrcg|]}d|v| Srr8)r>es r0r@zTestLognorm.rr2)FTrrrrctjd||||}i} |r|| d<|r|| d<|r|| d<ttj|fi| ddidS)Nrg)rrKrlrkrrrrrT)r6r(rrrs r0rz'TestLognorm.test_fit_MLE_comp_optimizers}  cYi%,3!@@  #"DJ  #"DL  '&DN &emT < >>a"&!"5"566666r2c`gd}tttjj|ddddS)Nrcrrrrr)rrr)r[rr6rrrs r0test_fit_bad_keyword_argsz"TestBeta.test_fit_bad_keyword_argss= OOi1$ & & & & & &r2c^gd}tttjj|dddS)Nrir)fafix_a)r[rr6rrrs r0#test_fit_duplicated_fixed_parameterz,TestBeta.test_fit_duplicated_fixed_parameters0 OOj%*.!3GGGGGGr2zOverflow, see gh-14901reasoncpd\}}}ttj|||ddS)N)g?rVg0xAgx)>)rr6rr)r_rqr.r/s r0test_issue_12635zTestBeta.test_issue_12635s871a q!Q//1FGGGGGr2c>tjgd}tjgd}d}tj||dzd|z }t ||tj||dzd|z }t ||dS)N)g@3@?g^?gNC?)rfrgrrrr)rZrr6rrrr)r_inv_R count_listrqinvrs r0test_issue_12794zTestBeta.test_issue_12794s11122Xooo.. jnnQ Q0CDDU###jmmCa*1DEEQr2cd}tjdd}d}d|z |dz||z }}}tj|||}tj|||}t |d|z dS)Nh㈵>rrr)rZrr6rrrvr) r_alpha_2count_nobsrzr.r/rvrs r0test_issue_12796zTestBeta.test_issue_12796s1b!!g+vz4&=a1jnnQ1%%jnnS!Q''Q[)))))r2cd\}}ttjd||tjd\}}ttjd||tjd\}}ttjd||dttjd||dd\}}ttjd||dttjd ||ddS) Nrr)rLrr)rrr+ph)rrrO)rr6rrorZr)r_r.r/s r0rzTestBeta.test_endpointss1UZ^^Aq!,,bf5551UZ^^Aq!,,bf5551UZ^^Aq!,,a000UZ^^FAq1115551UZ^^Aq!,,a000UZ^^Ha33Q77777r2cTd\}}}tj|||dS)N)gףp= ?gvH7B@0B)r6rr)r_rzr.r/s r0test_boost_eval_issue_14606z$TestBeta.test_boost_eval_issue_146064s+'1a q!Qr2ra, b)r)@)rrcHd} ||||dS#t$rYdSwxYw)Nr) OverflowError)r_rr.r/rqs r0 test_beta_ppf_with_subnormal_a_bz)TestBeta.test_beta_ppf_with_subnormal_a_b8sG   F1aOOOOO    DD s  !!z x, a, b, ref)rrr~g>׵NlIq)& .!>rr~g'rOcltj|||}t||ddSr)r6rrrr_rer.r/rrs r0rzTestBeta.test_logcdfQs8""1a++%000000r2)rrr~gp}^U)rqrr~g 1*cjtj|||}t||ddS)Nr)r6rrrr_rer.r/rrs r0rzTestBeta.test_logsfYs5   Aq))sE*****r2r))rrgο)rrg)rrg&׾k )rrg*)Mcpttj|||dSrzrr6rrErs r0rlzTestBeta.test_entropyjs2  1a((0022C88888r2za, b, ref, tol))rrfgCpr)rfrg8EOr)gNAgNAg(4Fr)SAgSAg8TAUr()rg _Bg[VVuD&r)rQrQgR#Lr)rmrg?r5r)rmr\r)rfrgnQc}4r)rfrg{CEr)rfrQ%\r)rrmrr)rrrr)rQrfrrctttj||||dSrr)r_r.r/rrSs r0rzTestBeta.test_extreme_entropyrs8H  1a((0022CcBBBBBBr2c ptjtj}tjgd}tjgd}|||}tj||d|d||d|d||d|d||d|dg}t ||dS)N)rrgrrf)rrrgrrrrrmr)r6make_distributionrrZrrEr)r_Betar.r/rrs r0test_entropy_broadcastingz"TestBeta.test_entropy_broadcastings$&uz22 J*** + + J*** + +dQ!nnn$$&&j$$11...6688$11...6688$11...6688$11...6688:;; S!!!!!r2N)rrrrrgrjrnrrskipif MACOS_INTELrrrwr}rrrr6rrrrrrrlrrr8r2r0r`r`s,,,777&&& HHH  [ ,DEE H HFE H [ ,DEE  FE " [ ,DEE * *FE *888.    [X  'GHH [Vnn%EFFGFIH. [^GCEFF11FF1  [^GEGHH++HH+ [[DDDEE 99 EE 9 [   . C C/. C " " " " "r2r`cxeZdZgdZdZdZejdgddZ ejdedZ d Z ejd egd zd Z ejd d dgdZ dZdZdZdZdZdS) TestBetaPrime) )rY@rAD>?)rrrAm嗽?)rrArcgPK?)rrrAg%p?)rrArcg#|/?)rrrgsM <)rrAr$5Є*?)^ 9^;rArcgompP?)rrrg7j"!9)rrArz ^J?)rrArcgܷ"+>)rrrgrNs: )rrArgK>cd\}}tjgd}tj||}t tj||t| |tj ||dS)Nrdre) rZrr6r r rCrrrrorrfs r0rzTestBetaPrime.test_logpdfs t H___ % % OE4 ( ( AHHQKK((,,..///a"&!"5"566666r2ctjddd}t|dd\t jgd}tj|}t t j|tj j fd|D}t||dd dS) NrrLryrrdrec@g|]}tj|Sr8)r6r )r>rDrrgen_cdfs r0r@z*TestBetaPrime.test_cdf..s+JJJ''%/3t<<JJJr2-=ri) r6r rvrrZrr rCrrC _cdf_singler)r_rercdfs_grrrs @@@r0rWzTestBetaPrime.test_cdfs O  3 , ,Q t H___ % %""1eT22 D!!%%''(((%1JJJJJJJJJf15999999r2zp, a, b, expected))rrr~gV)?)rrr~gWJB9*=)r3rr~gOGJ<)rrg@gΣ01)?rgrg8ǘ`?)>q?rArcgMDcltj|||}t||ddSr)r6r rr)r_rqr.r/rTres r0rzTestBetaPrime.test_ppfs8 O  1a ( (8%000000r2z x, a, b, pchttj||||ddSr)rr6r r)r_rer.r/rqs r0test_ppf_gh_17631zTestBetaPrime.test_ppf_gh_17631s1++Aq!44aeDDDDDDr2ctjd}tjd}tjd}ttj|||dddS)NrOrrr)rZrrr6r _ppf)r_r.r/rqs r0 test__ppfzTestBetaPrime.test__ppfsX HSMM HSMM HSMM,,Q155sGGGGGGr2zx, a, b, expected))rrrr)rrArcgV[?)rrArcrchttj||||ddSr)rr6r rv)r_rer.r/rTs r0test_cdf_gh_17631zTestBetaPrime.test_cdf_gh_17631s3 ++Aq!44hUKKKKKKr2)rQrArcg%?)rQrrAgoXr?c|tj|||}|dksJt||ddS)NrOgh㈵>r)r6r rvr)r_rer.r/rTr.s r0test_cdf_extreme_tailsz$TestBetaPrime.test_cdf_extreme_tails sE O  1a ( (3wwww8$//////r2cgd}gd}gd}gd}tj|||}t||ddS)N)rrrmrArArArArrrArArArr)rrmrrcrcrcrcrArArrrrr)rrꌠ9Y>)Frrrrrrrrrrr)g/:g U/7gKH9g<![a?gw 4?g)J?g5?rrrrg%?gsM  [ B B B111 [\844EE54EHHH [      LL  L [ . / 12200 220444*111000000 " " " " "r2rc teZdZdZdZdZdZdZdZe j ddd gd Z e j d gd d Z e j dgde j dgde j dgde j dddge j dddge j dddgdZdS) TestGammactjddd}t|dtjddd}t|ddS) NZirLrg CTb?rrfgBΖ?)r6rrorrUs r0rMzTestGamma.test_pdfPsZkoob#To22C---kooa4o00C+++++r2cftjdd}t|ddSr)r6rrrrbs r0rzTestGamma.test_logpdfXs1##Aq))FA&&&&&r2c^gd}tttjj|dddS)Nrirr)rr)r[rr6rrrs r0rjz#TestGamma.test_fit_bad_keyword_args^s. OOi!!8LLLLLLr2ctjtjddddsJtjtjdddd sJdS) NrrgplC@rrrrgg1}t@r)rZiscloser6rrr^s r0rzTestGamma.test_isfbs"z%+//%33+%999 9 9 9z%+//%55+%999 9 9 9 9 9r2cvd}d}d}tj||}t||ddS)NPrgޟ򑁺rr)r6rrrrs r0rzTestGamma.test_logcdfxsC  $##Aq))%000000r2cvd}d}d}tj||}t||ddS)NrrgDmrr)r6rrrrs r0rzTestGamma.test_logsfsC  % !!!Q''s//////r2rlrOrPc|tj|dz|dzd|}t|dddS)Nrrrg>S*rr)r6rr rr_rlrms r0r zTestGamma.test_delta_cdfsF &&uSy%)Qe&LL6UCCCCCCr2z a, ref, rtol))rgt.r)rmrr)rggX>k-־ @r)rgwM7@r)gNgmCg%og$6@r)roܘ#]@rcdttj|||dSr)rr6rrE)r_r.rrs r0rlzTestGamma.test_entropys/  ++A..$??????r2r.)rrrrk)rrrrmTFrr9cHtjd}tj|||d|}i} |r|| d<|r|| d<|r|| d<dt | z } | dkrPd } tjt| 5tjj |fd d i| dddn #1swxYwYdStjj |fd d i| } tj| } | d kr4t| tj || dkr8t| dtj |dz| dkr:t| dtj |dzdSdS)Nrrgr<rlrrrrr r rrrrm)rZr[r\r6rrrrr rrrrr)r_r.rkrlrmrr9r]rrrr@thetar?s r0 test_fit_mmzTestGamma.test_fit_mmsi##$788{qcS,/11  DJ  DL  #"DNCII  A::MIz;;; ; ; ::T:T::: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; F ::T:T::{E" A:: DIIKK 7 7 7 A:: DKKNNBGD!G,<,< = = = A:: DKKNNBGD!G,<,< = = = = = :sB66B:=B:N)rrrrMrrjrrrrrrr rlrr8r2r0rrOs,,,''' MMM999,111000 [WsCj11 D D21 D [^BBBCC@@CC@ [S...11 [UNNN33 [Wnnn55 [WtUm44 [Yu 66 [[4-88>>987654654321 >>>r2rcd}tjd|dzz d|dzz dd}t|dddS) Nrg;f?rmrrrjrOgV{q@)r6rrro)jitterZs r0test_pdf_overflow_gh19616rsTF 6FAI-q619}!1MMMAAEE#JJ 122222r2ceZdZdZejdgddZejdgddZejdgdd Z d Z d S) TestDgammactjd}d}|d|}|d|}t j||}t jtj ||dz }t||t j|}t|||ddS)NlOP($rfrlr)rrrmrr) rZr[r\normalrr6dgammarorrr)r_r]rrer.rrr?s r0rMzTestDgamma.test_pdfsi##$788 JJRdJ + + KKRdK + +lq!$$koobfQii++a/S!!!|A Su555555r2zx, a, expected))rrggrU>)rrg$IC<)irg2Wj<)rtg~)A.=)rrgf?ctj||}t||dtj||}t||dtj| |}t||dtj||}t|| ddSr)r6rrvrrrr)r_rer.rTrvrrrs r0test_cdf_ppf_sf_isf_tailz#TestDgamma.test_cdf_ppf_sf_isf_tailslq!$$XE2222lx++QU++++ \__aR # #H51111lx++aRe,,,,,,r2r ))rgmqn@)?g?)rgx?cdttj||ddSrrr6rrEr s r0rlzTestDgamma.test_entropys/  ,,Q//5AAAAAAr2))rr)rg>_)r6g5i)rgo@)rg4Fa3@)rgrO]@cdttj||ddSrrr s r0test_entropy_entreme_valuesz&TestDgamma.test_entropy_entreme_valuess/"  ,,Q//5AAAAAAr2ctjgd}tj|}t t |D]3}||tj||ksJ4dS)N)rrrr6)rZrr6rrErr)r_rer.rs r0test_entropy_array_inputz#TestDgamma.test_entropy_array_input!s~ H''' ( ( L  # #s1vv 6 6AQ45<//!5555555 6 6r2N) rrrrMrrrrrlrrr8r2r0rrs 6 6 6, [-:::;; -- ;; - [X88899 B B 99 B [X:::;; B B;; B66666r2rceZdZdZejdgddZejdgddZdZ ejdgd d Z d Z d S) TestChi2cttjddddttjdddddS)Nrgޞw1D?r*rRrgg6:֜?rr6chi2ror^s r0rzTestChi2.test_precision+sjEJNN4668N$& ( ( ( (EJNN3446J$& ( ( ( ( ( (r2rU))gp@rg~#e)g^@r:g tA)rrgzĀ׿cjtj||}t||ddSr)r6rrr)r_rerrrs r0rzTestChi2.test_logcdf2s6""1b))%000000r2))rr:r)rrxgc)rrfg]3cjtj||}t||ddSr)r6rrr)r_rerrrs r0rzTestChi2.test_logsf=s6   B''s//////r2cd}tjd|}t|ddtjd|}t|ddd}tjd |}t|d dtjd |}t|d ddS) Nr7gλm:=6g'bd5)rgƯʉ?)rggn>@)g͔v0@)rg9:3@crttj||ddSr)rr6rrErs r0rlzTestChi2.test_entropy_s3  2..00#EBBBBBBr2cdttjdddddS)Nrrmrr*rr^s r0test_regression_ticket_1326z$TestChi2.test_regression_ticket_1326hs*EJNN322C<<<<SrYr^s r0r`zTestGumbelL.setup_methodnrar2ctjdd}tj|}tj|}t ||dSNrr)rZrTr6rrvrrr`s r0rzTestGumbelL.test_cdf_ppfrsS Kb ! ! N  q ! ! ^   " "2r2ctjdd}tj|}tj|}tj|}tj| }t||dSr) rZrTr6rrrrrexpm1r)r_rer.rurs r0rzTestGumbelL.test_logcdf_logsfxsr Kb ! ! N ! !! $ $ N  # # F1II ]1   1r2ctjdd}tj|}tj|}t ||dS)Nrr)rZrTr6rrrrr`s r0rzTestGumbelL.test_sf_isfsS KQ   N  a  ^   " "2r2rkrrctjd||j}tj||\}}t ||dS)Nrgrr)r6rrr]rr)r_rkr fitted_locrs r0test_fit_fixed_paramz TestGumbelL.test_fit_fixed_paramsV~!!s$(!KK**4c*:: AZ%%%%%r2N) rrrr`rrrrrrrr8r2r0rrms555   [URG,,&&-,&&&r2rceZdZdZdZdS) TestGumbelRcdttjddddS)Nr8?~T}%m;rr)rr6rrr^s r0rzTestGumbelR.test_sfs= ))"--/E" $ $ $ $ $ $r2cdttjddddS)Nrrrr)rr6rrr^s r0rzTestGumbelR.test_isfs= **5113D" $ $ $ $ $ $r2N)rrrrrr8r2r0rrs2$$$$$$$$r2rc eZdZdZejddZejdZejdZejdZ ej j ej dej d ej d ej j gej d d dgej dgdej dddgdZej jej dddgdZdZej dej dddgej dd dgd Zd!Zd"Zd#Zej j ej d$ej gd%gd&gd'ej gd(gd)gd*ej j ej gd+ejd,d-d.ejd/dd0ej j gd1Zej d$ej gd%gd&gd'ej gd(gd)gd*ej j ej gd+ejd,d-d.ejd/dd0ej j gd2Zej d3d4dgej d5d6d7gd8Zej d9d:d;gdd?d4ejejejfgd@dAggdBZej dCgdDej dEe j!j"dFejdGd4dHdIfe j!j#dFejdGd4dHdIfe j!j"dJejd4dKdHdFfe j!j#dJejd4dKdHdIfgdLZ$ej dMgdNdOZ%ej jej dMgdPdQZ&ejdRZ'dSZ(dTZ)dUS)VTestLevyStablecNtjd|_dS)NlYrYr^s r0r`zTestLevyStable.setup_methodrar2T)autousecdtj_dtj_dtj_tjjtj_dS)z2Setup default parameters for levy_stable generatorS1 piecewiseN)r6rparameterizationcdf_default_methodpdf_default_method _levy_stable _QUAD_EPSquad_epsr^s r0reset_levy_stable_paramsz'TestLevyStable.reset_levy_stable_paramss<.2*/:,/:,%*%7%A"""r2ctjttjdz }tj|jd}|S)a Sample data points for pdf computed with Nolan's stablec See - http://fs2.american.edu/jpnolan/www/stable/stable.html There's a known limitation of Nolan's executable for alpha < 0.2. The data table loaded below is generated from Nolan's stablec with the following parameter space: alpha = 0.1, 0.2, ..., 2.0 beta = -1.0, -0.9, ..., 1.0 p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5, and the equivalent for the right tail Typically inputs for stablec: stablec.exe << 1 # pdf 1 # Nolan S equivalent to S0 in scipy .25,2,.25 # alpha -1,-1,0 # beta -10,10,1 # x 1,0 # gamma, delta 2 # output file z.data/levy_stable/stable-Z1-pdf-sample-data.npyx,p,alpha,beta,pctrrZrrrrrrTrys r0nolan_pdf_sample_dataz$TestLevyStable.nolan_pdf_sample_datasM6w NN ! < =  v  /C DD r2ctjttjdz }tj|jd}|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.npyrrrrys r0nolan_cdf_sample_dataz$TestLevyStable.nolan_cdf_sample_datasNJw NN ! < =  v  /C DD r2cbtjttjdz }|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)rZrrrrrys r0nolan_loc_scale_sample_dataz*TestLevyStable.nolan_loc_scale_sample_datas1w NN ! ? @   r2 sample_sizer8r@marksr S0r z alpha,beta))rOr)rOr)rr)r'rz gamma,deltarrr{c|tj_tj||||}tj|||j|j\}} | dksJdS)N)rrrlrkrrA)r6rr rDrr]rv) r_r rrrrmrlsrrqs r0rEzTestLevyStable.test_rvs sr(.>*  d%U   | FF $(F ; ;RV  14xxxxxxr2rrrcd}d}d}tj||||d|j}tj|d||||f\}}|dksJd S) z3Additional test cases for rvs for alpha equal to 1.rOrrrr<rrWrN)r6rrr]rD)r_rrrkrlrestatrqs r0test_rvs_alpha1zTestLevyStable.test_rvs_alpha1*s|   ! !%3e'+$( " D D,q-%*D#u$=???a4xxxxxxr2cgd}tj|\}}}}t|dddt |ddt |dd t |d d|gd z}tj|\}}} } t |dt |d t | d d t | dd dS)N)wgr(rrrr羼u?r)r)r)r)67',?r*r*r*r*tA}˜.?r+r+r+r+Gz?rrra)\(̿rmgۧ1?rg9]c?)r+r+r+r+r+rgv?r*)r6rrqrrr r_realpha1beta1loc1scale1rpalpha2beta2rrs r0rvzTestLevyStable.test_fit7s    ',&7&A&A!&D&D#tV148888E4+++FGQ/// '1   999 9&+&7&A&A"&E&E#tVVQUBFFA...D&!,,,,,r2zUnknown problem with fitstart.rozalpha,beta,delta,gamma)rrrmr)rOrrmrparametrizationc|tj_tj||||d|j}tj|}|\}} } } t ||||g|| | | gddS)z7Test that fit agrees with rvs for each parametrization.rr<rrN)r6rr5rr]rqr) r_rrrmrr5rr alpha_obsbeta_obs delta_obs gamma_obss r0 test_fit_rvszTestLevyStable.test_fit_rvsOs-<) $$ 4U%e$(%  ))$//471 8Y  D% ' )Y 7      r2cxtjgd}tj|\}}}}tj| \}}}} t |d|dksJt ||t || t || t | |dS)N rrrrrfrfrfr6r6rgrgrr)rZrr6rrqrr) r_rer/r0r1r2r3r4rrs r0test_fit_beta_flipz!TestLevyStable.test_fit_beta_fliphs H??? @ @&+&7&A&A!&D&D#tV&+&7&A&A1"&E&E#tVUAqyyyyFF+++EE6***D4%(((FF+++++r2cVd}tjgd}tj| \}}}}tj| |z\}}} } t ||t ||t | ||zt | |dS)Nrr=)rZrr6rrqr) r_SHIFTrer/r0r1r2r3r4rrs r0test_fit_delta_shiftz#TestLevyStable.test_fit_delta_shiftts H??? @ @&+&7&A&A1"&E&E#tV&+&7&A&A1"u*&M&M#tVFF+++E5)))D$,///FF+++++r2cgd}tj|\}}}}|dks Jd||t|ksJdt|d|gd}tj|\}}} } |dks Jd|| t |ksJdt |d| dS) N) rrrrrfrfrfr6r6rCrzExpected alpha < 1, got zExpected loc < z, got ) rrrrrfrfrfr6r6rDzExpected alpha > 1, got zExpected loc > )r6rrqrrr.s r0test_fit_loc_extrapz"TestLevyStable.test_fit_loc_extraps 6 6 6&+&7&A&A!&D&D#tVzzz>f>>zzzc!ff}}}DADDdDD}}} 7 7 7&+&7&A&A"&E&E#tVzzz>f>>zzzc"gg~~~FRFFFF~~~~~r2z pct_range,alpha_range,beta_range)rrr)rcrrm)rrr)rrArrAr)rcrrrrm)grrryrr) rrArcrgffffff?r?rrrArrcrmrrrc|}tj}|jdko |jdkd|j|j|jg}ddfdgddfd gddfd gdd fd gd dfdgd dfdgg}t |D]\} \} } } | tj_ | || |n|} d}tj 5tj d|ttj| d| d| ddd}tjd5t#| gd|tj|| dz tj|| dz tj| dz g}dddn #1swxYwY||d| ktj|z}d| d | d!|d"|jjd#| }t-|| d| |d$%dddn #1swxYwYdS)&z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnir(c rtj|dtj|dztj|dz|ddk|ddkz|ddk|ddkz|ddkzz|ddktj|dd d gzz|dd ktj|dd d gzz|ddktj|dddgzz|ddktj|dddgztjtj|dgdzz|ddktj|ddgztjtj|ddgzz|ddktj|dddgztjtj|dgdzz|ddk|ddkz|ddkzz|ddk|ddkz|ddkzz|ddk|dd kz|ddkzz|ddktj|ddgztjtj|dgdzz|ddktj|dddgztjtj|dgdzz|ddktj|dd d gztjtj|dddgzz|ddkzzS)NpctrrrrrrrrrryrArArLrcrgr)rrrrFrG)gٿ333333ӿryrrrOrOrcrLryr)rrrOr"r)rZisinrr alpha_range beta_range pct_ranges r0rLz7TestLevyStable.test_pdf_nolan_samples..sGAeHi00GAgJ 445GAfIz223 vY!^uX_.vY#-wZ3.0uX_. wZ3.GAeHsCj99: wZ3.GAeHsCj99:$wZ3.GAeHr2h778%,wZ3.GAeHsCj99:GBF1V9$5$5|||DDE-6wZ3.GAeHrd334GBF1V9$5$5t<<=7@wZ3.GAeHsCj99:GBF1V9$5$57M7M7MNNOA#JwZ3.vY#-/uX-/K(TwZ3.vY$.0uX-/U-^wZ3.vY#-/uX-/_2hwZ2-GAeHrd334GBF1V9$5$57G7G7GHHIi7rwZ2-GAeHsCj99:GBF1V9$5$5|||DDEs<|wZ2-GAeHsCj99:GBF1V9$5$5RyAAB}AF7s*GC,EHr2r rctj|dtj|dztj|dz|ddkz|ddkzS)NrNrrrLrOrZrQrRs r0rLz7TestLevyStable.test_pdf_nolan_samples..sqGAeHi00GAgJ 445GAfIz223wZ#%'wZ2% 'r2c|ddk ztj|dzdvztj|dzS)NrrOrNrrW)rrSrT is_linux_32rUs r0rLz7TestLevyStable.test_pdf_nolan_samples.. s_wZ2%$_&GAeHi001;&(GAfIz22 3r2g& .=ctj|dtj|dztj|dz|ddkzS)NrNrrrLrWrRs r0rLz7TestLevyStable.test_pdf_nolan_samples..s^GAeHi00GAgJ 445GAfIz223wZ3&(r2 fft-simpsonr6c|ddktj|dztj|dztj|dzS)Nrr'rNrrWrRs r0rLz7TestLevyStable.test_pdf_nolan_samples.. s^wZ3&GAeHi001GAgJ 445GAfIz223r2rqctj|dtj|dztj|dz|ddkz|ddkzS)NrNrrrr'rWrRs r0rLz7TestLevyStable.test_pdf_nolan_samples..(spGAeHi00GAgJ 445GAfIz223wZ!^%wZ#% 'r2Nz0Density calculations experimental for FFT methodrrerrrrrlrkrcalcabserrrelerrrqrbz pdf test  failed with method 'z ' [platform: z]  Ferr_msgverbose)platformunamesystemmachinejoin processorrjr6rrrrrsrrurorZrrrisnanrrr)r_rrUrSrTrri platform_desctestsixdefault_methodr filter_funcsubdatar,rqsubdata2failuresmessagerYs ``` @r0test_pdf_nolan_samplesz%TestLevyStable.test_pdf_nolan_sampless4%  lg-I%-62I  \5=%/ :<< tJJJJJJL ^U%%%%%% U%%%%%%% W'''''' t&&&&&& t&&&&&& kC L"+5!1!1( (  B3AE  0 + 7;;t,,=A DC(**" " '#~FFF%))CLG$FO *[h///  0444F1ws|#344F1ws|#344rvgcl7K7KK  H               $H%-(1++ WWWWW"/WW4.~sGAeHi00GAgJ 445GAfIz223 wZ2-GAfI/A/A/ABBCuX-/ wZ2-GAfI??@uX-/  r2rActj|dtj|dztj|dz|ddktj|dgdz|ddkzz|ddktj|dgdz|ddkzzSr{rWrRs r0rLz7TestLevyStable.test_cdf_nolan_samples..sGAeHi00GAgJ 445GAfIz2237r)& +=+=+=>>?5T)+ 7r)& ???;;<5T)+ r2r[r6ctj|dtj|dztj|dz|ddkzS)NrNrr333333?rWrRs r0rLz7TestLevyStable.test_cdf_nolan_samples..s^GAeHi00GAgJ 445GAfIz223wZ#%'r2rctj|dtj|dztj|dz|ddkz|ddkzS)NrNrrrrrWrRs r0rLz7TestLevyStable.test_cdf_nolan_samples..qGAeHi00GAgJ 445GAfIz223wZ#%'wZ3& (r2rctj|dtj|dztj|dz|ddkz|ddkzS)NrNrrrrrWrRs r0rLz7TestLevyStable.test_cdf_nolan_samples..rr2rctj|dtj|dztj|dz|ddkz|ddkzS)NrNrrrOrrWrRs r0rLz7TestLevyStable.test_cdf_nolan_samples..rr2NrzZCumulative density calculations experimental for FFT method. Use piecewise method instead.rerrrrr^rr_rqrbz cdf test rcz' rdFre)rjr6rrrrrsrrurvrZrrrrnrrr)r_rrUrSrTrrprqrrrrsrtrqrurvrws ``` r0test_cdf_nolan_samplesz%TestLevyStable.test_cdf_nolan_samplesas2%U%%%%%% ,T$$$$$$ &t&&&&&& t&&&&&& t&&&&&& t&&&&&& GL \"+5!1!1( (  B3AE  0 + 7;;t,,=A (**# # '>" $$$ %))CLG$FO *[h///  0444F1ws|#344F1ws|#344rvgcl7K7KK  H               $H%-(1++ArAAAA&n2AA6>AACL#! ;# # # # # # # # # # # # # # #  ( ( s9A'G7A(E+ G+E/ /G2E/ 3AGG "G rrrrorvctj}|jdkodtjdv}|r|dkrt jd|}dt j_dt j_ ||d|k}d|t j_ |d vsJ|dkrt jj nt jj }||d |d |d d d} t| ||ddS)zGTests for pdf and cdf where loc, scale are different from 0, 1 rI32bitrroz4Test unstable on some platforms; see gh-17839, 17859r rS)rorvrerrrmrr^r6N)rhrirj architecturerrr6rrrr rorvr) r_rrrrirYrrtrrNs r0test_location_scalez"TestLevyStable.test_location_scales  lg-W'X=R=T=TUV=W2W   P45== KN O O O*0;,/:,tG}-.-8[[*~%%%%%)U]]E  ! !8I8M X CL''*GFO1!    GDM400000r2zmethod,decimal_placesrLrr c tjgd}tjgd}tjgd}tjd5tj5tjdt d|tj_ tj |d|dd }t||||d d d n #1swxYwYd d d d S#1swxYwYd S) z sample points extracted from Tables and Graphs of Stable Probability Density Functions - Donald R Holt - 1973 - p 187. )rrrrrrrrrmrmrmrmrrrrrrrr)gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g ?gDioɴ?g r?gH?g+?gHPs?gX?g&?g 0*?gv/?ga2U0*?)rrgrrrrgrrrrgrrrrgrrrrgrrrrzDensity calculation unstable.*)categoryrwrrr^N) rZrrrrrsrrur6rrror)r_rdecimal_placesxsdensitybetasros r0'test_pdf_alpha_equals_one_beta_non_zeroz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerosX H H H  (           [X & & &  (?(A(A    #H'8    4:E  0#''AuA1'EEC Wnf                                    s7C4,A$C C4C C4#C $C44C8;C8zparams,expected)r,r-rr)rmrrfr)rfr5rrctj|d|d|d|dd}t||dS)NrrrmrrrL)r6rr)r_rrTobserveds r0rzTestLevyStable.test_stats;sU$** 1IvayfQivay+   Hh/////r2r)rgrrzfunction,beta,points,expectedrOrrfrrrcd|cxkrdksnJt||||tjt||dS)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. rrrrN)rrZrr)r_rrrrrTs r0!test_distribution_outside_supportz0TestLevyStable.test_distribution_outside_supportIseP5}}}}1}}}}}} HV5t 4 4 4 GCKK * *     r2zx,alpha,beta,expected))r/iZ?s0?gz5F?)r~H?|/mg>m?)r.d5 ?L ,ٿg깃\?)r>?ЀjoؿgA]4?)rpa2?Յ пgqQ?cdtj_ttj||||dS)aTest pdf for x equal to zeta. With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0 will be close to zeta. When case "x equal zeta" is not handled properly and quad_eps is not low enough: - pdf may be less than 0 - logpdf is nan The points from the parametrize block are found randomly so that PDF is less than 0. Reference values taken from MATLAB https://www.mathworks.com/help/stats/stable-distribution.html Afc=rNr6rrrror_rerrrTs r0test_x_equal_zetaz TestLevyStable.test_x_equal_zetawsJZ&-"   ! !!5t ! < <      r2) )rrrgz¶?)rrrgV?)rrrgRE)3\?)rrrgB?)rrrg/^?)-C6rrgH?)rrrgn?)rrrgx\?)rrrgVM%?)rrrgm?cdtj_ttj||||dS)aTest pdf for x near zeta. With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0 will be close to zeta. When case "x near zeta" is not handled properly and quad_eps is not low enough: - pdf may be less than 0 - logpdf is nan The points from the parametrize block are found randomly so that PDF is less than 0. Reference values taken from MATLAB https://www.mathworks.com/help/stats/stable-distribution.html rrNrrs r0test_x_near_zetazTestLevyStable.test_x_near_zetasJD&-"   ! !!5t ! < <      r2c(tjSrz) threadingLockr^s r0levy_stable_lockzTestLevyStable.levy_stable_locks~r2c Vtjj}tdddd}tj}t jd i|}|5d|_d|_|jd i|d|d d }|d|d  }tj||krJd|_d|_|jd i|d|d d }|d|d  } t| |t||ddddS#1swxYwYdS) Nr'rcrrOrrrkrlr r rf rr8) rZr[r\rr6rr rrr r_rr]runfrozenfrozen unfrozen_afrozen_a unfrozen_bfrozen_bs r0$test_frozen_parameterization_gh20821z3TestLevyStable.test_frozen_parameterization_gh20821si#Ccs#>>>$",,V,,  / /(,H %&*F #%UUURcc)nnUUUUJzzrIzGGHvh*455 5 5 5(,H %&*F #%UUURcc)nnUUUUJzzrIzGGH : . . . X . . . / / / / / / / / / / / / / / / / / /sC DD"%D"c (tjj}tdddd}tj}|5d|_t jd i|}|jd i|d|dd }|d|d }t||d |_t jd i|}|jd i|d|dd }|d|d } t| |ddddS#1swxYwYdS) Nr'rcrrOrr rfrrr r8) rZr[r\rr6rr rrrs r0%test_frozen_parameterization_gh20821bz4TestLevyStable.test_frozen_parameterization_gh20821bsi#Ccs#>>>$  / /(,H %&0000F%UUURcc)nnUUUUJzzrIzGGH : . . .(,H %&0000F%UUURcc)nnUUUUJzzrIzGGH : . . . / / / / / / / / / / / / / / / / / /sCDD D N)*rrrr`rrrrrrrrrrrErr&rvxfailr;r>rArErZrTrxrrrrrrr6rrvrorrrrrrr8r2r0rrs?555V^D!!!BB"!B ^^B ^))^)V ^  ^  [ [ FL  lfl4v{7GHHH   [/$>> [CCC []VV,<==>=?> $ [ [Vc1X..  /. ---0 [>?? [    [D$<   @?   , , , , , , G G G [ [* FL     FL(((###(((k&     FLDDD CB'' B2&&k'    - *~~+,~@ [* FL     FL(((###(((k&     FLDDD CB'' B2&&k'    - *zz+*zx [Wq!f-- [VeU^441154.-1@ [ AJ !  @ [ !RVRVRV!< =  / 000 [W&7&7&788 ['!% CB''  !% CB''  !% Ar2&&  !% Ar2&&  ' :  ;98<  [&   )8  98 0 [ [    !" 0 ^  ^ ///./////r2rceZdZdZdZdS)TestArrayArgumentcNtjd|_dS)Nl4crYr^s r0r`zTestArrayArgument.setup_methodrar2ctjtjdtjdd|j}t|jddS)Nrrr<) r6rrrZrrr]rr=rs r0test_noexceptionz"TestArrayArgument.test_noexceptionsQjnn")A,,rwqzz")BBSY(((((r2N)rrrr`rr8r2r0rrs2555)))))r2rceZdZdZdZdS) TestDocstringctjj2tdtjjvtjj4tdtjjvdSdS)Nr+r)r6r+rr lowerrr^s r0test_docstringszTestDocstring.test_docstringssn > ! - J%."8">">"@"@@ A A A ? " . K5?#:#@#@#B#BB C C C C C / .r2cRtjtjdSrz)r6rCrBr^s r0test_no_name_argzTestDocstring.test_no_name_args&  r2N)rrrrrr8r2r0rrs5DDDr2rctgd}t|dk|d\}}t|gdt|dgtddk|d\}}t||t|dgtj|zt|dk|d\}}t||t|dgtj|zdS)N)rrrmrrmrrrrm)rrmrmrrr)rrrrZrr.r/rs r0test_args_reducers ###$$A a!eQ " "DAqq///***q1# a!eQ " "DAqq!q1# *+++ a!eQ " "DAqq!q1# *+++++r2cReZdZgdZdZgdZejde dZ dZ dZ dZ d Zd Zd Zd Zejjejd ddgdZejd ddgdZdS) TestFitMethod)ncfrLrM irwinhallcNtjd|_dS)Nl=rYr^s r0r`zTestFitMethod.setup_method0rar2)rbrrrz dist,argsct||jvrtj|dtjdddddtjg}tjdddddtjg}tt|}tt|j |dtt|j |dd S) rz fit known to fail or deprecatedrrrrrrrxN) fitSkipNonFiniterrrZrrrr.r6r[rr)r_r?r0rer.distfuncs r0!test_fit_w_non_finite_data_valuesz/TestFitMethod.test_fit_w_non_finite_data_values6s 4( ( ( K4AAA B B B HfffffbfE F F HfffffbfE F F5$''j(,!<<<<j(,!<<<<<.mlefuncsAAB!""BKA&&Eufw{1~~566ufw{1~~5668DKr2)rtrgrrrr=rqrrm)rrrr6)r rrrrT)rrr)rrr r)rr rr) rZrr6rrrrrr[r)r_rrer.r/rkrldadbrprb2rrr.s r0test_fix_fit_betazTestFitMethod.test_fix_fit_beta~s    H''' ( ( :>>!!A>>>1c5S!UA1a((1a&t<<<< H''' ( ( :>>!!>DD1c5QS!UAAq!!BAD))))U$z~~bQQq~IIBfRT1VQR$$BAD))))B""" j%*.!#aHHHH HZZZ j%*.!!AFFFFj%*.!!A!LLLLj%*.!!A!LLLL j%*.!aQ ( ( ( ( ( (r2ctjgd}tj|\}}t |dt |dtj|d\}}t |dt |dtj|d\}}t |dt |ddS)N)rmrmrrrrrrrmrrxrrr)rZrr6rbrrrs r0test_expon_fitzTestFitMethod.test_expon_fits H--- . .[__Q'' US!UA[__Qq_11 US!UA[__QQ_// US!UAr2c tjgd}tj|dz }tj|d\}}}t ||dt|dt |tj | dtj|dd\}}}t |tj |tjdz dz dt|dt|dtj|dd \}}}t|d t|dt |tj | ddS) N)rrrfr:rrrrrr/r=rmr)rfix_s) rZrrr6r(rrrvrrrr)r_relnxm1r=rkrls r0test_lognorm_fitzTestFitMethod.test_lognorm_fits H--- . .q1u !M--aa-88sEuyy{{7777S!rvejjll33%@@@@!M--aa-BBsErw):Q(>'D'D'F'FGG" $ $ $ $S!UA!M--aat-DDsEUD!!!S!rvejjll33%@@@@@@r2ctjgd}tj|\}}t ||t |tj|tj|d\}}t |dt ||tj|d\}}t |dt |dtttjj|dtttjj|ddS)N)rOrrtrrrrfrxrrP) rZrr6rrrrrrr[rrs r0test_uniform_fitzTestFitMethod.test_uniform_fits# H))) * *]&&q)) US!%%''"""UBF1II&&&]&&qq&11 US!UAEEGG$$$]&&q&44 US!UBj%-"3QSAAAAj%-"3QsCCCCCCr2rMLEMMc vd\}}tj||d|j}tj|d|}tj|d|}t ||ddtj|d| }t ||ddtj|d | }tj|d | }t ||ddtj|d | }t ||ddt ttjj|dd|t ttjj|dddd|tj|ddd|} | \} } } } t| | | ggdd}tj |d|j}tj |||\} } } t| |dS)N)rrrgrr)rr)rlrrri)rmrr)r r)rr)rrrrm)rlrrrr)rlr rrr)rlrrr)rrr) r6rrr]rrr[rrr)r_rr.r/reres_1res_2res_3res_4res_5aabbrssrs r0 test_fshapeszTestFitMethod.test_fshapess 1 JNN1acN A A qR77 qR77u5u==== q6::u5u==== qR77 qR77u5u==== q6::u5u==== j%*.!aOOOO j%*.!aQv 7 7 7 7  qRa&IIBBb"b\:::... {qsBB[__Ta_?? BRr2ctj}|dd|j}t d}t t |j|fi|d|idS)Nrmrg)rrri) enikibenikir)r6rrr]rr[rr)r_rr?rr/s r0test_extra_paramszTestFitMethod.test_extra_paramssaxx!#DHx==t$$$i4FF3FFvFFFFFFr2N)rrrrr`rrrrrrrrrrrrrrrr r8r2r0rr,sW 1 1 1D555A@@ [[(33==43=@@@   $3$3$3L5(5(5(n   AAA(DDD$ [ [Xt}55$$65$L [Xt}55GG65GGGr2rc>eZdZdZdZdZdZdZdZdZ dZ d S) TestFrozenctj}tjdd}|d}|ddd}t|||d}|ddd}t|||d}|ddd}t|||d}|ddd}t|||d}|ddd}t|||}|dd}t||| }| dd}t||| }| dd}t||| }| dd}t||| }| dd}t||| d}| ddd}t||t|j|jt|j|jdS)Nrrrjrrgrm)r6rrorrvrrrrDrr=rvrErr.r/)r_r?rresult_frs r0rzTestFrozen.test_norm!szC000::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&99T??4s33Xv&&&==??S11Xv&&&;;==t3//Xv&&&::<<d#..Xv&&&::<<d#..Xv&&&>>##$c22Xv&&&==##QD44Xv&&&VXtv&&&VXtv&&&&&r2cd}tj}tj|}|d}|d|}t|||d}|d|}t|||d}|d|}t|||d}|d|}t|||d}|d|}t|||}||}t||| }| |}t||| }| |}t||| }| |}t||| }| |}t||| d}| d|}t||t|j|jjt|j|jjdS)Nrrrgrrm)r6rrorrvrrrrDrr=rvrErr.r?r/)r_r.r?rr rs r0 test_gammazTestFrozen.test_gammaTsa {Q::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&99T??q!!Xv&&&==??QXv&&&;;==1Xv&&&::<<!Xv&&&::<<!Xv&&&>>##aXv&&&==##Q""Xv&&&VXv{}---VXv{}-----r2ctjd}|d}|d|d}t||dS)Nrrmrr)r6r(rr)r_rm1rs r0test_regression_ticket_1293z&TestFrozen.test_regression_ticket_1293saq!! ]]1   V $$$]]1   Rr2cld}tj|}|j|\}}t ||gddgd}tjd|t |j|dt jgd}tj|}|j|\}}t ||gddgd}tjd|t |jj|jj ftj|tjd}t|j|judD]}t j |}tj|}|j|j }}t |dtt j |t j d}tj|\}}t||gdd gdS) Nr"rrrrcrrrr)r6rr?rrrorZrr.r/r rrr)r_rrr.r/rv1s r0rzTestFrozen.test_abs  _q ! ! !w##A&&1aVb#Y'''  A###RW))!,,q"&k:::  _q ! ! !w##A&&1aVb#Y'''  Aq!!!bgi+U_-I-I!-L-LMMMo$$$'((( / /A 1 A1%%%B4qA B    BKNN # # # 3A?//22DAq QFRI . . . . / /r2cTtttjddS)N rv_frozen)r r-r6r7r^s r0test_rv_frozen_in_namespacez&TestFrozen.test_rv_frozen_in_namespaces#+[99:::::r2ctj}tt|dd|_t |jtj dtj d}| d|dS)Nr*rTrr) r6rr r-rr get_staterZr[rr)r_rrndms r0test_random_statezTestFrozen.test_random_states//000!V(2244Y**2..88:: < < <y$$T**  -----r2ctjdd}tjd}tjgdgdf}|||fD] }d|_|d t j|}|d }t j|}|d }t||| d | d g} t| d | d t| | d | | d dS) Ngdsz@g@e?r)rrrmrrPrcrTrr@rrr) r6rrrBrrpickledumpsloadsrrrv) r_rpoissr\distfnrKr0 unpickledr1medianss r0 test_picklingzTestFrozen.test_picklings[z,.ABB b!!"<<<+?+?+?+ABBBUF+ 4 4F"&F  JJAJ    V$$A##B QIA&&B R zz# c(:(:;G WQZ 0 0 0 GAJ//"wqz22 4 4 4 4 4 4r2c d}tjddd}tjdd5||ddd }tj|d ddddd }dddn #1swxYwYt ||tjdd }||}tj|dd}t ||dS)Nc|Srzr8rs r0rz$TestFrozen.test_expect..funcsHr2rmrrrr)rdividerT)rub conditionalrmr0rkrlrr" r# r )rr0rk)r6rrZrrrr)r_rgmgm_val gamma_valrqp_val poisson_vals r0 test_expectzTestFrozen.test_expectsQ   [1!1 - - - [( ; ; ; I IYYtaTYBBF **4d./A4+III I I I I I I I I I I I I I I I  *** M! # # #m**4d*BB {+++++sAA==BBN) rrrrr r rr r r r, r8r2r0r r s 1'1'1'f2.2.2.h   */*/*/X;;; . . .4440,,,,,r2r cbeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdS) TestExpectc@tjddd}t|ddtjddd}t|ddtjd dd}tjd dd}tjd dd|| }t|d dtjddd||d}t|dddS)Nc|dz |dz zS)Nrr8rs r0rLz&TestExpect.test_norm..s1qs r2rrmrjrr*rRc|Srzr8rs r0rLz&TestExpect.test_norm.. sr2rArAcdSrr8rs r0rLz&TestExpect.test_norm..Qr2rkrlrr" rcdSrr8rs r0rLz&TestExpect.test_norm..ar2Trkrlrr" r# rO)r6rrrr)r_rrrr" prob90prob90cs r0rzTestExpect.test_norms J  33!  D DAq"---- J  mm!  < <Aq"---- Z^^Daq^ 1 1 Z^^Daq^ 1 1"";;AQ2""MMFC4444*##KKQaB204$66GR444444r2c Rtjdddd}t|ddtjd dd d }t|d dtjd dddd}tjddddd}tjddd d ||d}t|ddtjdddd||d}t|dddS)Nc|dz |dz zS)NUUUUUU@r8rs r0rLz&TestExpect.test_beta..s51U7(;r2rrrm)r0rkrlqq?rrRc|Srzr8rs r0rLz&TestExpect.test_beta..sr2rPrr< rArfrjrAcdS)NrOr8rs r0rLz&TestExpect.test_beta.. sRr2)rfrfFr% rcdSrr8rs r0rLz&TestExpect.test_beta..$r6 r2TrO)r6rrrr)r_rrr" rr8 r9 s r0 test_betazTestExpect.test_betas= J  ;;'"#1  . .Avr2222 J  kkRr  J JAub1111 Z^^D"baq^ 9 9 Z^^D"baq^ 9 9""<.-r3 r2)rrfrr& rrRc|dz dzSNrrmr8rs r0rLz+TestExpect.test_hypergeom..0sadQYr2r*c|dz dzSrE r8rs r0rLz+TestExpect.test_hypergeom..5sQrTAIr2r)r0rkrr" rcdSrr8rs r0rLz+TestExpect.test_hypergeom..<sqr2r/rQcdSrr8rs r0rLz+TestExpect.test_hypergeom..As1r2T)r0rkrr" r# cdSrr8rs r0rLz+TestExpect.test_hypergeom..Fs!r2r)r0rr" )r6rrrrKrh) r_m_truev_truerrv_bounds prob_true prob_boundsprob_bcprob_bs r0test_hypergeomzTestExpect.test_hypergeom(s..r2qb.AA O " ";;[b " I IAvr2222 O " "#6#6[') # + +Avr2222?))*=*=/:.0Q2*?? Hfb9999eo))1b'2r1!)DDHHJJJ o,,[[{13b-BB KB????/((;B,-"$)HHGQ3333'' ++,(44FAr222222r2c$tjdddd}dtjddz }t ||d tjd ddd }t |dd dS) NcdSrr8rs r0rLz)TestExpect.test_poisson..LsQr2r$ rF)r0rr# rrmr*rRcdSrr8rs r0rLz)TestExpect.test_poisson..Qsr2T)r6rrrvr)r_rN prob_b_trueprob_lbs r0 test_poissonzTestExpect.test_poissonJsm**;;Ta7<+>>  ))!Q/// KbAAAA-&&{{!37'99GQ333333r2ctj}|d}|d|d}t||ddS)N)rrW)rr*rR)r6genhalflogisticrr)r_halflogr*r.s r0test_genhalflogisticzTestExpect.test_genhalflogisticUsa'~~6~**F###~~6~**D$333333r2c ttjtjddttjtjddttjtjddttjtjdddS)NrwGz?cdSrr8rs r0rLz/TestExpect.test_rice_overflow..dr2)r] rWcdSrr8rs r0rLz/TestExpect.test_rice_overflow..er_ r2cdSNrr8rs r0rLz/TestExpect.test_rice_overflow..fr_ r2)r rZrCr6ricerorr^s r0test_rice_overflowzTestExpect.test_rice_overflow_s  EJNN35566777 EJ--kk-HHIIJJJ EJ--kk-HHIIJJJ EJ--kk-HHIIJJJJJr2c(d\}}tjd|f}t|||dz z t jd|z z dtjd|f|}t|||zddS) N)ryrc|Srzr8rbs r0rLz(TestExpect.test_logser..kr6 r2rWrOrrc|Srzr8rg s r0rLz(TestExpect.test_logser..qr6 r2r& )r6rrrrZr)r_rqrkres_0res_ls r0 test_logserzTestExpect.test_logserhs3 ##KKqd#;;QV rvb1f~~5E C C C C ##KKqd#DDus{777777r2cd\}}tjd||f}tjd||f}t|||z dt||dzz ||zddS)N)rr'c|Srzr8rs r0rLz)TestExpect.test_skellam..xAr2rWc |dzSrr8rs r0rLz)TestExpect.test_skellam..yrr2rrrm)r6rIrr)r_rp2r rs r0 test_skellamzTestExpect.test_skellamtsB ] ! !++RH ! = = ] ! !..Bx ! @ @BG%0000RU BG%888888r2c d\}}tjd||f}t|t dt ||D||z z ddS)N)rqc|Srzr8rs r0rLz)TestExpect.test_randint..r3 r2c3K|]}|VdSrzr8r>rs r0rz*TestExpect.test_randint..s"55!A555555r2rr)r6r<rrrhr)r_r+r,rs r0 test_randintzTestExpect.test_randint}sBm"";;R9955uR}}55555bA O O O O O Or2ctjt5tjddddddS#1swxYwYdS)Nc |dzSrr8rs r0rLz&TestExpect.test_zipf..s 1r2r$ )rwarnsrur6rrrr^s r0 test_zipfzTestExpect.test_zipfs \. ) ) 4 4 J  nnd 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4s"A  A A ctjdd}tjddddd}t||d dS) NcdSrr8rs r0rLz/TestExpect.test_discrete_kwds..rn r2r$ rWcdSrr8rs r0rLz/TestExpect.test_discrete_kwds..rn r2r r()r0maxcount chunksize tolerancer*rR)r6rrr)r_n0n1s r0test_discrete_kwdszTestExpect.test_discrete_kwdssd ] ! !++D ! 9 9 ] ! !++D+/2"OOBB//////r2cd}dD]=}tjd|}t|||d>dS)NcH|dzd|dzzzd|dzzzd|dzzz|zS)Nrrfrrrr:rmr8rs r0 poiss_moment5z-TestExpect.test_moment..poiss_moment5s8q52b!e8#bQh.BE9B> >r2)rrrrr)r6rrr)r_r rZm5s r0 test_momentzTestExpect.test_momentse ? ? ? ? ?B%%a,,B B b 1 1 > > > > > ? ?r2cttjdddttjdddttjdddttjdd ttjd d dS) NrGrOrjrxrfrc)rWr Ur )rr6rrrr_r^s r0test_challenging_cases_gh8928z(TestExpect.test_challenging_cases_gh8928s  ))b)<>$22!IOOD!44 #56H!I(*@*C" $ $ $ $)+A" $ $ $ $9>>&!,,IOOFA.. ,.@A."3%@@@@ >======r2c ~ttjddt dddS)Nrmir)rr6r rvrr^s r0test_cdf_large_nczTestNct.test_cdf_large_ncs0 aE%LL991=====r2zx, df, nc, expected)rrfrpgAs69)rhrrpgV1chttj||||ddSr)rr6r ro)r_rerr rTs r0test_pdf_large_nczTestNct.test_pdf_large_ncs1  aR00(GGGGGGr2N) rrrr r r r r r rrrr r8r2r0r r sCCC222$$$    >>>,>>>6 [2.+5   HH   HHHr2r c&eZdZdZdZdZdZdS)TestRecipInvGausscVtjdd}|dksJdS)Nrrr)r6 recipinvgaussrors r0test_pdf_endpointz#TestRecipInvGauss.test_pdf_endpoints+   # #As + +Cxxxxxxr2cltjdd}|tj ksJdS)Nrr)r6r rrZrrhs r0test_logpdf_endpointz&TestRecipInvGauss.test_logpdf_endpoint s/"))!S11wr2cntjdd}d}t||ddS)NrArg9V9s;rr)r6r rvrr_rqrTs r0test_cdf_small_xz"TestRecipInvGauss.test_cdf_small_x$s<   # #D# . .(8%000000r2cltjdd}d}t||ddS)NrrglH>> EJNN1N334488::;;; EJ--a2-6677;;==>>>  EJNN1N334488::;;;z622 D!!%%''(((  q!,,ejnnQ.B.BQ ( ( ( ( ( (r2ctjj}t|d|jjdt|dd|jjddS)Nr)r/rr)rr)r/rr)r6rc rrr]rr=rs r0 test_rice_rvszTestRice.test_rice_rvsXs[jnSS2DH555:A>>>SS2FBBBH&QQQQQr2ctjtjdddtjddd}gd}t ||tjddd}tj|dd}gd }t ||tjjd tjdd d}gd }t ||dS) Nrf)g/ Ƹ?g[jNJ\?g ?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?rcrg@_@rr) g<~@gwd @gC?@gb 0@g` A@@g'NxP@g33-a@g4pv@g$F@r)gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g< uQ@giffT@g9r[V@g3bXQY@gq xJ[@g`*DD^@g@`@gdAa@)r6rc rvrZrrrr5)r_rvcdf_exp probabilitiesrppf_exps r0test_rice_gh9836zTestRice.test_rice_gh9836]sjnnRYr333RYr35K5KLL OOO W%%% #q#.. jnn]En;; LLL W%%%k""3 "c2(>(>?? ;;; W%%%%%r2N)rrrr`r r r r8r2r0r r ?sS444(((*RRR '&'&'&'&'&r2r c eZdZdZdZdZdS) TestErlangcNtjd|_dS)NlILrYr^s r0r`zTestErlang.setup_methodrar2c tj5tjdtt tt jjdddd|jgd}t j |d}t j |d}t||d ddddS#1swxYwYdS) Nrnrrrrr<)rrOrrrrr) rrrsrtrur[r6erlangrr]rrr)r_r result_erlang result_gammas r0test_erlang_runtimewarningz%TestErlang.test_erlang_runtimewarnings$ $ & & D D  !'> : : : .%,*:CQ ! B B B B (''D!L,,Ta,88M ;??4A?66L M.scale_mles/FD4KA-..!c$ii-@RG Gr2rrrx)r6r+rr]rr)r_rr7rr scale_expectrkrls r0rvzTestRayleigh.test_fits~!!s(1"JJ H H H!yw// ^''7';; US'"""UL)))^''R'88 UUB ^''-- UUIIdC0011111r2r] rg̡=E?g@1d?ctjd|||j}t tj|dS)Nrrk)r6r+rr]r)r_rr7rs r0 test_fit_comparison_super_methodz-TestRayleigh.test_fit_comparison_super_methodsE ~!!s(1"JJ%end;;;;;r2c8ttjdSrz)rr6r+r^s r0rzTestRayleigh.test_fit_warningssEN+++++r2ctjd}d\}}}tj||||}tj|\}}|tj|ksJtj||\}}|tj|ksJ||ksJdS)Ni)r8rrrrx)rZr[r\r6r+rrr) r_r]rkrlrrrrrs r0test_fit_gh17088zTestRayleigh.test_fit_gh17088si##C(('UDn  e$S II^'',, $$$$"^//E/BB$$$$E!!!!!!r2N) rrrr`rrrrrrvr rr r8r2r0r r s555000""" [03K3K3MNN22NN20 [0D$<4> 3K3MNN<<NN<,,, " " " " "r2r cPeZdZdZdZdZejdgddZ ejdgdd Z ejdd d gd Z ejdd dgdZ dS) TestExponWeibcd}d}d}tj|||}tj|||}t ||gddgdS)NrcrOrg:23W+g~`9k)r6 exponweibrorr)r_rer.rrqrs r0test_pdf_logpdfzTestExponWeib.test_pdf_logpdfss    O  1a ( (%%aA..D /1DE G G G G Gr2c~tjddd}d}d}tj|||}tj||}t ||tj|||}tj||}t ||dS)Nrrrrrg)rZrr6r ro weibull_minrrr_rer.rrqrTrs r0 test_a_is_1zTestExponWeib.test_a_is_1s KB " "   O  1a ( ($((A..8$$$%%aA..$++Aq11h'''''r2cztjddd}d}d}tj|||}tj|}t ||tj|||}tj|}t ||dS)Nrrrf)rZrr6r rorbrrr s r0test_a_is_1_c_is_1z TestExponWeib.test_a_is_1_c_is_1s KAr " "   O  1a ( (;??1%%8$$$%%aA..;%%a((h'''''r2z x, a, c, ref))rr~rg=J ?)r8r~rg$+PR>)rr~rg ><)rr~rggX.X:)r?rgRy9)rr rg'vR0=)g_QPrrgQ:s8o!!!Q**Su------r2)rmrrg)rrrgl̇կcltj|||}t||ddSr)r6r rr)r_rer.rrrs r0rzTestExponWeib.test_logcdfKs8''1a00%000000r2)gR]jp2rrgr)r^rmrfgN~cltj|||}t||ddSr)r6r rr)r_rer.rrrs r0rzTestExponWeib.test_logsfSs8%%aA..s//////r2N) rrrr r r rrrrrrrr8r2r0r r sL G G G((( ( ( (> [ 5 5 5  --  -* [ 4 4 4...  [^AGIJJ11JJ1  [^IFHII00II000r2r ceZdZdZdZdS)TestFatigueLifecjtjdd}t|dddS)Nrr~X9rr)r6r!rrrs r0 test_sf_tailzTestFatigueLife.test_sf_tail]s8    , ,0u======r2cnd}tj|d}t|dddS)Nr r~rrr)r6r!rr)r_rqrzs r0 test_isf_tailzTestFatigueLife.test_isf_tailks: !   ! !!S ) )5u------r2N)rrrr r r8r2r0r r [s2 > > >.....r2r ceZdZdZdZejdddgdZdZ ejdd d gd Z d S) TestWeibullcftjdd}t|ddSr)r6r rrr s r0rzTestWeibull.test_logpdfts0   $ $Q * *Qr2cd}d}d}tj|||}t|t jddz tj|||}t|dt jdz tj|||}t|tj d tj |||}t|t jtj d tj |||}t|t jdtj |||} t| dtj ddd}t|t jd tj ddd} t| d d }tj|||}t|t jddz tj|||}t|dt jdz tj|||}t|t jdtj |||}t|dtj |||}t|tj d tj |||} t| t jtj d tj d dd}t|tj d  tj d dd} t| t jtj d  dS) Nrrrrrrr6rmrrSg& .gCe)r6r rorrZrrrrvrrrrr weibull_max) r_rer.r/rqr3rlcrKr#s r0test_with_maxima_distribz$TestWeibull.test_with_maxima_distribys.      ! !!Qa ! 0 026%==?+++   % %a! % 4 4EBF1II-...   ! !!Qa ! 0 0GM%000111   % %a! % 4 4BFGM%$8$8#899:::   AQ / /26%==)))   $ $Q $ 3 3E"""   Qa 0 026$<<(((   $ $R! $ 4 4D!!!    ! !!Qa ! 0 026%==?+++   % %a! % 4 4EBF1II-...   ! !!Qa ! 0 026%==)))   % %a! % 4 4E"""   AQ / /GM%000111   $ $Q $ 3 3BFGM%$8$8#899:::    3 3GM*@AAABBB   $ $UAQ $ 7 7BFGM2H$I$I#IJJKKKKKr2rlrOrccxtj|dz|dzd|}t|ddS)Nrrrrg>)r6r r rrs r0r zTestWeibull.test_delta_cdfsI"!,,U3Ya38-::566666r2ctjd}d\}}}tj|||}|d|}tj|dd\}}} tj|dd\} } } || cxkrdksnJ|| ksJtj|ddd \} }}|dksJtj| ||}|d }tj|tj|f}t||dS) Nl>)rmr7rrgrrrrrrrrr) rZr[r\r6r rrrr>r)r_r]rrkrlr?rc2rrc3rrc4rrrrrs r0 test_fit_minzTestWeibull.test_fit_minsTi##$788# 3 C//hhCch22!,00c0BBD& ,00c0BBD&t    q      Rxxxx!,00a$0OOD&{{{{!"dF33kk$k''gcllEJsOO+S!!!!!r2r')r8rr)rrgq뮕qH)cttj|||dttj|||ddSrP)rr6r rrr+s r0rzTestWeibull.test_sf_isfsZ ),,Q22CeDDDD)--c155quEEEEEEr2N) rrrrr rrrr r rr8r2r0r r rs RLRLRLh [WsCj1177217("""< [[+J,D+EFFFFFFFFFr2r ceZdZdZdZdS) TestDweibullcBtjd}d|ddz}tj|}tj|tjdz }t||ddS)Nq>~).rfrgrrrr) rZr[r\rr6dweibullrEr rr)r_r]rrrs r0rlzTestDweibull.test_entropy si##$788  2 .. .n$$Q''''**RVC[[8Su------r2cPtjd}d|ddz}d|z}t j||}dt j||z}t||ddS)Nr rfrrrrr) rZr[r\rrr6r rr r)r_r]rrerrs r0rzTestDweibull.test_sfsi##$788   ,, ,  n1%%E%((A...Su------r2N)rrrrlrr8r2r0r r s2 . . ......r2r cDeZdZdZdZdZdZdZdZdZ dZ d Z d S) TestTruncWeibullcrtjddgddd}t|ddgdS)Nrcrg)\(?gףp= ?r)r6truncweibull_minrorr s r0test_pdf_boundsz TestTruncWeibull.test_pdf_bounds#s<  " & &Sz3d C CQc #####r2ctjdddtj}t |dtjdddd}t |ddS)NrrOrrg~?)r6r rrZrrrr s r0rzTestTruncWeibull.test_logpdf(se  " ) )#sC @ @Q  " ) )#sC = =./////r2crtjddgddd}t|ddgdS)NrrOrrc)r6r rrr s r0test_ppf_boundsz TestTruncWeibull.test_ppf_bounds0s<  " & &Sz3S A AQc #####r2cgd}tj|ddd}tj|ddd}t ||dSN)rrcrgrrrrOrrr)r6r rrvrr_rzreq_outs r0test_cdf_to_ppfz TestTruncWeibull.test_cdf_to_ppf5s[ 0 0 0  " & &q"b" 5 5&**1b"b995!!!!!r2cgd}tj|ddd}tj|ddd}t ||dSr )r6r rrrr s r0test_sf_to_isfzTestTruncWeibull.test_sf_to_isf;s[ 0 0 0  " & &q"b" 5 5&))!RR885!!!!!r2c d d d fdtjd }t|dtjd }t fd \}}t ||tjd }t fd  \}}t ||tjd }t fd  \}}t ||tjd } t fd  \} }t | | dS)NrrOrcT||ztj|zSrz)r6r ro)rerpr.r/rs r0xnpdfz)TestTruncWeibull.test_munp..xnpdfFs)a4.221aA>>> >r2rrc|dSrr8rer s r0rLz,TestTruncWeibull.test_munp..Ma r2rmc|dSrr8r s r0rLz,TestTruncWeibull.test_munp..Qr r2rc|dSrb r8r s r0rLz,TestTruncWeibull.test_munp..Ur r2rc|dS)Nrr8r s r0rLz,TestTruncWeibull.test_munp..Yr r2)r6r rrrr)r_rr m1_expectedrr m2_expectedm3 m3_expectedr m4_expectedr.r/rr s @@@@r0 test_munpzTestTruncWeibull.test_munpAs    ? ? ? ? ? ? ? # * *1aA 6 6R  # * *1aA 6 63333Q:: QK(((  # * *1aA 6 63333Q:: QK(((  # * *1aA 6 63333Q:: QK(((  # * *1aA 6 63333Q:: QK(((((r2c ^d}d}d}tjdtjdtjdtjdz zz }tj||||}t|dtj||||}t|tjd tj d|||}t||tj ||||}t|dtj ||||} t| tjd tj d|||} t| |dS)NrOrrrrr ) rZrrrr6r rvrrrrrr) r_r.r/rx_medrvr rrr#rs r0test_reference_valuesz&TestTruncWeibull.test_reference_values\so   BF3"rvbzz/0B)C)C#CDDDEE$((1a88S!!!  # * *5!Q : :RVBZZK((($((aA66U###  # & &uaA 6 6C    # ) )%Aq 9 9RVBZZK((($((aA66U#####r2c*d}d}d}tj}d}tj|||}tj|||||}t ||tj|||}tj|||||} t || tj|||} tj|||||} t | | tj |||} tj |||||} t | | tj |||}tj |||||}t ||tj |||}tj |||||}t ||tj dd||d}t |tj d tj dd||d}t |d dS) Nrrrrrr6rmrr) rZrr6r ror rrrvrrrr)r_rerr.r/rlrqp_truncr3lp_truncrv cdf_truncr lc_truncrKs_truncr#ls_truncs r0test_compare_weibull_minz)TestTruncWeibull.test_compare_weibull_mintse    F   ! !!Qe ! 4 4(,,Q1au,EE7###   % %a% % 8 8)00Aq!50IIH%%%##Aq#66*..q!Q.GG Y'''   % %a% % 8 8)00Aq!50IIH%%%   AU 3 3(++Aq!Qe+DD7###   $ $Q $ 7 7)//1a%/HHH%%%  " % %b!Q % ; ;26$<<(((  # ) )"aAQ ) ? ?D!!!!!r2cd\}}}tj||d}tj||||}tj||||}tj||tj||z }tj|||z }tj||tj||z |z } tj||tj|| dS)N)r~rgrrg) rZrTr6r rorvr rr) r_rr.r/rerrsrrrus r0test_compare_weibull_min2z*TestTruncWeibull.test_compare_weibull_min2s"1a K1c " "%))!Q155%))!Q155 $$Q**U->-B-B1a-H-HH $$Q**T1!%%a++e.?.C.CAq.I.II4O ""4... ""4.....r2N) rrrr rr r r r" r% r- r/ r8r2r0r r !s$$$ 000$$$ """ """ )))6$$$0'"'"'"R/////r2r cfeZdZdZdZejdgddZdS) TestRdistctj}gd}t|||dd|ddS)Nrg@rrR)r6rdistrrvr)r_r r]s r0test_rdist_cdf_gh1285zTestRdist.test_rdist_cdf_gh1285sX$$$FJJvzz&%'@'@%HH"A / / / / / /r2c tjddd}d}tdtj|dz |dz |dzdz ztj||dS)NgGzrrfg@rrmr)rZrTrr6rror3 )r_rers r0test_rdist_betazTestRdist.test_rdist_betas KtR ( ( C 1Q3! 4 4 8 8!a% C CC!KNN..q11 3 3 3 3 3r2r'))rig?)rcg;|bZ?)rig79)riUg޻S/cfttj|||ddSrP)rr6r3 rr+s r0 test_rdist_sfzTestRdist.test_rdist_sfs/  q!,,c>>>>>>r2N) rrrr4 r6 rrrr9 r8r2r0r1 r1 st///333 [   ?????r2r1 c2eZdZdZdZdZdZdZdZdS) TestTrapezoidcVgd}|D]}d|dg}ttj|||tj||ttj|||tj||dS)N)rryrrrr)rr6rrotriangrv)r_modesmoderes r0test_reduces_to_triangz$TestTrapezoid.test_reduces_to_triangs    ; ;DD! A  3 3AtT B B % 0 0D 9 9 ; ; ;  3 3AtT B B % 0 0D 9 9 ; ; ; ;  ; ;r2cbtjddd}ttj|ddtj|ttj|ddtj|dS)Nrrrf)rZrTrr6rrorrvrs r0test_reduces_to_uniformz%TestTrapezoid.test_reduces_to_uniforms K1b ! !EO//1a88%-:K:KA:N:NOOOEO//1a88%-:K:KA:N:NOOOOOr2cnttjddddttjddddttjddddttjddddttjd ddd ttjdddd ttjd ddd ttjd ddd ttjddddttjddddttjd dddttjdddddS)NrrmrrrrrLrOrcg?rrr rtg?)rr6rrorvr^s r0 test_caseszTestTrapezoid.test_casessEO//1a88!<<<EO//1a88!<<<EO//Q<</ 1 1 1EO//S#>>/ 1 1 1 EO//S#>>FFFEO//S#>>EEEEO//S#>>FFFEO//S#>>HHHEO//S#>>FFFEO//S#>>DDDEO//S#>>HHHEO//S#>>DDDDDr2c d\ z z z z z z z f\}}}}d z z z z fd}|d}|d|dzz }d z z z z z z z z tjd z z z zz}ttj|||||dttj|||||dttj|||||dttjddd d d dttjddd d ddttjddd d d ddS) N)rrrmrrmc|dzz|dzzz z z |dzz|dzzz z z z z|dzz |dzz S)Nrmrr8)rpr.r/rdrks r0rz6TestTrapezoid.test_moments_and_entropy..momentsn!ac(Q1X-!A#6!Hq1Q3x/AaC89:qSqS" #r2rrrrRrrr/rr)rZrrr6rrr=rE)r_rrp rkrlrrr=rEr.r/rrG rks @@@@@r0test_moments_and_entropyz&TestTrapezoid.test_moments_and_entropys" 1acac]QqSQqSM1acABU 1QqM # # # # # # # # # vayyfQii$'!1Qq/QqSU1W-sac!eAg0G0GGEO00ReDD " . . . .EO//BUCC - - - -EO33BCGG#R 1 1 1 1 EO00Ar1==r2NNNNEO00Ar1==q"MMMMEO//1b!<rrrrr)rZrr6rrobroadcast_arraysemptyrrrrravelrr;r=rr)r_rrG rerccddrrindrroc1d1s r0test_trapezoid_vectz!TestTrapezoid.test_trapezoid_vects  H___ % % Hc3Z D ) H&&& ' ' O  1a ( ((Aq11 Bhrwbh///i   bhhjj"((**bhhjjII 5 5MAr2r_((R44CFF3;;qw//e<<<< Ju,,Q6,BB C C$Q**Bh|$$i  S"((**bhhjj99 C CIAr2_**2r6*BBCFF35==11>>>>>>r2ctjd}d}tj|}|d|}tj|}|dd\}}tj|ddrJtj|ddrJtj||}tj||} | |ksJdS) Nl\"MW)ryrrrmrrrmrrcr) rZr[r\r6rrrrr) r_r] true_args true_distre fitted_argsfitted_cfitted_dtrue_llf fitted_llfs r0&test_trapezoid_fit_convergence_gh23503z4TestTrapezoid.test_trapezoid_fit_convergence_gh23503)s i##$899# OY/ MM$SM 1 1o))!,, )!_(;x555555;x555555?'' 155_))+q99 H$$$$$$r2N) rrrr@ rB rD rH rR r[ r8r2r0r; r; sw;;;PPP EEE(MMM6???4%%%%%r2r; ceZdZdZdS) TestTriangctjd5ttjdddttjdddttjdddttjdddttjdddttjddd ttjdddttjddd ttjdddttjdddttjddd ttjdddddddS#1swxYwYdS) NraiserrrrrOrrrmrrg)rZrrr6r= rorvr^s r0test_edge_caseszTestTriang.test_edge_casesCs [W % % % 6 6 ))!Q// 4 4 4 ))#q112 6 6 6 ))!Q// 4 4 4 ))!Q// 3 3 3 ))#q112 6 6 6 ))!Q// 3 3 3 ))"b112 6 6 6 ))#r22D 9 9 9 ))#r22C 8 8 8 ))"b112 6 6 6 ))#r22D 9 9 9 ))"b111 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6sH)I  IIN)rrrr` r8r2r0r] r] Bs#66666r2r] ceZdZejdddgdZejdgddZdZd Z d S) TestMaxwellr)rgCR5&.)rg7q?cdttj||ddSr)rr6maxwellrr5s r0rzTestMaxwell.test_sf[s/  ((++Su======r2rQ))rg1!@)g?g?)g>>>>>r2cld}tjd}t||ddS)Ngi6urrr)r6rd rr)r_rrs r0rzTestMaxwell.test_logcdfks7%%%a((%000000r2cld}tjd}t||ddS)Ng_OԺr(rr)r6rd rr)r_rrs r0rzTestMaxwell.test_logsfqs7% ##D))s//////r2N) rrrrrrrrrrr8r2r0rb rb Vs  [X::<==>>==>  [X:::;;?? ;;?111 00000r2rb ceZdZdZdZdS) TestMielkecd\}}ttj||dtjttj|ddtjt t jtj|dddS)N)g rh@gv?rrOr3)rr6mielkerrZrr rC)r_rbrKs r0r%zTestMielke.test_momentsys1U\!Q''..q1126:::U\!S))0033RV<<< ELD1188;;<<=====r2ctjddd}d\}}ttj||||z tj|||dS)Nrrgr8)g@gHzG@)rZrTrr6burrrork )r_rerbrKs r0test_burr_equivalencez TestMielke.test_burr_equivalences^ Kc2 & &1 q!QqS115<3C3CAq!3L3LMMMMMr2N)rrrr%rn r8r2r0ri ri xs7>>>NNNNNr2ri c&eZdZdZdZdZdZdS)TestBurrc ntjddgtjddgtjddgtjddgtjddgtjddgtjd d gg}d |D}d |D}t ||d |D}d|D}t ||dS)Nrr)rrm)rr)rmrrrrO)rrmrc<g|]\}}}|j|jg|RSr8rrs r0r@z0TestBurr.test_endpoints_7491..rr2cg|]\}}}| Sr8r8rs r0r@z0TestBurr.test_endpoints_7491..rr2c<g|]\}}}|j|jg|RSr8)rr.rs r0r@z0TestBurr.test_endpoints_7491..s4@@@<2uayry&&&&@@@r2c>g|]\}}}tj|Sr8)rZrrs r0r@z0TestBurr.test_endpoints_7491..s)FFF)=UI26)$$FFFr2)r6fiskrm burr12r)r_rrrs r0test_endpoints_7491zTestBurr.test_endpoints_7491sZq ! Z1 % Z # Z1 % \8S ) \63 ' \63 ')>====>>>>>!#w///@@4@@@FFFFF!#w/////r2cd\}}tj||\}}d\}}t||t||dS)N)rPr)g4U?g&MI?)r6rm r)r_rrG rvariancemean_hc variance_hcs r0test_burr_stats_9544zTestBurr.test_burr_stats_9544s_1Aq))//11h Gg&&&+.....r2cd\}}tj||\}}ttj|ttj|d\}}tj||\}}ttj|ttj|d\}}tjtjgd||\}}}}ttj|ttj|ttj|ttj|d\}}tjgd||\}}}}ttj|ttj|ttj|ttj|d\}}tjgd||\}}}}ttj|ttj|ttj|ttj|d\}}tjgd||\}}}}ttj|ttj|ttj|ttj|d\}}tjgd||\}}}}ttj|ttj|ttj|ttj|dS)N)rr)rrr)r~r)r7r)r5r)r6rm r rZrnrCrr) r_rrG rr{ e1e2e3e4s r0test_burr_nan_mean_var_9544z$TestBurr.test_burr_nan_mean_var_9544sb1Aq))//11h""###1Aq))//11h D!!"""""###1))"(<<<*@*@!QGGBB    1)),,,1==BB B      1)),,,1==BB B    B     1)),,,1==BB B    B    B    1)),,,1==BB B    B    B    B     r2cd\}}gd}gd}ttj||||ddS)N)rPr)rcrrr2)g+&?gI$_@gKT@gؗVArr)rr6rm r)r_rrG rzrs r0 test_burr_isfzTestBurr.test_burr_isfsV1 & & &### q!Q//5AAAAAAr2N)rrrry r~ r r r8r2r0rp rp sV000( / / /(!(!(!TBBBBBr2rp ceZdZejdddgdZdZejdgddZd S) TestBurr12zscale, expected)rOgd~)r7gR톇T crtjdddd|}t||ddS)NgjAgjArrrrr)r6rx r r)r_rlrTrms r0r zTestBurr12.test_delta_cdfs?( ''S!Qe'DDxe444444r2c d\}}tjdz }dtjdzdz z }tjdzd|dzzz }tj}||||g}tj||d }t ||d dS) Nryrrrmrprr rrrr)rZrprr6rx r) r_rrG rr=r>rrrs r0test_moments_edgezTestBurr12.test_moments_edges 1uQw"%(2+ouaxCH%6S$)l1a  &&v..Su------r2z p, c, d, ref))rrrggx4/@)gҶOɃ;rrgI8aS@)rrg#gj\/@)g#aMR/rgr g!GAcltj|||}t||ddSr)r6rx rr)r_rqrrG rres r0test_isf_near_zerozTestBurr12.test_isf_near_zero s8 L  Q1 % %3U++++++r2N) rrrrrrr r r r8r2r0r r s [.<;=>>55>>5( . . .  [ 0 0 0,,,,,r2r c eZdZgdZgdZgdZejeeefZgdZ ddddd ej gZ gd Z e eee e e eZd d ddej d fddej dfddej dfgZejjdZejjdZejeZdZeejee5Z e!j"e Z#dddn #1swxYwYej$de#ddZ%ej$de#ddZ&ejjej'dej$de#ddZ(ejjdZ)ejjdZ*ej$ded Z+ejjej'dd!Z,ejjd"Z-d#Z.d$Z/d%Z0dS)&TestStudentizedRange)gQ1@g33333F@g ףp=*K@gHzM@g/$@g~j!@g33333$@g{Gz&@gh|?5 @gQ8@g&1@g|?5@g@gOn@g!rhm@gB`"@rtgʡEs@g|?5^@g/$@gV-@g/$@gF@g?5^I @)gRV@gffffffl@gp@gr@gʡ @gHzG/@gQ82@gQ3@g!rh@g@g +@gʡEs @gjt@gB`"[@g@gnJ@gV- @gFx@gsh|?@g+N@g/$ @g @g@gGz@)gfffff"@ii i gHzG2@g(\A@gQC@gfffffE@g @gNbX9"@gHz$@g(\&@g-@gn@@gw/@g= ףp @gJ +@g-'@gn@gHz@gV-@gnJ@g$@g/ݤ@)rArrrrrfrx)rmrr*r)rcri)#gupm1f?)rrfrg?<-=A?gv"?rgd暕?ga-A?c|jD]>\}}|\}}}tj|||}t ||d?dS)Nrr)rr6studentized_rangervr)r_pvkrz p_expectedrrbres_ps r0test_cdf_against_tablesz,TestStudentizedRange.test_cdf_against_tables; s_i : :FC" J1+//1a88E E:D 9 9 9 9 9 : :r2c|jD]>\}}|\}}}tj|||}t ||d?dS)Nrr)rr6r rr)r_r q_expectedrqrrbres_qs r0test_ppf_against_tablesz,TestStudentizedRange.test_ppf_against_tablesB s^#y : :OCGAq!+//1a88E E:D 9 9 9 9 9 : :r2z&data/studentized_range_mpmath_ref.jsonN case_resultcdf_datac|d}|d}|d|d|df}tjj|}t|||d|ddS Nsrc_case mp_resultrzrbr expected_atol expected_rtolri)r6r rvrr_r r r qkvrs r0test_cdf_against_mpz(TestStudentizedRange.test_cdf_against_mpN sz* , smXc]HSM9%)3/Y%o6%o6 8 8 8 8 8 8r2pdf_datac|d}|d}|d|d|df}tjj|}t|||d|ddSr )r6r rorr s r0test_pdf_against_mpz(TestStudentizedRange.test_pdf_against_mpY r r2z+intermittent RuntimeWarning: invalid value. moment_datac|d}|d}|d|d|df}tjd5tjj|}dddn #1swxYwYt |||d|d  dS) Nr r rrbrrrr r ri)rZrr6r rr)r_r r r mkvrs r0test_moment_against_mpz+TestStudentizedRange.test_moment_against_mpd sz* , smXc]HSM9[ * * * 7 7)0#6C 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 Y%o6%o6 8 8 8 8 8 8sAA!$A!cd\}}ttjjdtj||f}t |dddS)NrrfrrWr)rr6r rorZrr)r_rbrrs r0test_pdf_integrationz)TestStudentizedRange.test_pdf_integrationu sG15*.26AGGGA"""""r2cd\}}tjddd}tj|||dd}tj|||}t ||}t||ddS) Nr rrfr)steprrr)rZrr6r rvrorr)r_rbrrey_cdf y_pdf_rawy_pdf_cumulatives r0test_pdf_against_cdfz)TestStudentizedRange.test_pdf_against_cdf| s1 Ia$ ' ' ''++Aq!44QRR8+//1a88 / 1== (%d;;;;;;r2 r_case_resultc|\}}}}tjd5tj|||}dddn #1swxYwYt ||dS)Nrr)rZrr6r rvr)r_r rzrbrr_resrs r0test_cdf_against_rz'TestStudentizedRange.test_cdf_against_r s'1a [ * * * 7 7)--aA66C 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7U#####s"A  AActjd5tjddgddgddg}dddn #1swxYwYt |jd tjtd 5tjdddggd ddddS#1swxYwYdS) Nrrrrmrrrfrr$ z...could not be broadcast...r )rfrrQ) rZrr6r rrr=rr rrs r0test_moment_vectorizationz.TestStudentizedRange.test_moment_vectorization sh[ * * * H H'--q!fq!fr2hGGA H H H H H H H H H H H H H H H &&& ]:-K L L L C C  # ) )!aV\\\ B B B C C C C C C C C C C C C C C C C C Cs#(A  AA&B88B<?B<ctj5tjd5tjdt t jgd\}}}}dddn #1swxYwYdddn #1swxYwYtt j ||dS)Nrrr ) rrrsrZrrtrr6r rqr _argcheck)r_rbrrs r0test_fitstart_validz(TestStudentizedRange.test_fitstart_valid sN  $ & & G G H(E(E(E G G  !(,> ? ? ?1;;IIIFFKAr1a G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G '11!R8899999s5BAA7+ B7A; ;B>A; ?BBBctjddtj}tjddd}t ||ddtjddtj}tjddd}t ||dddS)Nrrf韆rri)r6r rorZrrrv)r_r res_finites r0test_infinite_dfz%TestStudentizedRange.test_infinite_df s%))!R88,00B>> Zd>>>>%))!R88,00B>> Zd>>>>>>r2cZtjddd}tjddd}tjddd}ttt ||ddt ||ddtjddd}tjddd}tjddd}ttt ||ddt ||dddS)Nrrfrr irqri)r6r ror[AssertionErrorrrv)r_rr res_sanitys r0test_df_cutoffz#TestStudentizedRange.test_df_cutoff s%))!R88,00B>> ,00B>> nosJd , , , , JTEEEE%))!R88,00B>> ,00B>> nosJd , , , , JTEEEEEEr2cd\}}}tj|||}t|dd|dksJdS)N)gaRA@riSrrr)r6r rr)r_rzrbrrqs r0 test_clippingz"TestStudentizedRange.test_clipping sO.1a  # & &q!Q / /15))))Avvvvvvr2)1rrrq05q01q001rZrrqspsrvskslistrr%rr_datarrrr rr ospathdirnamer path_prefix relative_pathopenrlfilejsonrpregenerated_datarr r xfail_on_32bitr r r r r r r r r r8r2r0r r  s ' ' 'C  ' ' 'C  ( ( (D c4( ) )B   B QBRV $B B 4GGBB'',, - -D *( Arv() Arv() B)* F [:::  [::: '//(++Kg}XEQ=gѭEG>>,,RVS99::;;;..rvs;;<<===++BFC8899:::,,RVS99::;;;//<<==>>>,,RVS99::;;;,,RVS99::;;;#<<<<<<<<<<<<<<<<< >Fa0000 Xem''d':: ; ;Fa0000 Xem''d';; < >H!444444s4CCCctjd}tjd|}tj|}d}t||ddS)Ni rgr)g ףp= ?gʡE?rrR)rZr[r\r6rrrr)r]rrrTs r0test_regression_ticket_1530r !sf )   ' 'C ,  #  6 6C \  c " "FH!444444r2c tjd}|d}dD]K}tj||z\}}t||dt|ddLdS)NrTr )rg6ArOrr)rZr[rrandnr6rrr)r]reoffsetrkrls r0test_gh_pr_4806r !s )   % %C " A'..\%%a&j11 UV#....s-----..r2cttjtjdddS)Nr@rN)r rZrCr6rr5r8r2r0test_poisson_logpmf_ticket_1436r !s2 BK ,,T377 8 899999r2cddg}|D]6\}}tj|d}t||7dS)aTest the powerlaw stats function. This unit test is also a regression test for ticket 1548. The exact values are: mean: mu = a / (a + 1) variance: sigma**2 = a / ((a + 2) * (a + 1) ** 2) skewness: One formula (see https://en.wikipedia.org/wiki/Skewness) is gamma_1 = (E[X**3] - 3*mu*E[X**2] + 2*mu**3) / sigma**3 A short calculation shows that E[X**k] is a / (a + k), so gamma_1 can be implemented as n = a/(a+3) - 3*(a/(a+1))*a/(a+2) + 2*(a/(a+1))**3 d = sqrt(a/((a+2)*(a+1)**2)) ** 3 gamma_1 = n/d Either by simplifying, or by a direct calculation of mu_3 / sigma**3, one gets the more concise formula: gamma_1 = -2.0 * ((a - 1) / (a + 3)) * sqrt((a + 2) / a) kurtosis: (See https://en.wikipedia.org/wiki/Kurtosis) The excess kurtosis is gamma_2 = mu_4 / sigma**4 - 3 A bit of calculus and algebra (sympy helps) shows that mu_4 = 3*a*(3*a**2 - a + 2) / ((a+1)**4 * (a+2) * (a+3) * (a+4)) so gamma_2 = 3*(3*a**2 - a + 2) * (a+2) / (a*(a+3)*(a+4)) - 3 which can be rearranged to gamma_2 = 6 * (a**3 - a**2 - 6*a + 2) / (a*(a+3)*(a+4)) )rO)rrrr)r)gUUUUUU?r= g^cQg333333rrN)r6rr)rVr. exact_mvskrs r0test_powerlaw_statsr !s[>, = ?E44 :~##Av#66!$ 333344r2cftjdd}t|ddS)Nrrr)r6rrrrqs r0test_powerlaw_edger !s/ a##ACr2cxtjdd}t|dtjdgd}t|t jddgtjdgd}t|t jdt j gdS)Nrrr)rgrOrrO)r6rErrrorZrr s r0test_exponpow_edger !s a##AC 1...//ARVS#&''' a!1!1!122ARVS26'*+++++r2chtjddd}t|ddS)NrrrO)r6gengammarorr s r0test_gengamma_edger !s1 1a##ACr2za, c, ref, tol))g`6Arg2j!@r)rrggA@r)rrrr)rrg#@r)g`FArgI~mr)gl$W}Lrg.I#Urcfttj||||dSr)rr6r rE)r.rrrSs r0test_gengamma_extreme_entropyr !s1"EN**1a00#C@@@@@@r2ctjddd}|dksJtjddd}|tj ksJdS)Nrrrr)r6r rorrZr)rqrs r0!test_gengamma_endpoint_with_neg_cr "sV 1a$$A 8888 > Ar * *D BF7??????r2ctjddd}t|dtjddd}t|ddS)NrrNrOg>rfgqq?)r6r rrr s r0test_gengamma_munpr "sZ Rb))A:&&& RR((A6"""""r2ctjgd}tjd5tj5tjddt tjddttj |dddn #1swxYwYddddS#1swxYwYdS)N)0g>X*ȿgPix#?g=?g&^?goϿg뵏˿gO_ZQ?g\?g~?g)/?gRܶ?g핚οgH߃[g?g S"gm_ пg7k?g#BF?g KU= ?gT?gZg[Qs?g2?g6Hwƭ8?g*- ?ga]?g'?g޻?g?J_?g~sw?g0FfͿgg"@ӿg?%:˿g&zM?g?Gg F?g~,g HgW2ҿgTzy?gwm ǿg@gW=ֿg 't?g".v1glg.Hꮿg,?g*˿rrz:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integer) rZrrrrrsrrrur6rLr)rG s r0test_ksone_fit_freezer "sS  / / / 0 0A X & & &    $ & &    #L"     #?    KOOA                                    s6B:AB" B:"B& &B:)B& *B::B>B>c rtjttddd }gd}t t j||dt t j|dzj|dt j|dzd z j }tj t j |t j|z }t ||d dS) Nrr r)gDB.g8_$g%`OAgjhwHRgWMB@v`g7VY}igۦx\Arg xg#g/dg3$gegd)gNq{3g يGǓgr 4g37' gfFg?dJgضg2, gm%gӅJgz;pg ɿ{gk2gij<%giVSͶgBR4g Q/Mr(ry+=y|=r) rZrr rrr6rrrealimagrr)rerTderivderiv_expecteds r0test_norm_logcdfr! 7"s  Dq#q))** + ++A000HEJLL''**H4@@@@EJLL''F 338(NNNNZ  q6z * *5 0 6EVEJ--a005:3D3DQ3G3GGHHNE>666666r2ctjgd}tjgd}tj|}t ||ddS)N)gMb{Gzg{Gztg~jtX)g#]>g~666UZ^^Aryc':':A>>BBB""1biS&9&91==>>>>>>>>>>>>>>>  BK   # # % %&&&  " "MMg~666UZ^^E1b111555 ))%B779KLLLMMMMMMMMMMMMMMMMMMs%BB11B58B5A9FF F zmethod, expectedrvg u%>g ;Q=roggRz\R>rgʎK$/gԆX1rgfHu@ge:@czttj|dddgd}t||ddS)Nrcrrrf)r rrr)r.r6r/ r)rrTrs r0test_ncx2_zero_ncr6 "sE )WUZ ( (!QB ? ? ?FFH5111111r2ctjddd}tjdd}t ||ddS)Nrfrr)rr r)rrrr)r6r/ rrr)rrTs r0test_ncx2_zero_nc_rvsr8 "sOZ^^raa^ 8 8Fz~~!~44HFH5111111r2cdtjddz}ttjdd|ddS)Nrfrrrrr r)rZrrr6r/ rv)r s r0test_ncx2_gh12731r; "sB RYq"   Bb11155555r2ctjgd}d\}}tj|||}gd}t ||ddS)N) gю] @gj%@gb y/7@gH@gIZ@g Xl@g'/2?8@gݰmА@gU @gy]`'@g@g*\@g48c@)rgh?8@r: ) rOrOrOrOrOg?gy[qD?rrrrrrrr)rZrr6r/ rr)renurr sf_expecteds r0test_ncx2_gh8665r? "st """ # #A %GB qRC ( (B'''K B %000000r2c d}d}tjtjd||tjd||d}tj|||}tj|||ztjd|zd|zz}t||d dS) Ni,irrrr+ rmrrr) rZrTr6r/ rrorrr)rr rencx2_pdf gauss_approxs r0test_ncx2_gh11777rC "s B B EJNN5"b11JNN5"b11u > > >Az~~aR((H:>>!R"Wbga"fq2vo.F.FGGLHl666666r2zx, c, expected))rmrg|1q?)rmrmg~?)rrV<3T1=)7yQCru lY<)rgvHGBg^b!*1=)rtrNgS?chtj||}t||ddSNr)r6 foldcauchyrrrerrTrs r0test_foldcauchy_sfrK #s4    Q " "BB%(((((r2r))rmg?)rrD )rE rF )g6ްPg8R#/cftj|}t||ddSrH )r6rIrr)rerTrs r0test_halfcauchy_sfrM #s2    Q  BB%(((((r2z p, expected))g?g*wӄZ>)333333?gN9?)rrO)rg8<,O@)rg:B)gl ׶w/gMb}[Pcdtj|}t||dSrz)r6rIrr)rqrTres r0test_halfcauchy_isfrP (#s0 QAAx     r2cxtjdd}t|dddS)Nrrr)r6r*rrv)rs r0test_foldnorm_zerorR 4#s6  # # #BAr2))rmrgwo {?)rrgGd-P/)rfr:gof?)rr:g Oul";chtj||}t||ddS)Nr)r6r*rrrJ s r0test_foldnorm_sfrT H#s3   1a BB%(((((r2ctjgddd}tjddgdd}td|D}t||tjgd}tjddg}td |D}t||dS) N)rrrOrrrOc3RK|]"}tjtj|fV#dSrzrZrIrrv s r0rz-test_stats_shapes_argcheck..W#s/88q"% *888888r2)rmr9rrmr9c3RK|]"}tj|tjfV#dSrzrW rv s r0rz-test_stats_shapes_argcheck..]#s/88q"%26 *888888r2)r6r"tuplerr()mv3mv2 mv2_augmenteds r0test_stats_shapes_argcheckr] R#s .  3 7 7C .  Sz1c 2 2C88C88888M$$$ -  lll + +C -  q#h ' 'C88C88888M$$$$$r2ceZdZdZdS) _distr_gencdSNr r8r_rer.s r0_pdfz_distr_gen._pdfh#srr2Nrrrrc r8r2r0r_ r_ g#s#r2r_ ceZdZdZdS) _distr2_gencd|z|zSra r8rb s r0_cdfz_distr2_gen._cdfm#Avzr2N)rrrrh r8r2r0rf rf l#s#r2rf ceZdZdZdZdS) _distr3_genc ||zSrzr8r_rer.r/s r0rc z_distr3_gen._pdfr#s 1u r2cd|z|zSra r8rb s r0rh z_distr3_gen._cdfu#sAvzr2Nrrrrc rh r8r2r0rk rk q#s2r2rk ceZdZdZdZdS) _distr6_genc||z|zSrzr8rm s r0rc z_distr6_gen._pdf}#ssQwr2cd|z|zSra r8rm s r0rh z_distr6_gen._cdf#ri r2Nro r8r2r0rq rq {#s2r2rq cteZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdZdS)TestSubclassingExplicitShapescrtdd}t|ddddS)Ndummyr.rrrrur r_ rror_ dummy_distrs r0test_correct_shapesz1TestSubclassingExplicitShapes.test_correct_shapes#s: gc::: [__Q!_,,b11111r2cvtdd}tt|jdfit ddS)Nrw Arx rru)r_ r[rrorrz s r0test_wrong_shapes_1z1TestSubclassingExplicitShapes.test_wrong_shapes_1#s> gc::: i!AAtayyyAAAAAr2c~tdd}tddd}tt|jdfi|dS)Nrw za, b, crx rrmrr)r_ rr[rro)r_r{ r/s r0test_wrong_shapes_2z1TestSubclassingExplicitShapes.test_wrong_shapes_2#sJ gi@@@ Q!q!!!i!;;s;;;;;r2cXtdd}tttfi|dS)Nrw r rx )rr[rr_ r_r/s r0test_shapes_stringz0TestSubclassingExplicitShapes.test_shapes_string#s2+++i33s33333r2cXtdd}tttfi|dS)Nrw z(!)rx rr[ SyntaxErrorr_ r s r0test_shapes_identifiers_1z7TestSubclassingExplicitShapes.test_shapes_identifiers_1#s2...k:5555555r2cXtdd}tttfi|dS)Nrw 4chanrx r r s r0test_shapes_identifiers_2z7TestSubclassingExplicitShapes.test_shapes_identifiers_2#2000k:5555555r2cXtdd}tttfi|dS)Nrw zm(fti)rx r r s r0test_shapes_identifiers_3z7TestSubclassingExplicitShapes.test_shapes_identifiers_3#s2111k:5555555r2cXtdd}tttfi|dS)Nrw za=2rx r r s r0"test_shapes_identifiers_nodefaultsz@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaults#s2...k:5555555r2cXtdd}tttfi|dS)Nrw z*argsrx r r s r0test_shapes_argsz.TestSubclassingExplicitShapes.test_shapes_args#r r2cXtdd}tttfi|dS)Nrw z**kwargsrx r r s r0test_shapes_kwargsz0TestSubclassingExplicitShapes.test_shapes_kwargs#s2 333k:5555555r2cXtdd}tttfi|dS)Nrw za, b, c, lambdarx r r s r0test_shapes_keywordsz2TestSubclassingExplicitShapes.test_shapes_keywords#s3(9:::k:5555555r2cGddtj}|d}t|ddtjddzdS)NceZdZdZdS)FTestSubclassingExplicitShapes.test_shapes_signature.._dist_gencFtj||zSrzr6rrc rb s r0rc zKTestSubclassingExplicitShapes.test_shapes_signature.._dist_gen._pdf#zq))A--r2Nrd r8r2r0 _dist_genr ## . . . . .r2r r.rrrmrur6rCrrorr_r r?s r0test_shapes_signaturez3TestSubclassingExplicitShapes.test_shapes_signature#s| . . . . .+ . . .y$$$TXXcQX'')<)?????r2cGddtj}|d}tt|jdfit dddS) NceZdZdZdS)STestSubclassingExplicitShapes.test_shapes_signature_inconsistent.._dist_gencFtj||zSrzr rb s r0rc zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.._dist_gen._pdf#r r2Nrd r8r2r0r r #r r2r rr rrrmr)r6rCr[rrorr s r0"test_shapes_signature_inconsistentz@TestSubclassingExplicitShapes.test_shapes_signature_inconsistent#so . . . . .+ . . .y'''i3AA$a...AAAAAr2cGddtj}|d}t|ddtjddzt|ddtjddzt t |jdfitddS) NceZdZdZdS)?TestSubclassingExplicitShapes.test_star_args.._dist_gencV|d}tj||zSNrr )r_rer0 extra_kwargs r0rc zDTestSubclassingExplicitShapes.test_star_args.._dist_gen._pdf#s$"1g zq))K77r2Nrd r8r2r0r r #s# 8 8 8 8 8r2r r r r!r )xxx)r6rCrrorr[rrr s r0test_star_argsz,TestSubclassingExplicitShapes.test_star_args#s 8 8 8 8 8+ 8 8 8 y ...TXXcrX22EJNN34G4G4JKKKTXXc2&& s(;(;B(>???i3??$2,,,?????r2cpGddtj}|d}t|dddtjddzdzt|dddtjddzdzdS) NceZdZdZdS)ATestSubclassingExplicitShapes.test_star_args_2.._dist_genc\|d}tj||z|zSr r )r_rer r0r s r0rc zFTestSubclassingExplicitShapes.test_star_args_2.._dist_gen._pdf#s)"1g zq))K7&@@r2Nrd r8r2r0r r #s( A A A A Ar2r zoffset, extra_kwargr ror )r r r r s r0test_star_args_2z.TestSubclassingExplicitShapes.test_star_args_2#s A A A A A+ A A A y 5666TXXc#2X>>Z^^C((+c1 3 3 3TXXc3++Z^^C((+c1 3 3 3 3 3r2cGddtj}|d}t|ddtjddS)NceZdZdZdS)BTestSubclassingExplicitShapes.test_extra_kwarg.._distr_gencr|dd}tj||zS)Nr r)popr6rrc )r_rer0kwargsr s r0rc zGTestSubclassingExplicitShapes.test_extra_kwarg.._distr_gen._pdf#s0%jj:: zq))K77r2Nrd r8r2r0r_ r #s# 8 8 8 8 8r2r_ r r rrr r )r_r_ r?s r0test_extra_kwargz.TestSubclassingExplicitShapes.test_extra_kwarg#sw 8 8 8 8 8, 8 8 8z///TXXaQX//1B1BCCCCCr2cGddtj}|d}t|dtjddS)NceZdZdZdS)ITestSubclassingExplicitShapes.test_shapes_empty_string.._dist_genc@tj|Srz)r6rrors r0rc zNTestSubclassingExplicitShapes.test_shapes_empty_string.._dist_gen._pdf#sz~~a(((r2Nrd r8r2r0r r #s# ) ) ) ) )r2r r rr r s r0test_shapes_empty_stringz6TestSubclassingExplicitShapes.test_shapes_empty_string#sq ) ) ) ) )+ ) ) )y###TXXc]]EJNN3$7$788888r2N)rrrr| r r r r r r r r r r r r r r r r r8r2r0ru ru #s"222BBB<<< 444 666 666666666666666666 @@@BBB @ @ @ 3 3 3 D D D99999r2ru ceZdZdZdZejeddZ ejeddZ dZ dZ d Z d Zd S) TestSubclassingNoShapescptd}t|ddddS)Nrw rrrur ry rz s r0test_only__pdfz&TestSubclassingNoShapes.test_only__pdf#s8 g... [__Q!_,,b11111r2cptd}t|ddddS)Nrw r rru)rf rrorz s r0test_only__cdfz&TestSubclassingNoShapes.test_only__cdf$s8!w/// KOOAO33Q77777r2docstring strippedroctd}t|jdt|jdt jd|j}tt|dkdS)Nrw r rr.zlogpdf\(x, a, loc=0, scale=1\)) r_ rnumargsrrefindallrr rr_r{ rs r0test_signature_inspectionz1TestSubclassingNoShapes.test_signature_inspection$sr!g... [(!,,,['---j:$,..CA r2ctd}t|jdt|jdt jd|j}tt|dkdS)Nrw r rmrz!logpdf\(x, a, b, loc=0, scale=1\)r) rq rr rr r rr rr s r0test_signature_inspection_2argsz7TestSubclassingNoShapes.test_signature_inspection_2args$sr"w/// [(!,,,['000j=$,..CA r2c>tttddS)Nrw r )r[rrk r^s r00test_signature_inspection_2args_incorrect_shapeszHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapes$si7;;;;;;r2cxGddtj}tt|fit ddS)NceZdZddZdS)>TestSubclassingNoShapes.test_defaults_raise.._dist_genr cdSra r8rb s r0rc zCTestSubclassingNoShapes.test_defaults_raise.._dist_gen._pdf$$rr2N)r rd r8r2r0r r #$s(      r2r rw r r6rCr[rrr_r s r0test_defaults_raisez+TestSubclassingNoShapes.test_defaults_raise!$Z     +    iAAd.@.@.@AAAAAr2cxGddtj}tt|fit ddS)NceZdZdZdS)>TestSubclassingNoShapes.test_starargs_raise.._dist_gencdSra r8)r_rer.r0s r0rc zCTestSubclassingNoShapes.test_starargs_raise.._dist_gen._pdf+$r r2Nrd r8r2r0r r *$#     r2r rw r r r s r0test_starargs_raisez+TestSubclassingNoShapes.test_starargs_raise($r r2cxGddtj}tt|fit ddS)NceZdZdZdS)._dist_gencdSra r8)r_rer.r s r0rc zATestSubclassingNoShapes.test_kwargs_raise.._dist_gen._pdf2$r r2Nrd r8r2r0r r 1$r r2r rw r r r s r0test_kwargs_raisez)TestSubclassingNoShapes.test_kwargs_raise/$r r2N)rrrr r rrrDOCSTRINGS_STRIPPEDr r r r r r r8r2r0r r #s222888  [+4HIIJI [+4HIIJI<<<BBBBBBBBBBBr2r r cgd}tjD]l}tt|}t|tjtjzr.|D]+}t tj||j du,mdS)N)z,\s*,z\(\s*,z^\s*:) r6rNr.r?rBrCr r searchr)badonesdistnamer?regexs r0rr7$s---GM@@uh'' dU.1DD F F @  @ @ %66$>???? @@r2cttjtjdddttjtjddddS)Nrfrrrrcr)rr6rIrrZrr/ rh r8r2r0test_infinite_inputr A$sR ((R88!<<< 377;;;;;r2ctjtjddd}t |ddSr)r6lomaxrrvrr s r0test_lomax_accuracyr F$s=  22A66AAvr2ctjtjddd}t |ddSr)r6rArrvrr s r0test_truncexpon_accuracyr L$sC U-11&!<,,Q22A66A3++++++r2ctjd5}tjdtjddtjddtjddtjtj dt|}t|dddddS#1swxYwYdS)zregression test for gh-6219T)recordalwaysrrrN) rrrsrtr6r-rvrorrrZrrr)rnumber_of_warnings_throwns r0 test_genextreme_give_no_warningsr X$s   - - -3h''' R### R### R### ---$'FF!.222333333333333333333sB?C""C&)C&cPtjtjdtjddgd}tj}tjdzdz }dtjdztj d ztjd zz }d }||||g}tjgd zx}}gd }t|ddd f|dt|dddf|t|dddf|dt|ddd f|dS)NrrrSrrrmr/rQrr9r)rrrr/rrr) rZrr6r-r euler_gammarprrzetarr) rrr=r>r?ref_0ref_1ref_3ref_2s r0test_moments_gh22400r f$s# *U%++S"&!T,BF+SS T TC >D %(Q,C  ?W\!__ ,ruax 7D D 3d #EVHQJEE MMEC1Iu51111QQQTE"""C1Iu51111QQQTE"""""r2cd}tjd}t|d|zdzdtjd}t||dzdtjd}t |dtjd d }t||d zt jd zdzdtjd }t|d |zdzdtjd}t|d|zdzddS)Ngox?rrmrrrrrOrrfrrrrhr)r6r-rErrrZr)r rks r0test_genextreme_entropyr |$sD$K   &&AAq}q(u5555   ##AA{QU3333   %%AA   R 00AA{1}rvbzz1A5EBBBB   $$AAr+~)6666   %%AAr+~)666666r2cRd}tj|d}t|dtj|d}t||d}tj|d}t|dtj|d}t||d}tj|d}t|dtj|d}t||dS) Nrrvg'b%4gQ@rtgؗҜ;rg.l6?)r6r-rrr)rerKrps r0test_genextreme_sf_isfr $s 2 A Av&&AA-...    a ( (BB A Au%%AA()))    a ' 'BB A Aq!!AA-...    a # #BBr2cld}tj|dd}t|ddS)Nr~rmrgH&8>)r6rx rr)probr s r0test_burr12_ppf_small_argr $s9 D|a++HH455555r2cd d}tjgd}tj|d|\}}}t |dd|dksJt |d dd S) a? Test fitting invweibull to data. Here is a the same calculation in R: > library(evd) > library(fitdistrplus) > x = c(1, 1.25, 2, 2.5, 2.8, 3, 3.8, 4, 5, 8, 10, 12, 64, 99) > result = fitdist(x, 'frechet', control=list(reltol=1e-13), + fix.arg=list(loc=0), start=list(shape=2, scale=3)) > result Fitting of the distribution ' frechet ' by maximum likelihood Parameters: estimate Std. Error shape 1.048482 0.2261815 scale 3.099456 0.8292887 Fixed parameters: value loc 0 r8rc,t||||ddS)Nr)r0dispxtolftol)r#)rx0r0r s r0rz&test_invweibull_fit..optimizer$sD"4dUKKKKr2)rrrmr~rtrrrrrrfrQ@c)rrg`?ryrg [@N)r8r)rZrr6r$rr)rrerrkrls r0test_invweibull_fitr $s.LLLL HHHIIA$((i(HHMAsEAxd++++ !8888E8$//////r2))rrg7Ըh?)rrgz]r>)rg"@goBڱ9)rrg$=cC;cjtj||}t||ddSr)r6r$rr)rerrTr@s r0test_invweibull_sfr $s7 ""1a((HHhU333333r2zp, c, expected)rr~g9?)geK@g&4I,)?)decimals)r6rrvrrZround) scipy_val check_vals r0test_ncf_cdf_spotcheckr) #%sG  b!R..IIIrx A>>>?????r2ctjddd}d|d<dtjj|gR}fd|D}t ||dS)Nrrrr~)rcrmrrrc>g|]}tjj|gRSr8)r6rr)r>xipars r0r@z,test_ncf_ppf_issue_17026..3%s- . . .b%)- !S ! ! ! . . .r2)rZrTr6rrr)rerzq0r- s @r0test_ncf_ppf_issue_17026r/ -%sl Aq#A AaD C a#A . . . .A . . .BArr2c2eZdZdZdZdZdZdZdZdS) TestHistogramc^tjd|_tjgdd}t j||_t j ddd|j}tj|d }t j||_ dS) Nl&')rrmrmrrrrrrrrrrrrr/r/r/r/rrrrrrrbinsrOr~rr<r8) rZr[r\r] histogramr6rDtemplaterr norm_template)r_r5 rnorm_histograms r0r`zTestHistogram.setup_method8%s9((44L"@"@"@FGIII *955 z~~#Su48~TTd444"/??r2ctjgd}tjgd}t|j||t |jddt |jddt |jddt |jddtjd d d }t|j|tj |d d ddS)NrrrOrrr~rr7rr5rP@rrrrr !@rr;)rrrHrH{Gz?r= Q?r> {Gz?r? rLrLr? r? r> r> r> r> rrr r> r< rrrrrmrfrOr~rjrcr) rZrrrr6 rorrTr7 r6r)r_r] pdf_valuesres r0rMzTestHistogram.test_pdfH%sXMMMNNZ!I!I!IJJ  ))&11:>>> DM--c22H===DM--c22H=== DM--c22H===DM--d33X>>> KAr " "*..q11 qc==C I I I I I Ir2c6tjgd}tjgd}t|j||t|j|dd|ddtjddd}t|j|j||tjddd}t|j|j||tjd dd }t|j|tj |dd d dS)Nr: )rrrrrHr= r> ףp= ?Q?{Gz?rrr(\?RQ?= ףp=?)\(?r( rOrOrmrrOrrgrrrfr~rjrcr) rZrrrr6 rvrrTr7 r6r)r_r] cdf_valuesres r0rzTestHistogram.test_cdf_ppfb%sMMMNNZ!M!M!MNN  ))&11:>>> ))*QrT*:;;VAbD\JJJ KS# & & ))$-*;*;A*>*>??CCC KS# & & ))$-*;*;A*>*>??CCC KAr " "*..q11 qc==C I I I I I Ir2cDd}|j||j}tt j|dkdt t j|dkd|zdt t j|d kd |zdt t j|d kd |zd t t j|dkd|zd t t j|dkd|zd t t j|dkd|zd t t j|dkd|zdt t j|dkd|zdt t j|dkd|zdt t j|dkd|zdt t j|dkd|zdt t j|dkd |zdt t j|d!kd"|zdt t j|d#kd$|zdt t j|d%kd|zdt t j|d%kd|zdtt j|d%kddS)&NrrrOrrrHrLrr~r= rr> rcr7rB rrC r5rD rPrrAr; rrrrrE rrF rrG r rH r< r( r)r6 rr]rrZrhr)r_r-r\s r0rEzTestHistogram.test_rvsx%s """AARVFSL))3///v}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--x!|#FFFFv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHv}--y1}4HHHHRVFSL))3/////r2ctdD]R}t|j|t jdd|dSdS)NrrOr~rAr)rrr7 rr6rrr{s r0r" zTestHistogram.test_munp%sxq G GA D.44Q77!JsC0077:: G G G G G G Gr2ct|jtjddddS)NrOr~rjrAr)rr7 rEr6rr^s r0rlzTestHistogram.test_entropy%sT*2244 **s#*>>T K K K K K Kr2N) rrrr`rMrrEr" rlr8r2r0r1 r1 7%s@@@ III4III,000,GGG KKKKKr2r1 cddggd}}tj||fd}tj|ddgddg|dksJtj||fd}tj|ddgd |d ksJd }tjt| 5tj||f}|d ksJ dddn #1swxYwYtj|gd f}|dksJdS)Nr)rrrF)rrrNrTg'^P?gH@z(Bin widths are not constant. Assuming...r r=) r6rDrZrrrorDrrz ru)countsr4 r?rws r0test_histogram_non_uniformrO %sFLLLDF  vtne < < i##$78811%%kk!QTk**#//555hhDsh33#//555 4%% %hhqkkCRCQRR("---Aq BF1II-. T*****r2N) rrrrX rrrrZ r\ r8r2r0rQ rQ %sd444" [Xt}55  65 +++++r2rQ ceZdZdZejdddgddgddggd Zejd d d gd ZejdgddZ ejdgddZ ejdgddZ ejdgddZ ejdgddZ ejdgddZejdgdd Zejdgd!d"Zd#S)$ TestArgusctjddd}ttjd|ddS)Nr8rErrrR)r6argusrrrrs r0test_argus_rvs_large_chiz"TestArgus.test_argus_rvs_large_chi%sR KOOBSsO ; ;EKOO0022AFFHHaHHHHHHr2zchi, random_statercr` rr7ctj|d|}tj|d|f\}}t |dkdS)Nrrra rAr6ra rrDr )r_rrrerrqs r0rEzTestArgus.test_rvs%sN KOOCc O E E|Aw001Dr2rrrqctj|dd}tj|d\}}t |dkdS)Nrie rcdd|dzz dzz S)Nrrmrr8rs r0rLz.TestArgus.test_rvs_small_chi..%sa!Q$h#->)>r2rArf )r_rrrrqs r0test_rvs_small_chizTestArgus.test_rvs_small_chi%sN KOOCcO ? ?|A>>??1Dr2zchi, expected_mean))rgщi?)rfg.憃?)rxg\paP?)ryg ?)r g,6?cltj|d}t||ddS)Nrrrr)r6ra rr)r_r expected_meanrs r0rzTestArgus.test_mean%s9 K  S  * *=u555555r2zchi, expected_var, rtol))rgLH'B?r)rfgo$?r)rxg =>r()ryg2W>r()r gb~P>r(cltj|d}t|||dS)Nrrr)r6ra r=r)r_r expected_varrrs r0r zTestArgus.test_var &s6 KOOCqO ) )r)rgF=r)rg߹Q#B=r)rqg0ޟ)rRr~g=~L]=)rRrgD,G '=cjtj||}t||ddSr)r6ra rr)r_rerrTrs r0test_sf_near_1zTestArgus.test_sf_near_1@&s4[^^As # #H5111111r2))r)g+&?gk?gμm/?)rL)g?CL\f?g^N?g]AͭR?)rc)ga>$?g;Lf?gaW?)r)gx?g43n?gwY?)r)go7🤎?g +-oGn?gIQ9‹Y?)r)g T?gGn?g@̋Y?)rq)gU?g{Gn?giG͋Y?)r)gDU?g{Gn?gH͋Y?ctjgd}ttj|||ddS)Nrq rr)rZrrr6ra rvrr s r0test_cdf_small_chizTestArgus.test_cdf_small_chiK&rt r2))r)g Q)?g6{?r)gB`"۹?)g?g8%?r)rc)g388?gV%?r)r)g*j?gRS%?r)r)g! |?gZ%?r)r)gy[|?gG%?r)rq)g"3|?gW%?r)r)g!3|?gW%?rcltj|d}t|||dS)Nrrr)r6ra r)r_rrTrrDs r0test_stats_small_chizTestArgus.test_stats_small_chiZ&s9kT22XD111111r2N)rrrrb rrrrEri rr ro rs rv ry r{ r} r8r2r0r^ r^ %sIII  [0 #J #J #J3        [UT4L1121 [188899 66 99 6  [6BBBCC 44 CC 4  [2DDDEE>>EE> [ M M M N NGG N NG  [ N N N O OFF O OF  [ 6 6 677 22 77 2  [ P P P Q QGG Q QG  [ C C C D D22 D D222r2r^ ceZdZdZdZdZdZdZej dgddZ ej dgd d Z d Z ej d gd dZej dej dgdej dgdej dgddZej dgdej dgddZdS) TestNakagamicNtjd|_dS)Nli{rYr^s r0r`zTestNakagami.setup_methodj&rar2cnd}d}tj||}t|ddS)Nr~rgM+)r6nakagamirr)r_r= rers r0rzTestNakagami.test_logpdfm&s< ~$$Q++122222r2cd}d}tj||}t|ddtj||}t||ddS)Nr~rPg"S+:rr)r6r rrr)r_r= r rros r0rzTestNakagami.test_sf_isf~&sm  ^  r2 & &1>>>> ^  B ' 'BU++++++r2cvd}d}d}tj||}t||ddS)NrrgU iּrr)r6r rr)r_rer= rrs r0rzTestNakagami.test_logcdf&sC  %&&q"--%000000r2cvd}d}d}tj||}t||ddS)NrArQgD&`Urr)r6r rr)r_rer= rrs r0rzTestNakagami.test_logsf&sC  %$$Q++s//////r2zm, ref))rg|Bd븿)rr)rfg/ۿcdttj||ddS)Ng^~z=rrr6r rEr_rrs r0rlzTestNakagami.test_entropy&s/ ..q113WEEEEEEr2))rg}Ô%I)rgq_)gScAgB4U)gcAgu1U)rgb >%)rgWҙ\c`ttj||dSrzr r s r0test_extreme_nuzTestNakagami.test_extreme_nu&s* ..q11377777r2ctjtjdsJtjtjdsJdS)Nrr)rZrCr6r _entropyr^s r0test_entropy_overflowz"TestNakagami.test_entropy_overflow&sT{5>22599:::::{5>226::;;;;;;;r2znu, ref))rg2H?)rg:U?)rg>cdttj||ddSr)rr6r r)r_r= rs r0rzTestNakagami.test_mean&s/ ++B//5AAAAAAr2z+Fit of nakagami not reliable, see gh-10908.ror= )rr~rrk)rrfr rl)rrrc d tj ||||j tj \}}}t ||dt ||dt ||d fd} fd} fd} t ||||dd t ||||dd t | |||dd dS) Nrgrr= rkrlrrLrcd|zdztjd|z z zd|z|dzz tj|z zzS)NrrrmrZrh)r= rkrlras r0 dlogl_dnuz(TestNakagami.test_fit..dlogl_dnu&sRUQY"&GcM):";";;d5!8mbfWs]&;&;;< =r2cdtj|ztd|z zdtjtj|z |z zztj|z |z dzz S)Nrrrm)rZrrrhr= rkrlr-ras r0 dlogl_dlocz)TestNakagami.test_fit..dlogl_dloc&svRVBZZ)Ar*:*::;rvw}&=>>???@fw}59::; .dlogl_dscale&sG!GbL5("fuz)BFGcMa3G,H,HHI Jr2rrr)r6r rr]rr) r_r= rkrlnu_estloc_est scale_estr r r r-ras @@r0rvzTestNakagami.test_fit&s] .$$!+0tx%II%*^%7%7%@%@"----3//// 5s3333 = = = = = < < < < < <  J J J J J J  &'9==qtLLLL 67I>>MMMM VWi@@!$OOOOOOr2cd}d}tj|||||j}tj||\}}}t j|} t jt j||z dz} t||dt|| dt|| ddS)Nrrgr rrmr(r) r6r rr]rrZrrrr) r_rkrlr= rprar r r loc_theo scale_theos r0 test_fit_nuzTestNakagami.test_fit_nu&s  .$$!+0tx%II%*^%7%7B%7%G%G"6'??WRWg&7A%=>>?? ....5555 :D999999r2N)rrrr`rrrrrrrrlr r rrrvr r8r2r0r r i&s(555333",,,&111000 [X % % %&& F F && F [X D D DEE88 EE8<<< [Y>>>??BB ??B [KLL [T???33 [UNNN33 [Wkkk22PP324343MLP8 [UNNN33 [Wkkk22::3243:::r2r c >eZdZdZdZdZdZej dddgej dd d e j ze j d e j d e j zd gej dgddZ dS)TestWrapCauchycNtjd|_dS)Nl3R"rYr^s r0r`zTestWrapCauchy.setup_method&rar2cLtjddgddgg}tjdgdgg}tj||}|jdksJdtj||fD}t||d dS) NQ?rgrrrOrrycTg|]%\}}tj||&Sr8)r6 wrapcauchyrv)r>rorP s r0r@z>TestWrapCauchy.test_cdf_shape_broadcasting.. 's?<<<%b")--b"55<<???!a")Brvbebdl/C/C,C"D"DRU"JJKKKKKr2rrrcrkrrrrmrgrl)rrrctj|||d|j}t j|dksJt j|dtjzksJdS)Nr)rrkrlrrrrm)r6r rr]rZrrp)r_rrkrlres r0test_rvs_lie_on_circlez%TestWrapCauchy.test_rvs_lie_on_circle'sn   1#U&* ! C Cva1f~~va1ru9n%%%%%%%r2N) rrrr`r r rWrrrrZrpr r8r2r0r r &s555 > > >,,,LLL [S5$-00 [UT2be8beVQqwPS$TUU [W&6&6&677&&87VU10&&&r2r cGddtj}|d}tjd}t t d5||ddddS#1swxYwYdS) NceZdZdZdS)/test_rvs_no_size_error..rvs_no_size_gencdSrr8r^s r0_rvsz4test_rvs_no_size_error..rvs_no_size_gen._rvs)'s1r2N)rrrr r8r2r0rvs_no_size_genr ('s#     r2r rvs_no_sizer i_Oz_rvs\(\) got (an|\d) unexpectedr r)r6rCrZr[r\r[rr)r r r]s r0test_rvs_no_size_errorr &'s%-"/}555K )   + +C y(J K K K**S)))******************sA>>BBzdistname, argscn|tvrtjd|dtt|}t |tjrt|dkrA|j|\}}t|tj t|tj d\}}|jg|||R\}}t|tj t|tj dS|j|\} } t| tj t| tj dS)Nz6skipping test for the support method for distribution .rr) $skip_test_support_gh13294_regressionrrr.r6r?rCrr rrZr) r r0r?a0b0r1r2a1b1r.r/s r0test_support_gh13294_regressionr 2's8777 0$,000 1 1 1 5( # #D$+,, t99>>!T\4(FB RV $ $ $ RV $ $ $  f2t2T26222BR   R     t|T"1QQr2c\tjgdgd\}}tjtj tj tj tjg}tjtjtjtjtjg}t||t|||j|jksJ|j|jksJtjgg\}}tjgtjg}}t||t|||j|jksJ|j|jksJtjgddg\}} tjdtjgz} tjdtjgz} t|| t| | |j| jksJ| j| jksJdS)N)rrrr)rrrrrr) r6rr rZrrrrr=) r r ex_a0ex_b0r r ex_a1ex_b1rrex_a2ex_b2s r0,test_support_broadcasting_gh13294_regressionr M's Z   mmm < >#u % % +v 5 5 5 5 5 5r2)gn! g:I"<)gQ @gE?cttj||ttj| |dSrz)rr6cosinervr)rerTs r0test_cosine_cdf_sfr t'sJEL$$Q''222ELOOQB''22222r2))rqgkM6O)rg0ӭ! )rN g;'u(@cttj||ttj|| dSrz)rr6r rr)rqrTs r0test_cosine_ppf_isfr |'sL EL$$Q''222EL$$Q''(33333r2ctjtj tjg}t |ddS)NgrB)r6r rrZrpr )rs r0test_cosine_logpdf_endpointsr 's: <   / /Dd./////r2cdtD}dtD}||ksJdtD}dtD}||ksJdS)NcBh|]\}}t|t|Sr8)r?rHr>rrs r0 z*test_distr_params_lists..'s:44474'c224$444r2ch|]\}}|Sr8r8r s r0r z*test_distr_params_lists..'sAAAgdATAAAr2ch|]\}}|Sr8r8r s r0r z*test_distr_params_lists..'s333wtQd333r2ch|]\}}|Sr8r8r s r0r z*test_distr_params_lists..'s999'$999r2)rrrr)discrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamess r0test_distr_params_listsr 's44l444AAAAA !6 6 6 6 633(333N99[999 . . . . . . .r2ctjddtjdddksJtjdddksJdS)Nrrbrwr)rr.r)r6r_statsrrr8r2r0test_moment_order_4r 'sr NAs+++ > qA . .# 5 5 5 5 >  1 % % , , , , , ,r2c eZdZejdZejdgddZejdgddZ ejj ejdej d d ejj ej d d ejj ej ddejj gdZ dS)TestRelativisticBWctjttjdz }tj|jd}|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.npyzx,pdf,rho,gammarrrys r0ROOT_pdf_sample_dataz'TestRelativisticBW.ROOT_pdf_sample_data'sMw NN ! ; <  v  /@ AA r2zrho,gamma,rtol))qVEB@gj+@rN)‰FC@Gz@r)ND@_LU?r/c||d|k|d|kz}|d|d}}t|tj||||dS)Nrhorrerorr)rr6rel_breitwignerro)r_r r rrrreros r0test_pdf_against_ROOTz(TestRelativisticBW.test_pdf_against_ROOT's$ !% (C /#G,5 7 cDK3 &**1c*??d      r2zrho, Gamma, rtol))r r r/)r r r/)r r g& .>cd}tjddd}tj|||}tj|||}||||z|}t |||dS)Nctj|dz|dz|dzzz}dtjdz|z|z|ztjtj|dz|zzz }||dz|dzz dz|dz|dzzzz Sr)rZrrp)ErGammarrbs r0rozFTestRelativisticBW.test_pdf_against_simple_implementation..pdf'sGAqDAqD5!8O455ERWQZZ!#e+e3EBGAqD5L1113AA1q(1a4q=89 9r2rArArfrr)rZrTr6r rror) r_r r rrorqrerrs r0&test_pdf_against_simple_implementationz9TestRelativisticBW.test_pdf_against_simple_implementation's : : : KdB ' '  ! % %aE % : :#''3e'<<c!SY&&St,,,,,,r2z rho,gammar r rr r r r cd}tj|}tj||d|}tj|d}t|d|df||fd|d dksJtj|d| }t|d|d |d |dfd|fksJd S) zpTests fit for cases where floc is set. `rel_breitwigner` has special handling for these cases. ls ; rl#rrrrrmrLrrr=rN)rZr[r\r6r rrr)r_r rrr]rrs r0 test_fit_flocz TestRelativisticBW.test_fit_floc's&#i##D))$(( u4c)  #''1'55QQ(3,TBBBB1v{{{{#''1U'CCA$////AAAu:------r2N)rrrrrr rrr r rrrr r8r2r0r r 'se ^^$ [       [/2 2 2  - -  - [ [ FL"F&+2B    FL!5 0A    FL & 0A       ..  ...r2r cZeZdZejdddgdZdS) TestJohnsonSUr)r# rrrg={?g?5mV>gn?g\}\1@)g`fo@g$ں _@rrgvUg Nv>>T!""XE222222r2N)rrrrrrr r8r2r0r r (sZ [V O J&KLL 33 LL 333r2r c8eZdZdZdZejdddgejdddgejdddgejdddgd Zd S) TestTruncParetocHd\}}tjdd}tj|||}tj||tj||z }t||dS)N)?333333@r r )rZrTr6 truncparetororrvr)r_r/rrerrs r0rMzTestTruncPareto.test_pdf(s1 KS ! !1%%))!,,l1oo!!!$$u|A':':1'='==S!!!!!r2c d\}}}tj||}|||z||zz z }|||dz zz}| }||z }|} d} tj||| | } t | ||t | |tj| |t | |ddtj| |ddt | |ddtj| |dddS)N)rrrrrr) rZrTr6r rrorrrrvrr) r_r.xminxmaxreCrr/rrlrkrs r0test_pdf_negativez!TestTruncPareto.test_pdf_negative!(sG 4 Kd # # TQY& '!A,B 4K  aC / /a#&&& RVAEE!HH%5%5666122ae )=)=>>>#2#QssV )=)=>>>>>r2rTFr9rrctjd}d\}}}} tj|||| } | d|} i} |r|| d<|r| | d<|r|| d<|r|| d <|rU|rS|rQ|rOd } t jt| 5tjj | fi| ddddS#1swxYwYdSttj| fi| dS) NlZ #Lm)r r rr~rjrrrrrr r r ) rZr[r\r6r rrr rrr)r_rr9rrr]r/rrkrlr?rrrws r0rvzTestTruncPareto.test_fit8(s} i##$788+1c5 A3e<<<xxSsx33  DL  #"DN  DJ  DJ  Ky KU Ku KKG|7;;; 4 4!%d33d333 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 *%*;T J JT J J J J JsB>>CCN) rrrrMr rrrrvr8r2r0r r (s"""???. [Yu 66 [[4-88 [WtUm44 [WtUm44KK54549876KKKr2r ceZdZdZdS) TestKappa3cdtjddz }tjdd}t ||dS)Nrrgj@)r6kappa3rvrr)r_sf0rts r0rzTestKappa3.test_sfV(sK%,""3,,,looc3''S!!!!!r2N)rrrrr8r2r0r r U(s#"""""r2r ceZdZejddZejdZejdZdZ dZ dZ dZ dZ d Zd Zd Zd Zd S) TestIrwinHallrrrfcVt|jdddS)Nr)rg?rgQ)r ih10r6r^s r0test_stats_ih10zTestIrwinHall.test_stats_ih10d(s) TY__V446JKKKKKr2cgd}fdtt|D}t||jd}d}t||dS)N) rgUUUUU9@g0a@igx@gn۶mˠ@g:PAg8)AgSAcJg|]}j|dz Srr )r r)r>rpr_s r0r@z3TestIrwinHall.test_moments_ih10..q(s-CCCQ49##AaC((CCCr2r8g2⍚H)rrr r r)r_rCrm50 m50_exacts` r0test_moments_ih10zTestIrwinHall.test_moments_ih10j(s~---DCCC%D 2B2BCCCWd+++ir""H S),,,,,r2ctjddd}|j|}|j|}t ||ddSNrrrgrfmaxulp)rZrTunifroih1r )r_ptspdf_unifpdf_ih1s r0test_pdf_ih1_unifzTestIrwinHall.test_pdf_ih1_unifx(sXk!Q$$9==%%(,,s##Whr::::::r2ctjd}d}tjdd|}tjdd|}d||dzdzdz ||dzdzd<||}t ||ddS)Nrmrdrrrfr )r6rrZrTror )r_ih2nptsr rTpdf_ih2s r0test_pdf_ih2_trianglez#TestIrwinHall.test_pdf_ih2_triangle(soa  k!Q%%;q!T**%&4!8/2B2B)C%C$(q!!"''#,,Whr::::::r2ctjddd}|j|}|j|}t ||ddSr )rZrTr rvr r )r_r cdf_unifcdf_ih1s r0test_cdf_ih1_unifzTestIrwinHall.test_cdf_ih1_unif(sVk!Q$$9==%%(,,s##Whr::::::r2ctjdd}tj|}||dz }tjdt |}t||ddS)Nrrfrmrr )rZrr6rrvrrr )r_rpihih_cdfexacts r0rWzTestIrwinHall.test_cdf(sg Ia   _Q  A #s1vv&&VU2666666r2c2gd}t|jtjd|dt|jdddd}t|jd|ddS) N) rg\xO~>g-P2?g8ʝi?gg{Ȇ?rg&M?g׈Y?gB?gD l?rrrfr rcg+|gP3NV?g*8f?gNgX?gjS?rrrfr )r r rorZrrs r0test_pdf_ih10_exactz!TestIrwinHall.test_pdf_ih10_exact(s\JII $ttt*,,TY]]29R==994KKKKKKr2c ,t|jtjdd|jtjdz d}t |jd|ddS)NrrrOrcrfr )rr rrZrrvr )r_rs r0test_sf_ih10_exactz TestIrwinHall.test_sf_ih10_exact(st RYr]]33QryQS}}9U9U5UVVV2TY\\$//R@@@@@@r2N)rrrr6rr rr r r r r r$ r( rWr. r0 r2 r8r2r0r r _(s 5=A  D %/!  C 5?2  DLLL - - - ; ; ;;;;;;;777CCC LLLAAAAAr2r ceZdZdZdS)TestDParetoLognormcd\}}}}}tj||||}tj||dtj||ddS)N)rrrtrrmg6Z?g@# ?)r6dpareto_lognormrZrrrorv)r_rerrKr.r/r?s r0test_against_Rz!TestDParetoLognorm.test_against_R(su, 1aA$Q1a00 ""488A;;0CDDD ""488A;;0CDDDDDr2N)rrrr7 r8r2r0r4 r4 (s(EEEEEr2r4 r))r NNNN)rNNNN)r(NNNN)r NNNN)rNNNNc|\}}}}}tjd}|pd}|pd}|pd}|pd}tt|}t t |}||} tj||} | | | } t| | ||dtj||dz } | | | } t| | ||dS) Nriirrrirr) rZrV r.r6rrrrrr) rr lp1lp2rrlpmr?r dist_frozenrrs r0test_sf_isf_overridesr= (s &*"Hc3d (3--C +C *C 91D =5D 5( # #D (^^H %F$-K +c3  C ..-- . .CC4d3333 bk#sB'' 'C ..-- . .CC4d333333r2rz)NF(rrrr rr rpathlibrr r rh numpy.testingrrrrrr r r rr r[numpyrZr rnumpy.lib.recfunctionsrr5rscipy._lib._utilrr6rrrr scipy.statsr6!scipy.stats._distn_infrastructurerscipy.stats._constantsrscipy.stats.distributions scipy.specialrrrscipy.stats._distr_paramsrrtest_discrete_basicrrscipy.stats._continuous_distnsr r!scipy.optimizer"r#r$ itertoolsr%flagsoptimizer rkrr r1r9rUrWrrrrr1r3rYrrrrrrr0r<rdrrrrrr rr&r-rGrLr_rir}rrr(rMrXr[rrrrr r$r:rHroryrrrrrrrrrr/rYrrrrprrrrr rr2r?rCrGrRr`rrrrrrrrrrrrr r. r r r r r r r r r r r1 r; r] rb ri rp r r r r r rr r r r r r r r r r r r r r r! r$ r& r) r- r1 r4 r6 r8 r; r? rC rK rM rP rR rT r] rCr_ rf rk rq ru r rr r r r r r r r r r r r r! r# r) r/ r1 rO rQ r^ r r r r r r r r r r r r r r r r r4 r= r8r2r0rO s!  DDDDDDDDDDDDDDDDDDDD ******""""""""444444//////333333333333888888(((((( 0000000000;;;;;;;;>>>>>>>>CCCCCCCC==========i(1,|x'M.>h.>.@.@H.L )6z'B$$$$$ 888   J@J@J@J@J@J@J@J@Z4444D....>>>?? 6 6 ?? 699999999>G,G,G,G,G,G,G,G,T********>O,O,O,O,O,O,O,O,d<B<B<B<B<B<B<B<B~D/D/D/D/D/D/D/D/N########>>>>>>>*7D7D7D7D7D7D7D7Dt C C C C C C C CA2A2A2A2A2A2A2A2H44444444DI6I6I6I6I6I6I6I6X********. G G G G G G G GFJ"J"J"J"J"J"J"J"Z=I=I=I=I=I=I=I=I@`&`&`&`&`&`&`&`&FjDjDjDjDjDjDjDjDZDDDDDDDD,DDDDDDDD,Y<Y<Y<Y<Y<Y<Y<Yw>w>w>w>w>w>w>t 3 3 3P6P6P6P6P6P6P6P6fB=B=B=B=B=B=B=B=J&&&&&&&&D$$$$$$$$*] /] /] /] /] /] /] /] /@))))))))         , , , lGlGlGlGlGlGlGlG^b,b,b,b,b,b,b,b,Jw;w;w;w;w;w;w;w;t]H]H]H]H]H]H]H]H@",",",",",",",",JE&E&E&E&E&E&E&E&P666666668="="="="="="="="@u0u0u0u0u0u0u0u0p.........SFSFSFSFSFSFSFSFl........2J/J/J/J/J/J/J/J/Z ? ? ? ? ? ? ? ?Fn%n%n%n%n%n%n%n%b66666666(00000000D N N N N N N N NRBRBRBRBRBRBRBRBj2,2,2,2,2,2,2,2,jCCCCCCCCL>6>6>6>6>6>6>6>6BD0D0D0D0D0D0D0D0N < < <'0EFF//GF/ <<<*5558555...:::#4#4#4L , , , )JJJKK A AKK A###:7772 - - -&&& 9 9 9%&%&%&P---MMM"+ HBHo7 8 89 HBHo7 8 89 xrx|4556 HBHk;/ 0 01 . 2 2  2222666 1116 7 7 7:);;;<<))<<):::;; )) ;; );;;<<!!<<! ();;;<< )) << ) % % %*$ %% %%%%u9u9u9u9u9u9u9u9p8B8B8B8B8B8B8B8Bv'0DEE@@FE@<<<   ,,, 3 3 3###,777.)))X 6 6 6000D)FFFGG 44 GG 4 )<<>??44??4  ! ! !" " " "#___ = =  = ***@@@^K^K^K^K^K^K^K^KB.3+3+3+3+3+3+3+3+lA2A2A2A2A2A2A2A2HR:R:R:R:R:R:R:R:j%&%&%&%&%&%&%&%&P * * *)?[+HII  JI 4###2666;467733773 7778844 884 000 / / /---(W.W.W.W.W.W.W.W.t 3 3 3 3 3 3 3 3 :K:K:K:K:K:K:K:Kz""""""""]A]A]A]A]A]A]A]A@EEEEEEEE*"G"G"GHH 44 HH 444r2