_MhIdZddlZddlZddlZddlZddlmZddlZddlZddl Z ddl m Z m Z m Z mZmZmZmZmZmZmZmZddlZddlmZddlZddlmZmZddlmZddlm Z dd l!m"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/m0Z0m1Z1m2Z2ddl3m4Z4m5Z5ddl6m7Z7m8Z8ddl9m:Z:m;Z;ddlZ>m?Z?ddl@mAZAejBjCdkZDej dkoe jEdkZFddgZGddZHdZIdZJGddZKddZLdZMejNOd gd!d"ZPGd#d$ZQGd%d&ZRGd'd(ZSGd)d*ZTGd+d,ZUGd-d.ZVGd/d0ZWGd1d2ZXGd3d4ZYGd5d6ZZGd7d8Z[Gd9d:Z\Gd;d<Z]Gd=d>Z^Gd?d@Z_GdAdBZ`GdCdDZaGdEdFZbGdGdHZcGdIdJZdGdKdLZeGdMdNZfGdOdPZgGdQdRZhGdSdTZiGdUdVZjGdWdXZkGdYdZZlGd[d\ZmGd]d^ZnGd_d`ZoGdadbZpGdcddZqGdedfZrGdgdhZsGdidjZtGdkdlZuGdmdnZvGdodpZwGdqdrZxGdsdtZyGdudvZzGdwdxZ{GdydzZ|Gd{d|Z}Gd}d~Z~GddZGddZGddZGddZGddZGddZGddZGddZddejddejzz zddejddejzz zddejddejzz zddejddejzz zddejddejzz zg fdejddejzz ddejddejzz zddejddejzz zdz ddejddejzz zdz ddejddejzz zdz g fddejdejzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dgfgZGddZGddZGddZGddZGddZGddZGddZGddZGdd¦ZGdÄdĦZGdńdƦZGdDŽdȦZGdɄdʦZd˄ZGd̄dͦZGd΄dϦZGdЄdѦZGd҄dӦZGdԄdզZGdքdצZGd؄d٦ZdڄZGdۄdܦZGd݄dަZGd߄dZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZd ZejNeDd  d Zd ZdZdZdZdZdZdZdZdZejNOdgddZÐdZĐdZŐdZƐdZǐdZȐdZɐdZʐd Zːd!Z̐d"ZejNOd#d$ejd%d&gfd'ejd(d)gfd*ejd+d,gfd-ejd.d/gfgd0Zΐd1Zϐd2ZАd3Zѐd4ZejNOd5gd6d7ZejNOd8gd9d:ZejNOd;gd<d=ZՐd>ZejNOd5gd?d@ZאdAZGdBdCe)jZGdDdEe)jZGdFdGe)jZGdHdIe)jZGdJdKZGdLdMZejNeDdN dOZdPZdQZdRZdSZdTZdUZdVZdWZdXZdYZejNOd5gdZd[ZejNOd\d]d^gd_ZejNOd`ddgdafdbdcgdafdddegdffgdgZdhZdiZdjZGdkdlZdmZGdndoZGdpdqZGdrdsZGdtduZdvZejNOdwe8e5zdxZdyZdzZejNOd8d{d|gd}ZejNOd;gd~dZdZdZdZGddZGddZGddZGddZGddZGddZejNOdgddZdS(z! Test functions for stats module N)Path) assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_ assert_warnsassert_array_lesssuppress_warningsassert_array_max_ulpIS_PYPY)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 d/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattrr45s; {00Q00 GAqMMs######cDttjjddS)Nf_gen)r4scipystats distributionsr5r3test_api_regressionr<;sEK-w77777r5cttjjj}dt D}dt D}gd}||z|z}ttd|}||ksJdS)Ncg|] }|d Srr;.0dists r3 z0test_distributions_submodule..Bs///d$q'///r5cg|] }|d Sr?r;r@s r3rCz0test_distributions_submodule..Cs111DQ111r5) rv_discrete rv_continuous rv_histogramentropytrapzcHt|d S)N<)str startswithss r3z.test_distributions_submodule..JsA(9(9#(>(>$>r5)setr8r9r:__all__rr!filter)actual continuousdiscreteotherexpecteds r3test_distributions_submodulerY@s *2 3 3F//h///J11L111H ! ! !EH$u,H6>>IIJJH X      r5c veZdZejdgdejdddejddgdZd Z d Z ejd gd d Z ejdgddZ dZ ejdgddZdZejjejdddgejdgdejdddgejdddgdZejjdZejd d!dgd"Zd#Zd$Zd%Zd&S)' TestVonMisesk)皙?r exrr dcd}d}||dd|||dd|||dd|||dd|||dd|||dd|dS)Nctj|||}t||||dtjz|zzdS)Nlocscale)r9vonmisesrpdfnppir\LrOr_vms r3check_vonmises_pdf_periodiczHTestVonMises.test_vonmises_periodic..check_vonmises_pdf_periodicSsSq222B q 266!q25y1}2E+F+F G G G G Gr5ctj|||}t||dz||dtjz|zzdzdS)Nrdr rg)r9rhrcdfrjrkrls r3check_vonmises_cdf_periodiczHTestVonMises.test_vonmises_periodic..check_vonmises_cdf_periodicWslq222B q A "qAIM': ; ;a ? A A A A Ar5rr r`r;)selfr\r_rorrs r3test_vonmises_periodicz#TestVonMises.test_vonmises_periodicPs H H H A A A $#Aq!Q///##Aq!Q///##Aq"a000##Aq!Q///##Aq!Q///##Aq"a00000r5cttjjtj ttjjtjdSN)rr9 vonmises_liner1rjrkr2rss r3test_vonmises_line_supportz'TestVonMises.test_vonmises_line_supportds:U(*RUF333U(*BE22222r5cttjd}t|dddS)N r?)r9rhrrq)rsrns r3test_vonmises_numericalz$TestVonMises.test_vonmises_numericalhs1 ^C BFF1IIs+++++r5zx, kappa, expected_pdf))r]{Gz?g|65?)r]9@g?U?)r]r{g"?)@r~gDfI?)rrg1<)rr{cjtj||}t||ddSNV瞯<rtol)r9rhrir)rsr_kappa expected_pdfris r3test_vonmises_pdfzTestVonMises.test_vonmises_pdfvs6n  E**\666666r5zkappa, expected_entropy))r gA ?)g,eޞ?)ragBb9d22)g G)g chtj|}t||ddSNvIh%<=r)r9rhrHr)rsrexpected_entropyrHs r3test_vonmises_entropyz"TestVonMises.test_vonmises_entropys5.((//!1>>>>>>r5chd}tj|}tj|}tj|}tjddd|}tjddtjzd|}tjdddtjzt|z dz|}t||dt||ddS) Ni@}r rrd random_statergratol) rjrandom default_rngr9rhrvsrkabsr)rsseedrng1rng2rng3rvs1rvs2rvs3s r3test_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//////r5zx, kappa, expected_logpdf))r]r~g EJ?)r]rgoι?)r]r{g0,)rr~gdty)rrgʹw[A)rr{gcjtj||}t||ddSr)r9rhlogpdfr)rsr_rexpected_logpdfrs r3test_vonmises_logpdfz!TestVonMises.test_vonmises_logpdfs6&&q%00e<<<<<.Ar5r rgcdSrr;rs r3rPz3TestVonMises.test_vonmises_expect..rr5c0tjd|zS)Ny?)rjexprs r3rPz3TestVonMises.test_vonmises_expect..sBF2a4LLr5 complex_funcN) rjrrr9rhexpectr issubdtypedtypefloatingrkanglecomplexfloating)rsrngrerlbresboundss r3test_vonmises_expectz!TestVonMises.test_vonmises_expectsi##$788A+UBnE22299++FFQ}SY 44444R!be)^#9enE2229++OOOOQ}SY 44444R!be)^#9enE2229:P:PS;ASSSPQSS sag777}SY(:;;;;;;;r5rvs_locrg rvs_shape)r raחAfix_locTF fix_shapec.|r|rtjdtjd}t j|d||}ddi}|r||d<|r||d<tt j|t jj fi|dS) NzNothing to fit.rr)sizererfscaler flocf0) pytestskiprjrrr9rhr_assert_less_or_close_loglikennlf)rsrrrrrdatakwdss r3test_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 Cr5c@gd}tj|}dtjz}tj||\}}}|tjtjksJttj|tjj d|dS)N)g!*Kg4,%OԿgZ۵?g ge_@g-8gPghn?grrgg d?)r8r9rhrrjrkrxs r3test_vonmises_fit_boundsz%TestVonMises.test_vonmises_fit_bounds sZ    !WA 666    "%'9"5!6Q ?????r5N)__name__ __module__ __qualname__rmark parametrizerjrkrtryr}rrrrrxslowrslowrrrrrr;r5r3r[r[Os [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-- ( (.- ( M M M999 @ @ @ @ @r5r[Fc ||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)rrsupertyperjanyallclose) rBrfuncmaybe_identicalrmle_analytical numerical_optll_mle_analyticalll_numerical_opts r3rrs! |yTXd++d++N/E$t**d++/====M 7vn 566666^T22tM400 !1 1 1 K)+;% H H H 2 1 1 ~~b!T&\11114b!T(^333333r5c 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,)rf1f2r rgr3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:rg) extra_keywordzToo many positional arguments.r )shapeslensplitdictziprjarangerr RuntimeErrorr ValueErrornaninf TypeError)rBparamnshapes all_fixedrs r3assert_fit_warningsr;sL X E {.dk'',,-- ###HWH--S #e** 5 56677I 99D |& ' ' '$$ #####$$$$$$$$$$$$$$$ zB D D D "& zB D D D "& y(D E E E(( Q'''((((((((((((((( y(H I I I..-SZZ!^,----..................sZB88B<?B<!D  DD1!EE"%E"F((F,/F,#G>>HHrB)alpha betaprime fatiguelifeinvgammainvgauss invweibull johnsonsblevylevy_llognormgibrat powerlognormrayleighwaldctt}||}tt|}t |j|jg|Rdt|j|jg|Rtj t |j|j g|Rdt|j|j g|Rtj dS)zgh-6235rN) rrgetattrr9rrir1rrrjrr2)rBdctargss r3 test_supportr1Rs x..C t9D 5$  D/$///333TV+d+++bfW555/$///333TV+d+++bfW55555r5c&eZdZdZdZdZdZdS) TestRandIntcDtjddSNrrjrrrxs r3 setup_methodzTestRandInt.setup_methode tr5cvtjddd}tt j|dkt j|dkztt |dktjddd}tt j|dkt|jj tdvtjdd}t|dk|dkztt|tj tt| tjddd }t|jj tdvdS) Nrrarrg2 AllInteger.r.r)r9randintrr rjrrshapercharr isinstance ScalarTypereprrrsvalsvals r3test_rvszTestRandInt.test_rvshsW}  BS 11tby!!BF419$5$55666D S !!!}  BW 55')*** 9\#::;;;mB''sRx())) 3 ..DcOODDDDmB##''** )L"99:::::r5ctjdd}tj|dk|dkzdd}tj|dd}t ||dS)Nr$rr:{Gz?)rjr_wherer9rApmfr)rsr\outrHs r3test_pdfzTestRandInt.test_pdfus` E!B$KhQ1r6*J::}  Ar**!$,,,,,r5ctjddd}tj|}tj|dk|dkgd|dz dzd z gd}tj|dd}t||d dS) NrrLrar:r?@r r decimal)rjlinspacefloorselectr9rArqr)rsr_r\rQrHs r3test_cdfzTestRandInt.test_cdf{s K2s # # HQKKib!q&)C!C%'F1C+DaHH}  Ar**!$R888888r5N)rrrr7rJrRr\r;r5r3r3r3dsP ; ; ;--- 99999r5r3cDeZdZdZdZdZdZdZdZdZ dZ d Z d S) TestBinomcDtjddSr5r6rxs r3r7zTestBinom.setup_methodr8r5ctjddd}tt j|dkt j|dkztt j|dkt|jjtdvtjdd}tt|ttjddd}tt|tj t|jjtdvdSNr`rr<r;rr>r) r9binomrr rjrrBrrCrrDintndarrayrGs r3rJzTestBinom.test_rvss {r4g66tqy!!BF42:$6$66777')*** 9\#::;;;koob$'' 3$$%%%k"d##''** 3 ++,,, )L"99:::::r5ctjddd}tjddd}t|dddt|ddddS)Nrar rrTrrrr9rbrPr)rsvals1vals2s r3test_pmfzTestBinom.test_pmfsd S!,, 3**sQ7777sQ777777r5ctjdd}tjgd}t t || }|}t||tjdd}|}t|dtjdd}|}t|ddS)Nrgr|)?r|rlrrT) r9rbrjrsumrrHrr)rsr2 expected_p expected_hhs r3 test_entropyzTestBinom.test_entropys K3  X///00 % J77888 IIKK:&&& K3   IIKKQ K3   IIKKQr5cjtj5tjdtt t jdddt t jdddddddS#1swxYwYdS)Nerrorrgrnp) warningscatch_warnings simplefilterRuntimeWarningrr9rbrstdrxs r3 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?rT)qrurv)r9rbrrsrus r3 test_ppf_p1zTestBinom.test_ppf_p1s2 {S11Q666666r5cd}d}tjd}tj|||}tj|||z}t ||ddS)NglyCgq]\ T3r) r9 bernoullirr rjrrBrrCrrDrcrdrGs r3rJzTestBernoulli.test_rvss""4g"66tqy!!BF419$5$55666')*** 9\#::;;;o!!$'' 3$$%%%od##''** 3 ++,,, )L"99:::::r5ctjd}dtjdzdtjdzz }|}t ||tjd}|}t |dtjd}|}t |ddS)NrlпrrrT)r9rrjlogrHrr)rsr2rorps r3rqzTestBernoulli.test_entropys OD ! !26$<<'$rvd||*;; IIKK:&&& OC  IIKKQ OC  IIKKQr5N)rrrr7rJrqr;r5r3rrsA ; ; ;     r5rceZdZdZdS) TestBradfordcd}tjdd}tj||}tj||}t ||dS)Nr])rjlogspacer9bradfordrqrr)rscr_rxxs r3 test_cdf_ppfzTestBradford.test_cdf_ppfs\  KR  N  q! $ $ ^  1 % %2r5N)rrrrr;r5r3rrs#r5rcFeZdZdZejdddddddd d d d ed fg dZejdgdejde j j dfe j j dfgdZ ejdgddZejdgdejde j jdfe j jdfgdZdS) TestCauchycTtjd}|dksJdS)NZbtir)r9cauchyrirs r3test_pdf_no_overflow_warningz'TestCauchy.test_pdf_no_overflow_warnings* L  U # #Cxxxxxxr5x, ref)r罡HP)gr)gIL8r)gOd@gHP)Mb@?gP)r]g*6y)?g8@(J)gNgmCg'K@$[U)rgonьgs 32crtj|| g}t|||gddSr)r9rrr)rsr_rlogps r3 test_logpdfzTestCauchy.test_logpdf s>|""Ar7++sCju555555r5))g7y1gu lY<)g^?)rrl)rr|)r r)rg)nE?)g7y1C?z method, sgnr rcF|||z}t||ddSrr)rsr_rmethodsgnrvs r3 test_cdf_sfzTestCauchy.test_cdf_sfs0 F3q5MM3U++++++r5))gRyXsg!;v+͋)(,* EgjLҳ)$@g )r9B.)g$gCį )g :@sgg>Z)g 5g*\Bctj|}t||dtj| }t||ddSN+g /)rl)r|r)rrT) !?gqmA)g?gqJRBcF|||z}t||ddSrr)rsrvrrrr_s r3 test_ppf_isfzTestCauchy.test_ppf_isf>s0 q M3U++++++r5N)rrrrrrrrrr9rrqrrrrisfrr;r5r3rrs [ # & % ' $ # # # # $ $ % ' ( (66 ( (6  [ % % %   [ , A  ,/2   ,,   ,  [X;;;<<00<<0 [ / / /   [ , A  , B  !"",, ""  ,,,r5rceZdZdZdZdZdZdZdZe j ddefd gd Z e j dgd d Z d S)TestChignT9;g2 >h?@cttjdd}t||jddS)Nr`rrr)r9chirr CHI_SF_10_4rsrOs r3test_sfzTestChi.test_sfZs5 ILLQ  4+%888888r5cttj|jd}t |dddS)Nrr`rr)r9rrrrrsr_s r3test_isfzTestChi.test_isf^s5 IMM$*A . .2E******r5crd}d}tj||}t|dddS)Nrr?ga rr)r9rrr)rsr_dfrs r3 test_logcdfzTestChi.test_logcdfbs?  !!!R(( 6UCCCCCCr5crd}d}tj||}t|dddS)Nr~r?@y`rr)r9rrr)rsr_rrs r3 test_logsfzTestChi.test_logsfis=   2&&5EBBBBBBr5df, ref@@)gļBgcAcdttj||ddSN-q=r)rr9rrrsrrs r3 test_meanzTestChi.test_meanvs-  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'Or|rrrerf)g3c}?g>t\?g˂ ?f'T)?#n?5-h J??u8n?vL1??#?||P?g:Q?rrrrrrrr)rjrYr9 crystalballrirrrsX calculatedrXs r3rRzTestCrystalBall.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 *5999999r5ctjddddd}tj|dd}tjgd }t ||d tj|dd }tjgd }t ||d tj|dd dd}tjgd}t ||d dS)rrrUrNrrTrr)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?r|r)go?rge?r gPU,?r gjݗ ?r g?r g_!Y?r ga?rgR?rg( ?rg܉x?r)rjrYr9rrqrrrs r3r\zTestCrystalBall.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 *5999999r5zx, beta, m, rootref))(@rTrgI9)"@@?gy <)r]gjt?g +,)grrgGA*?)g>r|rUg^v'?)gd~Qr皙?g眭?cntj|||}t||ddS)Nrrr)r9rrr)rsr_rrrootrefrs r3rzTestCrystalBall.test_sfs<  ! !!$! ! 4 4G%000000r5ctjgd}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 )rrTrrr)rrrrr)rTrTrTrTrTrMbP?r)gԚh@g [&@gͪ@g2dQ@gn6-@g?ޫV&̿gBgQCRgQF\jr g @gn(@rgg?Җ)rgMg'#@rg('UHrN)rjrr9r_munprr)rsrrexpected_0th_momentcalculated_0th_momentnormr1expected_1th_momentcalculated_1th_momentexpected_2th_momentcalculated_2th_momentexpected_3th_momentcalculated_3th_momentexpected_4th_momentcalculated_4th_momentexpected_5th_momentcalculated_5th_moments r3 test_momentszTestCrystalBall.test_momentssg 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+-BOOOOOOr5ctjdd}|}d\}}}tj|||}t t |||}t||ddS)Nrgr)ir:@ Hz>r) r9rrHrjrYrrrir)rscbres1lohiNr_res2s r3rqzTestCrystalBall.test_entropyLsy  q! $ $zz||& B KB " "bffQii!,,d......r5N) rrrrRr\rrrrr*rqr;r5r3rrs<:<:<:|<:<:<:D [ 0 0 0111+P+P+PZ/////r5rc&eZdZdZdZdZdZdS) TestNBinomcDtjddSr5r6rxs r3r7zTestNBinom.setup_methodXr8r5ctjddd}tt j|dktt j|dkt|jjtdvtjdd}tt|ttjddd}tt|tj t|jjtdvdSra) r9nbinomrr rjrrBrrCrrDrcrdrGs r3rJzTestNBinom.test_rvs[s|Dw77tqy!!"""')*** 9\#::;;;lr4(( 3$$%%%l2t$$((++ 3 ++,,, )L"99:::::r5c 2ttjtjdddtjdddtjjddd}t|ddS)Niigp= ף?rr ) rrjrr9r8logpmfrPr8r)rsrIs r3rjzTestNBinom.test_pmffsu|223TBBCC ((c488 : : :k ''1a00S!r5ctjgddd}tjtjgddd}t ||dS)N)rrrr333333@?rt)r9r8rrjrrqrrsrHrs r3test_logcdf_gh16159zTestNBinom.test_logcdf_gh16159nsb|""<<<3$"??fU\%%lllcT%BBCCc"""""r5N)rrrr7rJrjr?r;r5r3r5r5WsP ; ; ;#####r5r5ceZdZdZejjdZejjdZejjdZ ejjdZ dZ dZ dZ d Zd S) TestGenInvGausscDtjddSr5r6rxs r3r7zTestGenInvGauss.setup_methodvr8r5ctjdd}tj|dd|j\}}t |dkddS)Nffffff@rrr皙?Tr9 geninvgausskstestrrqrrsgigrrvs r3test_rvs_with_mode_shiftz(TestGenInvGauss.test_rvs_with_mode_shiftyWS))|CGGDGAA37KK1QXt$$$$$r5ctjdd}tj|dd|j\}}t |dkddS)NrrrErrrFTrGrJs r3test_rvs_without_mode_shiftz+TestGenInvGauss.test_rvs_without_mode_shiftsWT**|CGGDGAA37KK1QXt$$$$$r5ctjdd}tj|dd|j\}}t |dkddS)Nr]皙?rErrrFTrGrJs r3test_rvs_new_methodz#TestGenInvGauss.test_rvs_new_methodrMr5cd}t|dddt|dddt|ddddS)Nctj||}|dd}tj||jddkS)NrErrr rF)r9rHrrIrq)rvr2rKrs r3 my_ks_checkz4TestGenInvGauss.test_rvs_p_zero..my_ks_checksG#Aq))C''t$'77C<SW--a047 7r5rrQTrr)r)rsrUs r3test_rvs_p_zerozTestGenInvGauss.test_rvs_p_zerosm 8 8 8 [[C(($///[[C(($///[[C(($/////r5cttjdddddtjddddz dS)Nrgr`rrr r)rr9rHrrxs r3test_rvs_negative_pz#TestGenInvGauss.test_rvs_negative_psn!$**..BT.JJE%c1--11r1MMM O O O O Or5cHtjdddd}ttj|ddgddkd d t jd dd }}tj|dd|z | }t|tj ||tj |dd|z | }t|tj | |dS)NrErr r)rrvr2rr#r0333333?Trar~r`)rvr2rf) r9rHrrrIrjrYrirr#rq)rsigmur_pdf_igcdf_igs r3 test_invgausszTestGenInvGauss.test_invgausss   " " " M MU\"js;;;A>EtLLLR[q"--A"&&qDAF"&EEr 2 2 6 6q 9 9:::"&&qDAF"&EEr 2 2 6 6q 9 9:::::r5ctjgd}tjddd}t|tj|dddS)N) g;g8y8?g\}Z?ghܲ0|?gRq?r~rr`r|r )rjrrYrr9rHri)rsvals_Rr_s r3 test_pdf_RzTestGenInvGauss.test_pdf_Rsd,,,-- Ka $ $ 1 5 5aa @ @AAAAAr5cttjddddttjdddddS)Nrr|g>Ar=rg)rr9rHrirxs r3 test_pdf_zerozTestGenInvGauss.test_pdf_zerosTU&**1c377;;; U&**3A66:::::r5N)rrrr7rrrrLrOrRrVrYrardrfr;r5r3rArAus [%%%  [%%%  [%%%  [000OOO ; ; ; B B B;;;;;r5rAceZdZdZdZdZejdgddZ ejdgddZ d Z d Z d Z d Zd ZdZdS)TestGenHyperboliccDtjddSr5r6rxs r3r7zTestGenHyperbolic.setup_methodr8r5ctjgd}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?rgrgr r|rrdr`rrrr)rjrr9 genhyperbolicrYrri rsrclmbdarrr^deltar0ghr_s r3 test_pdf_rzTestGenHyperbolic.test_pdf_rs %ud EuU{DJ/  $Be < < < KR $ $q 6>>>>>>r5ctjgd}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?rkrlrdrmr`rư>rn)rjrr9rorYrrqrps r3 test_cdf_rzTestGenHyperbolic.test_cdf_rs %ud EuU{DJ/  $Be < < < KR $ $q 6======r5zx, p, a, b, loc, scale, ref) )rgrrr|rg8ɹvF(;)rxr`rrlr rg[ Ϡ?)rxr`rg?rr g✝`D;)rx?r):?rr g dL;)rryrrzrr gzK^7?)rrrzrr gj?)rr{rrr ga=vG:)rr{rr|rr g?)(r{rr|rr g1bV?)<r{rr|rr g?cttj||||||}t||ddSNrddy=r)r9rorqr) rsr_rvr1r2rerfrrqs r3test_cdf_mpmathz!TestGenHyperbolic.test_cdf_mpmathsB!%%aAqc%GGSu------r5))rrvrVrrr gC!,?)rr@@r rg,Ћf?)rrrrr rrT)rgrrr|rgm"چ >),r`rrlr rg:;)r~r{rr|rr gw=)Kr{rr|rr g3Z0&K.$sI  2U ; ; ; B B1 E Er5r rrrrn)ranger) rsrcrqrrvals_usr0rrr^s @@@r3test_moments_rz TestGenHyperbolic.test_moments_rs555%ud EuU{DJ/1a[[ ae<<<<<>>4 [% < < <  ..  . [% @ @ @  --  -===. % % %$"*r5rhceZdZejdddgdZejdddgdZd Zd S) TestHypSecantz x, reference)r:gA0=)r=g!b;chtj|}t||ddSr)r9 hypsecantrr)rsr_ referencers r3rzTestHypSecant.test_sfs4_   " "IE222222r5z p, reference)rvg9bT*@)rgTW-;@chtj|}t||ddSr)r9rrr)rsrvrr_s r3rzTestHypSecant.test_isfs4 O   " "95111111r5cd}d}tj|}t||dtj| }t||ddS)NI@g!brr)r9rrrrrs r3rzTestHypSecant.test_logcdf_logsfsh %''**%0000%%qb))s//////r5N) rrrrrrrrrr;r5r3rrs  [^9:<==33==3 [^89;<<22<<200000r5rceZdZdZdZdZejdgddZ dZ dZ d Z d Z d S) TestNormInvGausscDtjddSr5r6rxs r3r7zTestNormInvGauss.setup_methodr8r5ctjgd}tjgd}tj|dd}t ||ddS)N)gp~٧>g @X>g}e?g{)߳?gwH?irrr?r r|r1r2rr)rjrr9rrqr)rsr_cdfx_testvals_cdfs r3 test_cdf_RzTestNormInvGauss.test_cdf_Rsr <<<==,,,--%))&A)==%d333333r5ctjgd}tjgd}tj|dd}t ||ddS)N)gp϶>g\H55$?geСt&?go NiH?g]u>rr r|rrr)rjrr9rrir)rsr_pdfrvals_pdfs r3rdzTestNormInvGauss.test_pdf_Rsp<<<==,,,--%))&A)==%d333333r5zx, a, b, sf, rtol))rr r!7?r)rr r?=r)r rrXgy5`?r)r`rrXgMLC9rctj|||}t|||tj|||}t|||dSNrr9rrrr)rsr_r1r2rrrOrs r3test_sf_isf_mpmathz#TestNormInvGauss.test_sf_isf_mpmathsh   ! !!Q * *2D))))   " "2q! , ,14((((((r5cddg}ddg}d}ddg}tj|||}t||dd tj|||}t||d dS) Nrrr rrrrrrfrvrr)rsr_r1r2rrOrs r3test_sf_isf_mpmath_vectorizedz.TestNormInvGauss.test_sf_isf_mpmath_vectorizeds H F  "8 9   ! !!Q * *2E6666   " "2q! , ,14((((((r5ctjdd}tjddd}||}||}t ||dS)Nr rrrg)r9rrjrrrr)rsdstr_rrs r3 test_gh8718zTestNormInvGauss.test_gh8718s[ A&& IaQ   VVAYYggbkkQr5c.d\}}tj|dz|dzz }||z |dz|dzz d|z|tj|zz ddd|dzz|dzz zz|z f}t|tj||ddS) Nr r|rgrrr rmvskmoments)rjrrr9r)rsr1r2gammav_statss r3 test_statszTestNormInvGauss.test_statss11q!t $$u9adUAXosQw!bgenn:L/M!a!Q$hAo-.68We066q!V6LLMMMMMr5cd\}}tjgd}tj|||}t |tj|||dS)Nrrr|r)rjrr9rrrrq)rsr1r2rrHs r3test_ppfzTestNormInvGauss.test_ppfsf1---..!%%fa33 2 6 6tQ B BCCCCCr5N)rrrr7rrdrrrrrrrrr;r5r3rrs 4 4 4444 [0JJJKK )) KK ) ) ) )   NNNDDDDDr5rcPeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d S) TestGeomcDtjddSr5r6rxs r3r7zTestGeom.setup_methodr8r5ctjdd}tt j|dktt j|dkt|jjtdvtjd}tt|ttjdd}tt|tj t|jjtdvdS)Nrr<r;rr>r) r9geomrr rjrrBrrCrrDrcrdrGs r3rJzTestGeom.test_rvssz~~d~11tqy!!"""')*** 9\#::;;;jnnT"" 3$$%%%j""1%% 3 ++,,, )L"99:::::r5cPtjd}tjtjdd|}|jtjksJtj |tj tj j ksJdS)NlA:irr) rjrrr9rrrrint64riinfoint32max)rsrrs r3 test_rvs_9313zTestGeom.test_rvs_9313si##O44jnnRVC[[qsnCCyBH$$$$vcBHRX..223333333r5cntjgdd}t|gddS)Nr r|)r|rlry)r9rrPrrsrHs r3rjzTestGeom.test_pmfs8z~~iii--!$(:(:(:;;;;;r5c8tjtjgdd}tjgdd}t ||ddtjdd}t|ddS)Nr r|rrrfr r)rjrr9rrPr:rr)rsrhrirIs r3 test_logpmfzTestGeom.test_logpmf suz~~iii5566 !!)))S11u5q9999j1%%S#r5ctjgdd}tjgdd}t gd}t ||t |d|z dS)Nr r|r|r?r )r9rrqrrrrsrHvals_sfrXs r3rzTestGeom.test_cdf_sfsrz~~iii--*-- 3//+++,,!$111!'1X:66666r5c:tjgdd}tjgdd}t gd}t |t j|t |t j| dS)Nr r|r) r9rrrrrrjrlog1prs r3rzTestGeom.test_logcdf_logsfsz  C00*""999c22+++,,!$x(8(8999!'28XI+>+>?????r5ctjgdd}tgd}t ||dS)Nrr|)rTrr)r9rrrrrsrHrXs r3rzTestGeom.test_ppf!sEz~~000#66))!$11111r5cfttjdddddS)NrrTrr)rr9rrrxs r3test_ppf_underflowzTestGeom.test_ppf_underflow&s- ue44cFFFFFFr5cvtjd}t|dddS)Ng<,Ԛ?g۩@rr)r9rrHr)rsrps r3test_entropy_gh18226zTestGeom.test_entropy_gh18226*s; Jv   & & ( (,5999999r5ctjd}tjdd|dksJdS)NiKH9r`rr)rjr RandomStater9rrr)rsrs r3test_rvs_gh18372zTestGeom.test_rvs_gh183720sPy,,Y77  u2LIIAMRRTTTTTTTr5N)rrrr7rJrrjrrrrrrrr;r5r3rrs ; ; ;444<<<777@@@222 GGG::: UUUUUr5rc eZdZdZdZdZdS) TestPlanckcDtjddSr5r6rxs r3r7zTestPlanck.setup_method8r8r5ctjgdd}tgd}t ||dS)Nr rU)g|dy?g8'\>ggrU!>)r9planckrrrrs r3rzTestPlanck.test_sf;sQ|yyy"--22233 "$11111r5ctjgdd}tgd}t ||dS)N)r@@p@r)gP.gh>gTF)r9rrrrrs r3rzTestPlanck.test_logsfBsJ|!!"7"7"7??:::;;!$11111r5N)rrrr7rrr;r5r3rr7sA22222222r5rc&eZdZdZdZdZdZdS) TestGennormcgd}tj|d}tj|}t ||dSNr r )r9gennormrirrrspointspdf1pdf2s r3 test_laplacezTestGennorm.test_laplaceIsM}  ++}  ((D$'''''r5cgd}tj|d}tj|d}t ||dSNr rgg;f?rf)r9rrirrrs r3 test_normzTestGennorm.test_normPsO}  ++z~~fF~33D$'''''r5ctjdtjd}|d}tj||jjdksJtjd}|d}tj d}tj ||jdksJtjd}|d}tj dd }tj ||jdksJdS) Nrr|rr;r]r rgg;f?rfr) rjrrr9rrrIrqpvaluerks_2sampr)rsrBr rvs_laplacervs_norms r3rJzTestGennorm.test_rvsWs q}S!!hhDh!!|C**1C7777}QhhDh!!m''T'22 ~c;//6<<<<}QhhDh!!:>>t><<~c8,,3c999999r5ctjdtjddgddgg}|gd}tj|ddddftjdjdd ksJtj|ddddftjdjdd ksJtj|ddddftjdjdd ksJtj|ddddftjdjdd ksJdS) Nrr|rTrrU)rrgrgr;r r])rjrrr9rrrIrq)rsrBrs r3test_rvs_broadcastingz!TestGennorm.test_rvs_broadcastinghsC q}sBi"b233hhLLLh))|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJ|C1aL%-*<*<*@AA!DsJJJJJJr5N)rrrrrrJrr;r5r3rrHsU((((((:::"KKKKKr5rcZeZdZejdddgdZdS) TestGibratx, sfx)rgD.?)gJ]b>HH>>>r5rceZdZdZejdgddZdZdZ ejdgdd Z d S) TestGompertzctjtjddd}t |ddSN0.++r )r9gompertzrrqrrs r3test_gompertz_accuracyz#TestGompertz.test_gompertz_accuracysA N  u~11&!<g:0N<?)rrg:?cfttj|||ddSr)rr9foldnormrqrsr_rrs r3r\zTestFoldNorm.test_cdfs1 **1a00#EBBBBBBr5N)rrrrrrr\r;r5r3r+r+s[ [[+N+M+OPPCCPPCCCr5r+ceZdZejdddgdZejdgddZejdd d gejd gd ejd ddgejdddgdZdZ dS) TestHalfNormr)r |N?)r` Oul2;cttj||dttj||ddSr#)rr9halfnormrrrs r3rzTestHalfNorm.test_sf_isfsT ))!,,c>>>>**3//??????r5r))Ww'&l7g;G<^͛7)C]r2r rvs_scaler~rarrTF fix_scalectjd}tj||d|}|r[|rYd}t jt|5tj |||dddn #1swxYwYdSi}|r||d<|r||d<ttj|fi|d d idS Nrrrerfrrr r rrrrrT) rjrrr9r6rrrr halflogisticrr rsrr<rr>rr error_msgrs r3rz(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 < ctjd}tj||d|}|r[|rYd}t jt|5tj |||dddn #1swxYwYdSi}|r||d<|r||d<ttj |fi|dS) NrrrAr r rBrr) rjrrr9r6rrrr halfcauchyrrrDs r3rz*TestHalfCauchy.test_fit_MLE_comp_optimizers=i##$788~!!gYT/2"44  y %I|9=== K K $$T $JJJ K K K K K K K K K K K K K K K F  #"DL  '&DN%e&6EEEEEEErFctjt5tjgddddddS#1swxYwYdSrH)rrr#r9rNrrxs r3rIzTestHalfCauchy.test_fit_error.s ]< ( ( 4 4    3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4rJN)rrrrrrrrIr;r5r3rLrLs [Yt 55 [[4+66 [Yu 66 [[4-88FF98767665F,44444r5rLceZdZejdddgdZejdgddZdZd Z ejd d d gejd gdejdddgejdddgdZ dZ dS)TestHalfLogisticr)ra]6)L-cdttj||ddSr)rr9rCrr:s r3rzTestHalfLogistic.test_sf<s0 *--a00#EBBBBBBr5q, ref))rRra)rTrS)硏v?g .!>)g?g@guVJrr)r9rCrrrsr_rrs r3rzTestHalfLogistic.test_logcdfOs= $#**1--%000000r5cpd}d}tj|}t||ddS)Nrg+rr)r9rCrrrsr_rrs r3rzTestHalfLogistic.test_logsfVs= $"((++s//////r5rr;rr<r=rTFr>ctjd}tj||d|}i}|r[|rYd}t jt|5tj |||dddn #1swxYwYdS|r||d<|r||d<ttj|fi|d d idSr@) rjrrr9rCrrrrrr) rsrr<rr>rrrrEs r3rz,TestHalfLogistic.test_fit_MLE_comp_optimizer]s`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: < < < < < g+cfttj|||ddSN绽|=rrr9 truncnormrHrsr1r2rs r3rqzTestTruncnorm.test_entropys1$ //155sGGGGGGr5))rrghiɮ9?)rrr)g0.+rr)}Ô%IrZ_2?cfttj|||ddSr#rrs r3test_extreme_entropyz"TestTruncnorm.test_extreme_entropys1 //155sGGGGGGr5c tjgddddgdzd}tjtjdd dd d tjg}t ||dS) Nrrrr|H.?r rgrrTrrgrdr fO?l@r)r9rrrjrrrrs r3test_ppf_ticket1131z!TestTruncnorm.test_ppf_ticket1131n""#E#E#EsB()s1uA#778RVQ Az1bfMNN!$11111r5c tjgddddgdzd}tjtjdd dd d tjg}t ||dS) NrrrTrrrgrdrrrr )r9rrrjrrrrs r3test_isf_ticket1131z!TestTruncnorm.test_isf_ticket1131rr5cd\}}tj||ddd}t||cxko|cxko|kncd\}}tj||ddd}t||cxko|cxko|kncdS)N)irmrr r`r;)r` r9rrr minrrslowhighr_s r3test_gh_2477_small_valuesz'TestTruncnorm.test_gh_2477_small_valuess T O  T1ab  9 9aeegg........$..../// T O  T1ab  9 9aeegg........$..../////r5cd\}}tj||ddd}t||cxko|cxko|knct |||gfd\}}tj||ddd}t||cxko|cxko|kncd\}}tj||ddd}t||cxko|cxko|kncd\}}tj||ddd}t||cxko|cxko|kncdS) N)rar^rr r`r;)r)'i')i)r9rrr rrrLrs r3test_gh_2477_large_valuesz'TestTruncnorm.test_gh_2477_large_valuess T O  T1ab  9 9quuww1111!%%''1111T111122CdA4G4GGG T O  T1ab  9 9aeegg........$..../// T O  T1ab  9 9aeegg........$....///" T O  T1ab  9 9aeegg........$..../////r5cddgddgfD]\}}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)Nrrrrrrr r rTrTrr)rd._MT @BKg?rr)rrrrr rgr|rr|rTgĖy @gdv*?g,mj%V?rl) rjrrr9rrqrrirrrr)rsrrxvalsxmidcdfssfspdfs expected_cdfs expected_sfs expected_pdfspvalsppfs expected_ppfsris r3test_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$$G$G$6888/%%dC66C s=+;'; < rlrr) rjrrr9rrqrrirrrrrY)rsrrrrrrrrrrrrrrixvals2s r3test_gh_9403_medium_tail_valuesz-TestTruncnorm.test_gh_9403_medium_tail_values0sr(S#J/, P, PICHrvgsD"&9::EHc>D?&&uc488D/$$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)NrrFFg >x{{q#c((m++++saeeemm+,,---quu!u}},--.....r5cttjdrAtjdddtjdSdS)Nrrmrrr)r0rjrr9rrrrxs r3test_rvs_Generatorz TestTruncnorm.test_rvs_Generatorsh 29m , , F O  Ra-/Y-B-B-D-D  F F F F F F Fr5ctjtj tj dtj dg}tjtjtjddtjg}tjgd}gd}tt j||||tt j| | | |dS)Nr`r)r`@r r)g Oul"gځ=!gL!g>EG fg^K[X)rjrrrr9rrr)rsr1r2r_rXs r3test_logcdf_gh17064z!TestTruncnorm.test_logcdf_gh17064s HrvgwRVGR8 9 9 HbfbfaRV4 5 5 H*** + ++++ 1--44Q77BBBQB//55qb998DDDDDr5cztjddd}d}t||dS)Nrrrgl).0S?)r9rrr)rsrrs r3test_moments_gh18634z"TestTruncnorm.test_moments_gh18634s@ob!$$++A.. S!!!!!r5N)rrrr7rrrrqrrrrrrrrrjr_truncnorm_stats_datarr*rrrrrrr;r5r3rrsu [[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 ///FFF E E E"""""r5rceZdZejdgddZejdgddZejddd gd Zejd d d gdZ ejd ddgdZ ejdddgdZ dS)TestGenLogistic x, expected))ig4`n)ig4 ncg)rgX =)ragh@ X)rg h) r9 hypergeomrrjrrBrrCrrDrcrdrGs r3rJzTestHypergeom.test_rvs s""2r17";;vdai  26$!)#4#44444x~~((((z)L"99999o!!"a,,#s#####ob!R((,,Q//#rz*****y~.5sC***!!(GeOWeLL***r5)rgpR(g㘍R2gJޱp9g?Mf= G?r rgƠ>rn)g@r g@g@g@)r rg) 9g"1)rjrrr9rr) rs fruits_eatenrrX quantilesr3 expected2rrrs @@@r3test_precision2zTestHypergeom.test_precision2.sx = = =>>D ******(***8999::XAD99990// !!)Wu_guMM>>> iad;;;;;;r5c`tjddd}|}tjddg}tjt || }t||tjddd}|}t|ddS)Nrr rrlr) r9rrHrjrrmrrr)rshgrprnros r3rqzTestHypergeom.test_entropyAs _Q1 % % JJLLXtTl++ fU:z::;;; :&&& _Q1 % % JJLLQr5cd}d}d}d}tj||||}d}t||dd}d }d }d }tj||||}d }t||d dS)Nr cA.Aj@gorrWr @Xrg_7 j$r?)r9rrrrsr\rrur2resultrXs r3rzTestHypergeom.test_logsfMs    &&q!Q22FHa8888    &&q!Q22 FHb999999r5cDd}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)Nr rrrg)\UrrWr}rr=rg*@Vr?}rgר)r}r}r})r9rrrrjrfullrs r3rzTestHypergeom.test_logcdfesM    ''1a33FHa8888    ''1a33&FHb9999    ''1a33 FHb9999 H\\\ " "   ''1a3371122FHb999999r5cd}d}d}tj|||}||z |z}t||dS)NipiPi.)r9rrr)rsrrur2hmrms r3test_mean_gh18511zTestHypergeom.test_mean_gh18511sO    _ ! !!Q * * UQYBr5cd}d}tjdd}d|z}tj|dz |||}tj|dksJtjtj|dksJdS)Nr`rrr?rr r)rjrr9rrrdiff)rsrur2rpopulation_sizervs r3test_sf_gh18506zTestHypergeom.test_sf_gh18506s   Ia  q& O  q1uoq! < <va!e}}vbgajj1n%%%%%%%r5N)rrrr7rJrrrrrqrrr'rrrr+r;r5r3rrs 9 9 9>>>FFFLLL<<<&   :::0,:,:,:\     [ & & & & &r5rcVeZdZejdgddZejdgddZdZdZ d Z d Z ejd d d gdZ ejdgddZ dS) TestLoggammaz x, c, cdf))r rgg;Y%?)rgRٲa6_<)gHrgi|e?)rg6l ?)i+r]g֬CCf9)irgֺl ctj||}t||dtj||}t||ddSr)r9loggammarqrr)rsr_rrqrvys r3rzTestLoggamma.test_cdf_ppfsb N  q! $ $3U++++ N  sA & &15))))))r5zx, c, sf))rrgQOu3;)rag\Z{0)r/rgeɐ?)ig{Gzd?gr0T?ctj||}t||dtj||}t||ddSr)r9r1rrr)rsr_rrrOr2s r3rzTestLoggamma.test_sf_isfsb N  a # #2E**** N  r1 % %15))))))r5cjtjdd}t|dddS)N rgg@rr)r9r1rr)rslps r3rzTestLoggamma.test_logpdfs6 ^ " "4 + +G%000000r5cvd}d}tj||}d}t||ddS)Nr@gI.rr)r9r1rr)rsr_rrrs r3rzTestLoggamma.test_logcdfsC  &&q!,,%%000000r5cvd}d}tj||}d}t||ddS)Ng9 @g!{1+ҷrr)r9r1rr)rsr_rrrs r3rzTestLoggamma.test_logsfsC  $$Q**#s//////r5ctjgddd}|D]?\}}}}}tj|d}t |||||gd@dS)N)r|g"~jg46<@goŏrrTg h"lxg Q?gZd;333333@rg{/L@g??gгYҿgh|?5?rrmsvkrrrW)rjrreshaper9r1r)rstablerrvarskewkurtcomputeds r3rzTestLoggamma.test_statss wr1~~  ). 1 1 $AtS$~++Av+>>H %hsD$0G./ 1 1 1 1 1 1 1r5rr]rctj|d}tj|sJtj|}tjtj||kt|}| d}|j dcxkr |j ksnJdS)Nrr;r)confidence_levelr|) r9r1rrjisfinitermedian binomtest count_nonzeror proportion_cirr)rsrr_medbtestcis r3rJzTestLoggamma.test_rvss N  qv  . .{1~~!!#####n##A&& 0S 9 93q66BB  % 8 8v%%%%bg%%%%%%%%r5r'))r-g3H໱k3@)r r)r g8,[H^} )rg90$)rgtum\cdttj||ddSr#)rr9r1rHr)s r3rqzTestLoggamma.test_entropy s/ ..q113UCCCCCCr5N)rrrrrrrrrrrrrJrqr;r5r3r-r-sX [[EEEFF**FF* [ZBBBCC ** CC * 111111000 1 1 1 [S3,// & &0/ & [X<<<== D D == D D Dr5r-c^eZdZgdZejdedZdS) TestJohnsonsu))r6r r g?r-)rr r gH';vIh%,=)rr r g?x7rRrc|\}}}}}ttj||||dttj|||||dSNrRr)rr9 johnsonsurrrsrr_r1r2rtols r3rzTestJohnsonsu.test_sf_isf% j1aS**1a33ReDDDD++B155qsCCCCCCr5Nrrrcasesrrrrr;r5r3rQrQ sX ; ; ;E [VU++DD,+DDDr5rQc^eZdZgdZejdedZdS) TestJohnsonb))rr r rr-)rr r g0jA:rR)rr r gQbF5rRrc|\}}}}}ttj||||dttj|||||dS)NrRrr)rr9r%rrrVs r3rzTestJohnsonb.test_sf_isf; rXr5NrYr;r5r3r\r\, sX = = =E [VU++DD,+DDDr5r\ceZdZdZdZdZdZdZej dddgd Z d Z ej d d d gdZ dZdS) TestLogisticctjdd}tj|}tj|}t ||dSNrr)rjrYr9logisticrqrrrsr_r2rs r3rzTestLogistic.test_cdf_ppfD sS KR  N  q ! ! ^   " "2r5ctjdd}tj|}tj|}t ||dSra)rjrYr9rbrrrrcs r3rzTestLogistic.test_sf_isfJ sS KR  N  a  ^   " "2r5cd}d}ttjd|z |ttj||dS)Ng.funck sDAqD AqA~..RVTAXN33356689A>B$(a&$(a0014&$(a00146788:;>>$(#&(TAX.// &end;;;;;r5N)rrrrrrgrirlrrrryr}rrr;r5r3r_r_B s  888444)))  [03J3K3MNNCCNNC,FFF  [\D%=99 1 1:9 1<<<<r) r9logserrrjrrBrrCrrDrcrdrGs r3rJzTestLogser.test_rvs s|733vdai     x~~((((z)L"99999lt$$#s#####l4  $$Q''#rz*****y~rrrs r3r}z&TestGumbel_r_l.test_fit_comp_optimizer s|xxSgY%(**vv  '"Q;DL  +&]DN &dD99D99999r5z dist, sgnr rc|tjgdz}||\}}t||dzt|dddS)N)rrrrrrrgW@g@g3qtw>rvr)rjrrr)rsrBrzrerfs r3ryzTestGumbel_r_l.test_fit sf :::;; ;XXa[[ U S!334445DAAAAAAr5N) rrrrfixturerrrr9gumbel_rgumbel_lr}ryr;r5r3rr s=V^*%%%++&%+ [Venen%EFF [Y 33 [[***55 [1#UmeT];==::==6543GF :  [[ENA+>,1NB+?+ABBBBBBBBBr5rc eZdZdZdZejddZej dej ddd gej d d d gej d dd gdZ ej ddd gej d d d gej d dd gej dde ddgdDe jddZe jddZdZdZdS) 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)Nrsr|rrrTrrrrg?grq@rr;gffffff?gK~?g2@g۶m۶m?rUUUUUU?gqq?rr9g%I$I?gQ?gUUUUUU@grq?g88Nb@) rwrxryrzr9paretorrjrrrrrsrrrOr\s r3rzTestPareto.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)NgeArgrrrd)r9rrr)rsr_r2rfrvrXs r3rzTestPareto.test_sf$ sO   LOOAqauO 5 5!Ga<8$$$$$r5rrc@tjdSr5rrxs r3rzTestPareto.rng, rr5z2ignore:invalid value encountered in double_scalarsrr rgrrr<rc ,tjd||||}tj|ddd}tj|ddd}tj|ddd}||cxkr |cxkrdksnJtjd|||dz|}tj|d \} } } t | dz||dz } | jd} t | | tjtj | | z z t | ddS) Nrarr2rfrerrp= ף?)rr)rfix_b)rfbrgr) r9rrrrrrBrjrmr)rsrrr<rrshape_mle_analytical1shape_mle_analytical2shape_mle_analytical3 shape_mle_a loc_mle_a scale_mle_a data_shiftndatas r3ryzTestPareto.test_fit0 s |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"""""r5r]fix_shape, fix_loc, fix_scalecg|]}d|v| SFr;rArvs r3rCzTestPareto.P (---A!&! !+r5TFrrepeatignoreinvalidctjd||||}i} |r|| d<|r|| d<|r|| d<ttj|fi| dS)Nrarrrr)r9rrr rsrrr<rrr>rrrs r3rz&TestPareto.test_fit_MLE_comp_optimizerL s|SIY$+# ??  #"DJ  #"DL  '&DN%elDAADAAAAAr5c d\}}}tj|||dtjd}t tj|dS)N)r rr raið&r)r9rrrjrrr)rsrBlocationrfrs r3test_fit_known_bad_seedz"TestPareto.test_fit_known_bad_seedb sa ")x|xS-/Y-B-B7-K-K MM%elD99999r5cttjtttjjgddtttjjgddddS)Nr rgr)rrgrr rrB)rr9rr`r#rrxs r3test_fit_warningszTestPareto.test_fit_warningsl sgEL)))lEL$4iiiaHHHHlEL$4iiia      r5ctjddd|}t|dtj|}dS)Ni~r ra)rer2rrr)r9rrr r)rsrrrs r3test_negative_datazTestPareto.test_negative_datat sK|DACcJJ$""" L  T " "r5N)rrrrrrrrrfilterwarningsrryr(rjerrstaterrrrr;r5r3rr s%:N:N:Nx%%%V^*%%%++&%+ [!122 [[1a&11 [YA// [[1a&11##210/2122 #. [[2q'22 [YA// [[1a&11 [<--$q)I)I)I---..R[""" B B#"..210/32 BR["""::#":   #####r5rc eZdZdZdZdZdZdZdZdZ dZ d Z e j d d gd fd dddejdz ejgfddddejdzdgfdgdfgdZdZdS) TestGenparetocrdD]i}tj|}tj|\}}t |dt tj|jtjd}tj|\}}t||gddgdS)NrTrrr|) rjrr9 genpareto _get_supportrr isposinfr)rsrr1r2s r3test_abzTestGenpareto.test_ab s $ $A 1 A?//22DAq B    BKNN # # # # JsOO++A..1AS *****r5ctjd}tjddd}t ||tj|t ||tj|t ||tj|tjddd}t | |tj |dS)Nrrrrr:rTr`) r9rrjrYrrirgrqrrrsrvr_rs r3test_c0zTestGenpareto.test_c0 s_r " " " K3 # #q 5;??1#5#5666q 5;??1#5#5666a%+.."3"3444 KB # #q 5;??1#5#566666r5ctjd}tjddd}t ||tj|t ||tj|t ||tj|tjddd}t | |tj |t | d ddS) Nrrrrr:rrTr`r ) r9rrjrYrriuniformrqrrrrs r3test_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(((((r5ctjd}t|tj|tjgddgtt j| tjtjd}t|tj|tjgddgtt j| tjtjd}t|tj|tjgddgtt j| tjdS)Nr]rrrTr) r9rrrirjrrqr isneginfrrsrs r3 test_x_infzTestGenpareto.test_x_inf sC _s # # #82r(CCC BIIbf--../// _r " " "82r(CCC BIIbf--../// _s # # #82r(CCC BIIbf--../////r5ctjddd}dD]}tj||}dD]7}tj|||z}t ||d8tj||}dD]7}tj|||z}t ||d8dS) Nrr`r:rrrg+rr)rr)rjrYr9rrirrq)rsr_rpdf0dcpdfccdf0cdfcs r3test_c_continuityzTestGenpareto.test_c_continuity s K2r " " 8 8A?&&q!,,D% 8 8**1a"f55d77777?&&q!,,D$ 8 8**1a"f55d77777 8 8 8r5c ttjtjdddtjddddd tjdddz f}d D]\}tj||}d D]7}tj|||z}t||d 8]dS Nrr~r]baser r:FendpointrT)rrrr)rjrNrrYr9rrr)rsrrppf0rppfcs r3test_c_continuity_ppfz#TestGenpareto.test_c_continuity_ppf E"+eT444+dArE:::r{5$S9999: ; 8 8A?&&q!,,D% 8 8**1a"f55d77777 8 8 8r5c ttjtjdddtjddddd tjdddz f}d D]\}tj||}d D]7}tj|||z}t||d 8]dSr)rjrNrrYr9rrr)rsrrisf0risfcs r3test_c_continuity_isfz#TestGenpareto.test_c_continuity_isf rr5c \tjtjdddtjddddd tjdddz f}d D]P}t t jt j||||d QdS) Nrr~r]rr r:FrrT)r-gC]r2rgV瞯Ҽrr) rjrNrrYrr9rrqr)rsrrs r3test_cdf_ppf_roundtripz$TestGenpareto.test_cdf_ppf_roundtrip s E"+eT444+dArE:::r{5$S9999: ;/ + +A EO//0C0CAq0I0I1MME + + + + + + +r5cjtjdddd}t|ddS)Nrr~rr gpEȜ)r9rrrrks r3rzTestGenpareto.test_logsf s4$$T3155122222r5zc, expected_statsr)r r rgr3rlrgqq @r`rggqq?g?g$I$ ?rq?rgll0@r)r|UUUUUU?r333333cntj|d}t||dddS)Nrrrrrf)r9rr)rsrexpected_statsrs r3rzTestGenpareto.test_stats s;&&q&&99UGGGGGGr5chtjd}t|dddS)Nr-gvǼ ?rr)r9rrAr)rsrs r3test_varzTestGenpareto.test_var s3 O   % %,5999999r5N)rrrrrrrrrrrrrrrrjrrrrr;r5r3rr~ sA + + + 7 7 7 ) ) ) 0 0 0 8 8 8888888+++333  [ \\\  T2gbgajj="&1 2 ]T7271::$5v> ? """ # %&& HH && H:::::r5rc>eZdZdZdZdZdZdZdZdZ dZ d S) TestPearson3cDtjddSr5r6rxs r3r7zTestPearson3.setup_method r8r5ctjdd}tj|dksJ|jjtdvsJtjd}t|tsJtjdd}t|tj sJ|jjtdvsJt|dksJdS)Nr]r<r;AllFloatr|r) r9r,rrjrBrrCrrDrrdrrGs r3rJzTestPearson3.test_rvs s~!!#G!44x~~((((z)J"77777n  %%#u%%%%%nS!!%%a((#rz*****y~:!666663xx1}}}}}}r5ctjdgd}t|t jgddtjdd}t|t jdgdtjgd d}t|t jgd ddS) Nrgrr]rQ)gtT?g+q?g?rvrrr]ND}i?rrrrr )rgj?gdC?gs?g'M?)r9r,rirrjrrs r3rRzTestPearson3.test_pdf s~!!!___55bh'K'K'KLL! # # # #~!!"c**bh |444@@@@~!!"4"4"4c::bh(@(@(@AAGK M M M M M Mr5chtjdgd}t|t jgddtjdd}t|dgdtjgd d}t|gd ddS) Nrgr)grE?gTp]0?g~?rvrrr]gE&"J?r)giZ*J?gh+8w?gcK?g|. sG'''--17FCCAF'''r5)r9r,rqr)rsskewsrint_pdfsrrs @@r3test_negative_cdf_bug_11186z(TestPearson3.test_negative_cdf_bug_11186 su!  ~!!&%00''''' %'''h'''''r5c6tjdd}t|dt |t jsJtjdd}t|dt |t jsJdS)Nr rgrrv)r9r,rrrDrjnumber)rsrs r3test_return_array_bug_11746z(TestPearson3.test_return_array_bug_11746# s&&q!,,VQ&"),,,,,&&q(33VQ&"),,,,,,,r5cgd}d}tjtj|||}t ||t jdgdgg}t jdd}t tj||tj| | t tj||tj | | t tj||tj ||  dS)Nrr|rrrrg) r9r,rrqrrjrrYrirr)rsrrrrBr_s r3test_ppf_bug_17050zTestPearson3.test_ppf_bug_17050. s?!  n  !3!3FE!B!BEJJV$$$x$#(( KA  **1d33**A2u55 7 7 7**1d33))1"te44 6 6 6**1d33++Au555 7 7 7 7 7r5cgd}gd}gd}ttj|||dttj|dtj|ddS)N)r]r|rT皙)rUrrr%)g7>g~׼=gp'+7g;rrr)rr9r,rr)rsrBr_rs r3rzTestPearson3.test_sfA s%$$ " " ">>>))!T22CeDDDD))!Q//q1A1ANNNNNNr5N) rrrr7rJrRr\rrrrr;r5r3r r  s   MMMKKK ( ( ( - - -777& O O O O Or5r c8eZdZdZdZdZdZdZdZdZ dS) TestKappa4cgd}d}dD]T}tj|||}tj|| }t ||UdS)N)rr]rQr|rT) gffffffrr皙ɿr!r]rQr|rTffffff?)r9kappa4rqrrrsr_rpr\rH vals_comps r3test_cdf_genparetozTestKappa4.test_cdf_genparetoN sr   - -A<##Aq!,,D++Ar22I D) , , , ,  - -r5ctjddd}d}tjddd}tj|||}tj||}t ||dS)Nrrr`rrr)rjrYr9r'rq genextremerr(s r3test_cdf_genextremezTestKappa4.test_cdf_genextremeY st KAr " "  KAr " "|1a(($((A.. i(((((r5ctjddd}d}d}tj|||}tj|}t ||dS)Nrr`rTr)rjrYr9r'rqrgrr(s r3test_cdf_exponzTestKappa4.test_cdf_exponb sa K2r " "  |1a((KOOA&& i(((((r5ctjddd}d}d}tj|||}tj|}t ||dS)Nrrr`r)rjrYr9r'rqrrr(s r3test_cdf_gumbel_rzTestKappa4.test_cdf_gumbel_rk sc KAr " "  |1a((N&&q)) i(((((r5ctjddd}d}d}tj|||}tj|}t ||dS)Nrrr`rr)rjrYr9r'rqrbrr(s r3test_cdf_logisticzTestKappa4.test_cdf_logistict sc KAr " "  |1a((N&&q)) i(((((r5ctjddd}d}d}tj|||}tj|}t ||dS)Nrrr`rT)rjrYr9r'rqrrr(s r3test_cdf_uniformzTestKappa4.test_cdf_uniform} sc KAr " "  |1a((M%%a(( i(((((r5c0tjdddSrp)r9r'rxs r3test_integers_ctorzTestKappa4.test_integers_ctor s  Qr5N) rrrr*r-r/r1r3r5r7r;r5r3r#r#M s} - - -)))))))))))))))r5r#c,eZdZdZdZdZdZdZdS) TestPoissoncDtjddSr5r6rxs r3r7zTestPoisson.setup_method r8r5ctjd}tjgd|}d|dz |dzdz g}t ||dS)Nrgrr rgr|r)rjrr9rrPr)rsln2rHrXs r3test_pmf_basiczTestPoisson.test_pmf_basic sXfQii}  C00QQq)h'''''r5ctjgdd}gd}t||tjdd}t |ddS)Nr<r)r rrffffff?rr)r9rrPrintervalr)rsrHrXrBs r3test_mu0zTestPoisson.test_mu0 sc}  A..994***=))$22Xv&&&&&r5ctjdd}tj|dksJtj|dksJ|jjtdvsJtjd}t|tsJtjdd}t|tj sJ|jjtdvsJdS)Nr|r<r;rr>r) r9rrrjrrBrrCrrDrcrdrGs r3rJzTestPoisson.test_rvs s}  7 33vdai     x~~((((z)L"99999m$$#s#####mC  $$Q''#rz*****y~rCrJrr;r5r3r9r9 s_(((''' 9 9 9*****r5r9cVeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd S) TestKSTwocDtjddSr5r6rxs r3r7zTestKSTwo.setup_method r8r5c dD]}tjdd|z d|z ddd|z z dg}d|z |z}tj|dz}|dkrtj|nd}tjdd||zddt jd|zz tdd|zz ddg}t j ||}t||dS)Nr rgrr`rarrr|r rTrgr) rjrr8rgammalnrr9ksonerrkstworqr)rsrur_v1lgelgrXrs r3r\zTestKSTwo.test_cdf s) 0 0A!SUAaCaAgq9::Aa%!B&&qs++B!#q26":::aCxArCx!"Qu{~~c1'='=%=!=!$Q2Xs!3!3!$!&''H{q!,,H Hh / / / /# 0 0r5c tjddd}dD]}tjdd|z d|z ddd|z z dg}d|z |z}tj|dz}|dkrtj|nd}tjddd||zz dtj d|ztd|zddg}tj ||}t||dS)Nrr rrJr|rTrg) rjrYrr8rrKrr9rLrrrMr)rsr_rurNrOrPrXrs r3rzTestKSTwo.test_sf s K1b ! !) / /A!SUAaCaAgq9::Aa%!B&&qs++B!#q26":::aCxc!"R#X!"5;>>#q#9#9!9!$QrT3!455HknnQ**G GX . . . . / /r5c tjddddd}gd}|D]]}|tj|z }tj||}tj|}t|d^dS)Nrrgrr )r=rarSirrr-)rjrYrr9rMrqr)r )rsr_ns_xxnprobsdiffss r3test_cdf_sqrtnzTestKSTwo.test_cdf_sqrtn s K1b ! !!"" % , , , + +Bbgbkk!BKOOB++EGENNE eT * * * *  + +r5ctjddd}dD]U}tj||}tj||}t |d|z VdSNrr rrJ)rjrYr9rMrqrr)rsr_rurrs r3rzTestKSTwo.test_cdf_sf so K1b ! !) = =A{q!,,HknnQ**G %hG < < < < = =r5ctjddd}dD]l}|tj|z }tj||}tj||}t|d|z mdSrZ)rjrYrr9rMrqrr)rsr_rurUrrs r3test_cdf_sf_sqrtnzTestKSTwo.test_cdf_sf_sqrtn s K1b ! !) = =ARWQZZB{r1--HknnR++G %hG < < < <  = =r5c0tjddd}dD]|}||d|z k}tj||}d|k|dkz}tj||}t ||||d}dS) Nrr rrJr|rrr)rjrYr9rMrqrrrsr_rurUrcondrHs r3test_ppf_of_cdfzTestKSTwo.test_ppf_of_cdf s K1b ! !) = =A1s1u9B{r1--HLX_5D;??8Q//D DJ4t < < < < <  = =r5c0tjddd}dD]|}||d|z k}tj||}d|k|dkz}tj||}t ||||d}dS) Nrr rrJr|rTrr)rjrYr9rMrrr)rsr_rurUvals_isfr_rHs r3test_isf_of_sfzTestKSTwo.test_isf_of_sf s K1b ! !) = =A1s1u9B{r1--HLX^4D;>>(A..D DJ4t < < < < <  = =r5cVtjddd}dD]}|tj|z |d|z k}tj||}d|k|dkz}tj||}t||||dS)Nrr rrJr|rT)rjrYrr9rMrqrrr^s r3test_ppf_of_cdf_sqrtnzTestKSTwo.test_ppf_of_cdf_sqrtn s K1b ! !) 2 2Abgajj.!c!e),B{r1--HLX^4D;??8Q//D DJ4 1 1 1 1  2 2r5cVtjddd}dD]}|tj|z |d|z k}tj||}d|k|dkz}tj||}t||||dS)Nrr rrJr|r@)rjrYrr9rMrrr)rsr_rurUrr_rHs r3test_isf_of_sf_sqrtnzTestKSTwo.test_isf_of_sf_sqrtn s K1b ! !) 2 2Abgajj.!c!e),BknnR++GKGdN3D;??7A..D DJ4 1 1 1 1  2 2r5ctjddddd}dD]R}tj||}tj||}t ||SdSrZ)rjrYr9rMrrqr)rsrVrurUrs r3rzTestKSTwo.test_ppf st Aq"%%abb)) - -A**B{r1--H He , , , , - -r5c gd}tjgd}tjgdgdgdgdgdgdg}t|D]y\}}|tjd ztjtjd z |z z}t j||}t|||d zdS) N)r`r=rarSrr)rlgUUUUUU?r|r rgr)gRT>gr ?gK5 ?gn "5?gU ?gk?)g&6#>gb E>gI5?g\ ?g;?g%1?)g6>gL>g<?g䓀^?gO|6$?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?rgr;r) rjr enumeraterrrkr9rMrqr)rsrSratiosrXidxrur_rs r3test_simard_lecuyer_table1z$TestKSTwo.test_simard_lecuyer_table1& s+ * *888998 - - - - - - - - - - - - - - - - - -     mm @ @FC"RWRU1WQY%7%77A{q!,,H Hhsm$ ? ? ? ? ? @ @r5N)rrrr7r\rrXrr\r`rcrergrrmr;r5r3rGrG s000( / / / + + +============222222---@@@@@r5rGc eZdZdZdZdZdS)TestZipfcDtjddSr5r6rxs r3r7zTestZipf.setup_methodI r8r5ctjdd}tj|dksJtj|dksJ|jjtdvsJtjd}t|tsJtjdd}t|tj sJ|jjtdvsJdS)Nrr<r;r r>r) r9zipfrrjrrBrrCrrDrcrdrGs r3rJzTestZipf.test_rvsL sz~~c~00vdai     x~~((((z)L"99999jnnS!!#s#####joo!!!$$#rz*****y~rr) r9dlaplacerrjrBrrCrrDrcrdrGs r3rJzTestDLaplace.test_rvse s~!!#G!44x~~((((z)L"99999n  %%#s#####nS!!%%a((#rz*****y~@g @gGz@c\tjd}tjd||||}t ttjtjj}||}tj|}t||||dd}tj|dd}t||ttj||tj ||dz z dksJttj||dz ttj|dttj||tj dd dS) Nrra)rr^rerfrrrg)rrrr rB) rjrrr9r#rrrrrrrrand) rsrrr<rr super_fit super_fitted invgauss_fit __class__s r3rz(TestInvgauss.test_fit_MLE_comp_optimizer si##D))~!!sv&-YS"RR$u~..??C  y ~))$// \<000!yA1555 ~))$QA)>> \<000 &endIIIIvtw{+q011111%end1MMMM &endCCCC &end-/Y^^A->->q-A C C C C C Cr5cttjtjt 5tjgddddddS#1swxYwYdSrH)rr9r#rrr#rrxs r3test_fit_raise_errorsz"TestInvgauss.test_fit_raise_errors sEN+++ ]< ( ( 2 2 N  yyyq  1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2s$A$$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?)r r r r r 皙?r^r?gfFngr^:g9̗?rgx_;:g!?gٷ ??)r9r#rqrrr)rsr^rXrT cdf_actual sf_actuals r3rzTestInvgauss.test_cdf_sf s..."??##CB#//Xv&&&^''$'77  $9:::N%%cd%33  #7888 ##GV44 3444##Hf55 122222r5ctjdd}t|dtjdd}t|dtjdd}t|dtjdd}t|d dS) NrrrgiJ.rgr^ߺrgpgFgpQ^L)r9r#rrr)rsrrs r3rzTestInvgauss.test_logcdf_logsf s&&v$&77 1222&&sD11 5666$$Ut$445666$$S$//011111r5zmu, ref))rg,9)rg% !)r~g40)rgK' @)rg`p @cdttj||ddSrT)rr9r#rH)rsr^rs r3rqzTestInvgauss.test_entropy s/ ..r22CeDDDDDDr5)rrrr7rrrryrrrrrq __classcell__rs@r3rr s; [7')>?AA>>AA>: [7')>?AA C C C CAA CD222 !3!3!3F222. [Y)D)D)DEE EE EE EEEEEr5rc`eZdZejdgddZdZdS) TestLandauname)rirqrrrc|dvrtjdddf}ntjdddf}ttj|}ttj|}||}|g|ddR}t ||d dS) N>rrr]rrrr`r rr)rjrYr.r9landau levy_stabler)rsrr_ landau_method levy_methodrrs r3test_landau_levy_agreementz%TestLandau.test_landau_levy_agreement s > ! ! Ca(()AA B2&&'A d33 e/66 mQk#1#a####Su------r5cttjdtjfdzttjdtjdS)Nrrrr)rr9rrjrrrxs r3r*zTestLandau.test_moments& sUU\'''77"&1EEEU\((++RV44444r5N)rrrrrrrr*r;r5r3rr sW [V%G%G%GHH . .IH .55555r5rceZdZejdgdejdgddZejdgdfdZd Zd Z d Z d Z d Z xZ S) TestLaplacer)rrr rgr<)r rgrr`ctjd}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) Nrrarrrnrr{rgrB)rjrrr9rrrHrmrrrrrr`rrrr) rsrr<rrloc_mlerrerfs r3ryzTestLaplace.test_fit- 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>>>>>r5rvs_loc,rvs_scale))rr`r`r)r|rQctjd}tjd|||}d}tj|\}}tttjtj|\}} ||||} ||| |} | | kstj | | ddsJdSdS)Nrrrc dt| tjd|zzd|z tjtj||z zz zS)Nrrgr )rrjrrmr)rerfrs r3llz3TestLaplace.test_fit_MLE_comp_optimizer..lle sSCII%8E'26"&*<*<#=#==>? ?r5rrn) rjrrr9rrrrrr) rsrr<rrrrerfloc_opt scale_optll_mlell_optrs r3rz'TestLaplace.test_fit_MLE_comp_optimizer\ si##D))}  dy.1!33 ? ? ? ]&&t,, U"4 #6#6#(=2225#d)) C%%GY--"+ff38u#F#F#Fr5ctjgd}tj|d\}}t |dddtj|d\}}t |ddddS)N)rTrTrrUr%rr3rrrrnr{)rjrr9rrr)rsrrerfs r3test_fit_simple_non_random_dataz+TestLaplace.test_fit_simple_non_random_datas sx77788]&&t!&44 Uqu59999]&&tA&66 UQU777777r5cFd}tj| }|dksJtj|}|dksJtj|}|dksJtj| }|dksJdS)NrrrT)r9rrqr)rsr_p0p1s r3test_sf_cdf_extremesz TestLaplace.test_sf_cdf_extremes| s  ]  r " "Syyyy]  q ! !Syyyy ]  a Syyyy]  qb ! !Syyyyyyr5cd}tj|}t|t j| dz ddS)NrSrgrr)r9rrrrjr)rsr_rvs r3rzTestLaplace.test_sf sE  M  Q  261"::a>>6"+e&6&<&ctjd}tj|||d|}d|i}|r||d<|r||d<dt |z } | dkrUd } tjttf| 5tjj |fi|dddn #1swxYwYdSttj|fi|dS) NrrarArfcrrrr r ) rjrrr9rrrrrrrrr) rsrrerfrr>rrrnfreerEs r3test_fit_analytic_mlez$TestLogLaplace.test_fit_analytic_mle s=i##$788##A3e#14$66}  DJ  #"DNCII  A::MI j9KKK 3 3 $T22T222 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 F%e&6EEEEEEEsB66B:=B:N) rrrrrrrrrrr;r5r3rr sDDDEEE [S,,,//OO0/O [S///22 [\L>:: [WtUm44 [[4-88FF9854;:32FFFr5rc eZdZejdddgdZejddZejdgd ejd gd ejd gd ejdde ddgdDdZ dZ dZ dZ dS) TestPowerlawzx, a, sf)rlrg?)g?gp?gSQ>cfttj|||ddSr)rr9powerlawr)rsr_r1rs r3rzTestPowerlaw.test_sf s1 ))!Q//%@@@@@@r5rrc@tjdSr5rrxs r3rzTestPowerlaw.rng rr5r)r]r|rr rgrrr<rrcg|]}d|v| Srr;rs r3rCzTestPowerlaw. rr5TFrrc,tjd||||}t} |r|| d<|r5t j|tj | d<|r|| d<ttj|fi| ddidS)Nr")rr1rerfrrrrrT) r9rrrrj nextafterrrrrs r3rz(TestPowerlaw.test_fit_MLE_comp_optimizer s~!!siW(1"EEvv  #"DJ  =< RVG<> [Y 33 [[***55 [<--$q)I)I)I---..<<..6543?> <$ D D D444666666r5rc>eZdZejdgddZejdddgdZejdgdd Zejdgd d Z d S) TestPowerLogNormz x, c, s, ref))rarr ga!R()rrr g;?)rrr gE?)MDrr g=chttj||||ddSr)rr9r*rrsr_rrOrs r3rzTestPowerLogNorm.test_sfGs4 *--aA66%HHHHHHr5z q, c, s, ref)g?rr r~)gR4 -rr rchttj||||ddS)Ng|=r)rr9r*r)rsrrrOrs r3rzTestPowerLogNorm.test_isfQs4 *..q!Q775IIIIIIr5))rrr g?)rvrr gv6)rvrSr g+ 94|7)r~rSr g?chttj||||ddS)Ngt =r)rr9r*rqrs r3r\zTestPowerLogNorm.test_cdfWs4 *..q!Q775IIIIIIr5))rrr gS^Ռe 9)@xDrr g 0g;)g\)c=Hrr g7H7chttj||||ddS)NgAfc=r)rr9r*rirs r3rRzTestPowerLogNorm.test_pdfjs4 *..q!Q775IIIIIIr5N) rrrrrrrrr\rRr;r5r3rr6s<" [^EEEFF II FF I  [^ACEFFJJFFJ [^AAABB JJ BB J [^GGGHHJJ HHJJJr5rceZdZejdgddZejdgddZejdgddZd S) TestPowerNormr,))rr g|<)rrgge()rarg%!@6)rSr~gT;-cfttj|||ddSr)rr9 powernormrr0s r3rzTestPowerNorm.test_sfzs1 **1a00#EBBBBBBr5r))r;rgĿ)gwJ?rag!X)rrg缂U)rFrgͫ1@)r8rggD@)Jz5rgU!zYr@cfttj|||ddSNrr)rr9rrrs r3rzTestPowerNorm.test_isfs1 ++Aq113UCCCCCCr5))irg.u T9)rgr?)rrgsK-)rrgk8>)rrg^u1-cfttj|||ddSrT)rr9rrqr0s r3r\zTestPowerNorm.test_cdfs1 ++Aq113UCCCCCCr5N) rrrrrrrrr\r;r5r3rrrs [[CCCDD CC DD C [[===>>DD>>D [[BBBCC DD CC DDDr5rcxeZdZdZdZdZdZdZej dddgd Z d S) TestInvGammactj5tjdttjdd}gd}t ||gd}tj|d}gdtjdd gtj d d gtj tj d gf}t||D]\}}t|| ddddS#1swxYwYdS) Nrsg(\O3@rrw)g~?gCX&?g*7gS?gBqFq@)r@gffffff@)rg Ey?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@) rwrxryrzr9r"rrjrrrr)rsrrXr1r_r2s r3test_invgamma_inf_gh_1866z&TestInvGamma.test_invgamma_inf_gh_1866sU $ & & * *  !'> : : :>''%'@@D%%%H D( + + +A>''!V'<.4=== E1vrvbd#U###===r5cg|]\}}}| Sr;r;rArr _correct_s r3rCz(TestF.test_endpoints..>>>!5UI9>>>r5)r9frir1r)rsrrr_correctanscorrects r3rzTestF.test_endpointss&#&'#' ' ' Bx"&&&&&CC=====>>>>>!#w/////r5c^tjddd\}}}}ttj|ttj|ttj|ttj| dS)Nr@rr)r9rr rjrGrs r3test_f_momentszTestF.test_f_momentssW]]2sF];; 1a A A ABKNN"#####r5ctj5tjdttjdgdzgddddddS#1swxYwYdS)Nrsrr)rgrr3rrdfndfdr)rwrxryrzr9rrxs r3test_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$$A(+A(ctjdgdgg}tjddg}tj||d\}}}}||dz z gdz}t ||d|dzz||zdz z|z |dz dzz |dz z }t ||d|z|zdz tjd|dz zz|d z tj|||zdz zzz } t || d|d |zd z z||zdz z|dz |dz dzzzz} ||d z z|dz z||zdz z} | | z } t || dS) NrrrVrrrgrrr3r)rjrr9rrr) rsr r!rrrOr\rv2s2k2numk2denk2s r3test_stats_broadcastzTestF.test_stats_broadcastshbT{##hBx  W]]sV]DD 1aS1Wo q 2 aZ39q= )C /37Q, >#' J2us{Q"'!S1W+"6"66a273c A #677792cQsURZ(C#IM:Qw37Q,./0sQw37+sSy1}= U]2r5N)rrrrrr"r*r;r5r3r r sS000$$$HHH r5r c 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)Nrr3g?g?)rr9rr{rxs r3test_rvgeneric_stdzTestStudentT.test_rvgeneric_stds/!%'++q!f"5"5 J7OPPPPPr5cbttjddtjtjtjtjfttjdddtjtjtjfttjdddtjtjtjfttjddddtjtjfttjd d tjtjfttjd d dtjfttjd d dtjfttjd d ddS)Nr r)rr)\(?rrggGz@g i@rrvgGz@rg ףp= @)rgq@)rr9rrjrrrxs r3test_moments_tzTestStudentT.test_moments_tsUW]]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 FFFUW]]dD]99;RSSSSSr5ctgd}gd}ttj||ddS)N)r rgrra)g?@gTM]?ggY?U?rrrr9rrH)rsrrXs r3test_t_entropyzTestStudentT.test_t_entropy+sE __;;;++XEBBBBBBr5zv, ref)rar3)rrcdttj||ddSr#r4)rsrrs r3test_t_extreme_entropyz#TestStudentT.test_t_extreme_entropy2s- **Ce<<<<<&>???S*%zz!ZK.'A'ABBBBBr5ctjdtj|t}tjdd|j}tj||<tj |ddd}tj ddd }tj ||ddd}td D]G}t|||||t|||||Htj |dd }tj dd }tj ||dd }t|||t|||dS) Nrr;r`r;rr r)rrerfrrerfrrr<rd)rjrrrr=rrBrr9rrrrrH)rsr9rr res_ex_inf res_ex_noinfrs r3test_t_inf_df_stats_entropyz(TestStudentT.test_t_inf_df_stats_entropyYs qZ $777 Y  q":+;  < <:gmmrq6mBBZ%%!1f%EE w}}J;Qa,2%44 q ? ?A Q +Z] ; ; ; Q ,l1o > > > >goo!o44Z''AQ'77 w"j[/qJJ S_j111S*%|44444r5cgd}gd}gd}gd}ttj|||dttj|||ddS)N)r rr`r )rd~QJrr )gZ_2g 9g!ǟuIgdg)g73?rgմFhAW;gm0_?rr)rr9rrri)rsr_r logpdf_refpdf_refs r3test_logpdf_pdfzTestStudentT.test_logpdf_pdfps OO # # #@@@ >>>q"--zFFFF Ar**G%@@@@@@r5 x, df, ref))gRr?guSaG)rr?r)R@r?gGn`?ctj||}t||dtj| |}t||ddSr)r9rrrr)rsr_rrrrs r3rzTestStudentT.test_logcdf_logsf~s` 2&&%0000 qb"%%s//////r5N)rrrr.r1r5rrrr7rErJrOrr;r5r3r,r,sQQQ T T TCCC [X68:;; = =;; = [Z*<*<*<== [\QFQFQF-6YY ,B./VaV,<./S1#J,899CC 99== C  [\QFQFQF-6YY ,B./VaV,<./S1#J,89955 995& A A A [\CCCDD00 DD000r5r,cVeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd S)TestRvDiscretecDtjddSr5r6rxs r3r7zTestRvDiscrete.setup_methodr8r5cgd}gd}d}tjd||f}||}t|tjsJt ||D]>\}}tt||kt|z |z dksJ?|}t j t|tj sJdS)N)rrr rgrr)rr~rrr~rrsample)rvaluesr;rF) r9rErrDrjrdrrrmrrrinteger)rsstates probabilitysamplesrr_rOrvs r3rJzTestRvDiscrete.test_rvss$$$444   8V[4I J J J EEwE  !RZ((((( ,, > >DAqs16{{5>>1A566===== EEGG}T!WWbj1111111r5cftjgd}tjgd|f}t t || }|}t||tjgdgdf}|}t|ddS)N)rlr=r~r<rX)rTrrr) rjrr9rErmrrHrr)rsrrvrorps r3rqzTestRvDiscrete.test_entropys***++  iii%7 8 8 8%u--... IIKK:&&&  iii%= > > > IIKKQr5cgd}gd}tj||f}ddgddgg}t||dd gd d ggd dS)Nrr|r~rQr^rTrrrgr|rQrr~rr)r9rErrP)rsxkpkrr_s r3rjzTestRvDiscrete.test_pmfs YY __  r2h / / /"X!W q sc$*/ 1 1 1 1 1 1r5cgd}gd}tj||fgd}gd}t||dtfd|D|ddS) Nrr`r^)rrTrrrrrr)rr|r|r|rrr r rrc:g|]}|Sr;)rq)rArrs r3rCz+TestRvDiscrete.test_cdf..s#777777r5)r9rErrq)rsrarbx_valuesrXrs @r3r\zTestRvDiscrete.test_cdfs YY __  r2h / / /555555x(((???? 7777h777 u . . . . . .r5cgd}gd}tj||fgd}gd}t||dtfd|D|ddS) Nrr`r^)r]r|rrrrT)r r rgrgrrrrc:g|]}|Sr;)r)rArrs r3rCz+TestRvDiscrete.test_ppf..s#555q555r5)r9rErr)rsrarbq_valuesrXrs @r3rzTestRvDiscrete.test_ppfs YY __  r2h / / /000%%%x(((???? 5555H555 u . . . . . .r5c gdgdf}tj|}t|||jdddz|jdddS)N)r rgrrr)r]rQr~r~r]r^rr-r )r9rErrrqra)rsrHrs r3test_cdf_ppf_nextz TestRvDiscrete.test_cdf_ppf_nexts|!:!:!:;  d + + +266"&&ss"4"4t";<<59 & & & & &r5cBtjdd}tjgdgdgdg}t j||f}t |tj|j |j zddS)NrV)rr)r]r]r\rF)r]r]rFrFr^rr) rjrr?rr9rErrrmrarbrsrarbrs r3test_multidimensionz"TestRvDiscrete.test_multidimensions Yr]] " "6 * * X---------/00 r2h / / / RVBEBEM%:%:GGGGGGr5cgd}ddg}tttjfit ||fgd}tttjfit ||fgd}gd}tttjfit ||fgd}gd}tttjfit ||fddg}ddg}tttjfit ||fdS)Nr r|r^)r|333333?gffffff濩r rgrrr)r~r~r~r~r%r )r`rr9rErrsrarbs r3test_bad_inputzTestRvDiscrete.test_bad_inputs/ YY3Zj%"3MMtB87L7L7LMMM YYj%"3MMtB87L7L7LMMM YY   j%"3MMtB87L7L7LMMM __ ' ' 'j%"3MMtB87L7L7LMMMV3Zj%"3MMtB87L7L7LMMMMMr5ctjddtjdd}}t t t jfit||ftjddtjdd}}t t t jfit||ftjddtjdd}}tt j||f dddS) NrrgrgrgrgUUUUUU?r^r3rrgr) rjrr?r#r`rr9rErrrPrqs r3test_shape_rv_samplez#TestRvDiscrete.test_shape_rv_samples1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM1%%f--rwvs/C/CBj%"3MMtB87L7L7LMMM1%%f--rwvs/C/CBU&r2h777;;A>>DDDDDr5cgd}gd}tj||f}t|t j|j|jzddS)N)r rgrr3rr)r]rQrQrQrQr]r^rr)r9rErrrjrmrarbrls r3 test_expect1zTestRvDiscrete.test_expect1sd  + + +  r2h / / / RVBEBEM%:%:GGGGGGr5c 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-!_?r|gൄ|г?rgH}}?rg F%u?rrg^)ˀ?gv?rr^rrc3&K|] \}}||zV dSrvr;rArws r3 z.TestRvDiscrete.test_expect2..'s*99daAE999999r5c |dzSNrgr;rs r3rPz-TestRvDiscrete.test_expect2..* AqDr5c3,K|]\}}|dz|zVdS)rgNr;r~s r3rz.TestRvDiscrete.test_expect2..+s.<<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 7r5ctjdtjddzdz }tjddzdz }gd}gd}t t j|||t t j|||t t j |||dS)Nrr`rgr r) 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?) rjrrrrr9rrirqr)rsr1r_rirqs r3test_skewcauchy_Rz TestSkewCauchy.test_skewcauchy_R8s& q INN2   "Q & INN2   #a '%%%$$$ (,,Q22C888(,,Q22C888(,,S!44a88888r5N)rrrrrr;r5r3rr.s2777 9 9 9 9 9r5rceZdZdZejdZejdgddZ dS) TestJFSkewTc*dx}}|dz}gd}gd}tj||}tj|}t||||t||||t||||t|d|ddS)Nrrg)rrrTr)rr]rlrrrTr)r9 jf_skew_trrrirqr)rsr1r2rr_rjfrs r3test_compare_tzTestJFSkewT.test_compare_t\s A U ! ! ! - - - _Q " " GBKKq 15588,,,q 15588,,,q 15588,,,((!''&//:::::r5ctjttjdz }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)rjloadr__file__parentrec fromarraysr|s r3gamlss_pdf_datazTestJFSkewT.gamlss_pdf_datalsDw NN !$H H  v  [ 999r5za,b)ru)rr)rV c||d|k|d|kz}|d|d}}t|tj|||ddS)zCompare the pdf with a table of reference values. The table of reference values was produced using R, where the Jones and Faddy skew t distribution is available in the GAMLSS package as `ST5`. r1r2r_rirrN)rr9rri)rsrr1r2rr_ris r3test_compare_with_gamlss_rz&TestJFSkewT.test_compare_with_gamlss_r|sr  S !Q &?3+?1+D E cDK3U_Q2266q99FFFFFFr5N) rrrrrrrrrrr;r5r3rr[s{;;;  ^ : :^ : [U$>$>$>?? G G@? G G Gr5rrgrg@rgףp= 1@r?gRZ@igS㥛Ԋ@r]r^g&@iQi'i0ybilHO1Zi3rir`iraikrSi1rii4i Ni(lEI.r,iceZdZdZdZdZdZdZdZdZ e j de d Zd Zd Zd Zd S) TestSkewNormc.td|_dSr5)rrrxs r3r7zTestSkewNorm.setup_methods%d++r5ctjddd}ttj|dtj|dSr)rjrYrr9skewnormrirrs r3 test_normalzTestSkewNorm.test_normalsY KAs # #!%."4"4Q!"4"<"<"'*.."3"3 5 5 5 5 5r5cd}tjd||j}t ||jtjd||j}t ||jdS)N)rrrr)r1rrr)r9rrrrrB)rsrBr_s r3rJzTestSkewNorm.test_rvssm N  E  I IUAG$$$ N  %dh  G GUAG$$$$$r5ctjdtddd|j}t j|t j|tj|tj |g}tjdddd}t||dtjd tddd|j}t j|t j|tj|tj |g}tjd ddd}t||ddS) Nrrrrg)r1rrerfrr)r1rerfrrWr) r9rrrcrrjrrArBkurtosisr)rsrrXrDs r3r*zTestSkewNorm.test_momentss, N  Sq,0H  6 6GAJJq 5:a==%.:K:KL>''!!V'LL!(Ha@@@@ N  #c((,0H  6 6GAJJq 5:a==%.:K:KL>''"!1f'MM!(Ha@@@@@@r5cgdgdgdgdgdgdgdg}|D]8\}}}tj||}t||d 9dS) N)r}rgEAV)r}rgV|@$a)r}rg0rY)r}r|Zk)rrr)rrļ)rggcrr-r)r9rrr)rs logpdfvalsr_r1 logpdfvalrs r3test_pdf_large_xzTestSkewNorm.test_pdf_large_xs 2 1 1 3 3 3 0 0 0 2 2 2 4 4 4 5 5 5 5 5 5  * 8 8OAq)>((A..D D)$ 7 7 7 7 7 8 8r5ctjgdd}t|t jddtjdd}t|dddS) N)r`rr:rrrrrrrT)r9rrqrrjonesrs r3test_cdf_large_xzTestSkewNorm.test_cdf_large_xsn N  |||R 0 0271::E2222 N  r3 ' '3U++++++r5cgdgdgdgdgdg}|D]l\}}}tj||}t||dtj| | }t||dmdS)N)rr gzbLe9)rrggn'/2;)rrg::)rrg|<)rmrr4r-r)r9rrqrr)rscdfvalsr_r1cdfvalrvs r3test_cdf_sf_small_valuesz%TestSkewNorm.test_cdf_sf_small_valuess . - - + + + , , , . . . / / /  $ 2 2LAq&""1a((A AvD 1 1 1 1!!1"qb))A AvD 1 1 1 1 1  2 2r5z a, momentsct|dD]7\}}tj||}t ||d8dS)Nr )startrr)rjr9rrr)rsr1rorderrXrs r3test_noncentral_momentsz$TestSkewNorm.test_noncentral_momentss[(::: 7 7OE8.''q11C C 6 6 6 6 6 7 7r5c ttjd}d\}}}tj|||}|d|}tj|dd\}}} tj|dd\} } } || cxkrdksnJ|| ksJtj|ddd \} }}|dksJtj| ||}|d }tj|tj|f}t||tj d d|}tj|}tj tj |sJtj|d \}}}tj |sJtj|tj|}}t|||tjdtjz zzt||dzd dtjz z ztj|d\}}}tj| d\}}}t|||g| | |gtj|d \}} }!tj| d \}"}#}$t|"|#|$g| | |!gdS)Nl# ke)rr;r|rarrXrrgmmrrmsrr rrgmle)rjrrr9rrrrrBrrrrGisinfrArrk)%rsrr1rerfrBra2loc2scale2a3loc3scale3a4loc4scale4dist4rrra5loc5scale5rra6ploc6pscale6pa6mloc6mscale6ma7ploc7pscale7pa7mloc7mscale7ms% r3ryzTestSkewNorm.test_fitsi##$788$ 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/FGGGGGr5cF tjgdddgzzdgz}tj|}tj||}tj|d}tj||}||dz ksJtjd d d d d } fd }tjtj|||}tj ||j ddS)N)rrr;rVr rT)superfitr|ly ND)rr)rmr`)rr`r1rerfc(t||S)N)r)r')funrrs r3 optimizerz0TestSkewNorm.test_fit_gh19332..optimizerHs)#v3??? ?r5)rrr) rjrr9rrrrrtestingrparams) rsr_rr params_superrrr fit_resultrs @r3test_fit_gh19332zTestSkewNorm.test_fit_gh193323s$ H***R1#X5; < <##A&&n!!&!,, ~))!d);; n!!,22S3Yi##$788y;GG @ @ @ @ @Yu~q&INNN  ""6:+<4"HHHHHr5cfttjdddddS)Nr~rgi}#%?rr)rr9rrrxs r3rzTestSkewNorm.test_ppfNs2 **4557HuUUUUUUr5N)rrrr7rrJr*rrrrrr_skewnorm_noncentral_momentsrryrrr;r5r3rrs,,,555 %%% A A A888 ,,,222" [\+GHH77IH7 .H.H.H`III6VVVVVr5rc&eZdZdZdZdZdZdS) TestExponc`ttjdddSr)rr9rgrirxs r3 test_zerozTestExpon.test_zeroVs&U[__Q''+++++r5cttjddttjtjdddS)Nr8r})rr9rgrqrrrxs r3 test_tailzTestExpon.test_tailYsRU[__U++U333U[__U[^^B%7%788"=====r5ctjdddddtjg}ttt jj|dSNo_?46@yX5ͻ@j+?UX @)rjrrr`rr9rgrrs r3test_nan_raises_errorzTestExpon.test_nan_raises_error]< HfffffbfE F Fj%+/155555r5ctjdddddtjg}ttt jj|dSr)rjrrr`rr9rgrrs r3test_inf_raises_errorzTestExpon.test_inf_raises_errorbrr5N)rrrrrrrr;r5r3rrUsP,,,>>>666 66666r5rcleZdZdZdZdZejdddgdZ dS) TestNormctjdddddtjg}ttt jj|dSr)rjrrr`rr9rrrs r3rzTestNorm.test_nan_raises_errori< HfffffbfE F Fj%*.!44444r5ctjdddddtjg}ttt jj|dSr)rjrrr`rr9rrrs r3rzTestNorm.test_inf_raises_errornrr5c\gd}tttjj|ddS)Nr shrimp)plate)r`rr9rrrs r3test_bad_keyword_argzTestNorm.test_bad_keyword_argss, IIi(CCCCCCr5rerr cd}tjd|zd|z|}t||dtjd|z d|z | }t||ddS)Ngg {F.:rrVrerr)r9r _delta_cdfr)rsrerXrrs r3test_delta_cdfzTestNorm.test_delta_cdfws) %%bfbf#%>>xe4444 %%3i2c6%EExe444444r5N) rrrrrrrrrrr;r5r3rrhsv555 555 DDD [UQF++ 5 5,+ 5 5 5r5rceZdZdZdZdZdS) TestUniformgh-10300ctjdddddtjg}ttt jj|dSr)rjrrr`rr9rrrs r3rz!TestUniform.test_nan_raises_error= HfffffbfE F Fj%-"3Q77777r5ctjdddddtjg}ttt jj|dSr)rjrrr`rr9rrrs r3rz!TestUniform.test_inf_raises_errorr r5N)rrr__doc__rrr;r5r3rrs7N888 88888r5rc 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)NrTr rgrrX@rr;)lamsigr^opK2exp_skewexp_kurts r3get_momsz,TestExponNorm.test_moments..get_momsszc#g\))DC#I>)D4L8Ha39q.0B77H3JC#s3w- 78L Lr5)rr r rTrrG)rrgr])rrr )rrr;)r9 exponnormr)rsrr^rrKstss r3r*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!788888r5ctjdddddtjg}ttt jj|dddS Nrrrrrrr rB)rjrrr`rr9rrrs r3rz#TestExponNorm.test_nan_raises_errorD HfffffbfE F Fj%/"5qqKKKKKKr5ctjdddddtjg}ttt jj|dddSr)rjrrr`rr9rrrs r3rz#TestExponNorm.test_inf_raises_errorrr5cvttjdddttjdddttjdddttjddddS)Ni|r rr~)rr9rrirxs r3test_extremes_xzTestExponNorm.test_extremes_xsEO//a88#>>>EO//a88#>>>EO//d;;SAAAEO//d;;SAAAAAr5zx, K, expected))rr~g6 N-)r r~g՜n+H?)rr~gi?)rr~gbJI-)r`r gI8?)r`rgQ3|-0?cfttj|||ddSr)rr9rri)rsr_rrXs r3 test_std_pdfzTestExponNorm.test_std_pdfs1 ++Aq118%HHHHHHr5zx, K, scale, expected)rr~r gVAҤ?)r{Gzt?r g'^ >)rr~rar)rr~rgbr ;)rrr gVMe?ctj|||}|dkr |dksJdSt||ddS)Nrrrr)r9rrqrrsr_rrfrXrvs r3test_cdf_small_KzTestExponNorm.test_cdf_small_KsU O  1E  2 2 s??888888 Axe 4 4 4 4 4 4r5)r`r~r gh G}$;)rgr%r g ]fJ?)rr%r|g31"g#;)r`r%r|gf +-)rr%r|r)rrr ga9S?ctj|||}|dkr |dksJdSt||ddS)Nrr-a=r)r9rrrr's r3test_sf_small_KzTestExponNorm.test_sf_small_KsU O  q!5  1 1 s??888888 Axe 4 4 4 4 4 4r5N) rrrr*rrr"rrrr$r(r+r;r5r3rrs9996LLL LLL BBB$ [-BBBCCIICCI [4>>>DDD444GGG??? ABB 55 BB 5& [4BBB@@@DDDFFF333@@@ BCC55CC555r5rceZdZdZdZejdgddZejdgddZ dS) TestGenExponcddlm}tjt jdddddd}t||ddddS) Nr)simpsonr`r~r|r)dxr )scipy.integrater/r9genexponrirjrr)rsr/rvs r3test_pdf_unity_areaz TestGenExpon.test_pdf_unity_area sd++++++ N  ryB55sC E EGGA$///A66666r5ctjtjdddddd}tjd|k|dkzsJdS)Nrr`r~r|rr )r9r2rqrjrr)rsrqs r3test_cdf_boundszTestGenExpon.test_cdf_boundssTn  1b$!7!7c3GGvqCxC1H-.......r5z x, p, a, b, c))r?gM(++Aq113WEEEE(,,S!44aeDDDDDDr5N)rrrrr;r5r3r:r::s(EEEEEr5r:ceZdZdZdS) TestExponpowcttjdddttjtjdddddS)Nrrrrr)rr9exponpowrqrrrxs r3rzTestExponpow.test_tailGsiEN..ub995AAAEN..u~/@/@B/G/GLL     r5N)rrrrr;r5r3r>r>Fs#r5r>c eZdZdZdZdZdS) TestSkellamctjdd}d\}}tjgd}ttj||||ddS)Nrmr?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~?rW)rjrrrr9skellamrP)rsr\mu1mu2skpmfRs r3rjzTestSkellam.test_pmfNsm Ic2  S - - - . . EM--ac::FBOOOOOOr5ctjdd}d\}}tjgd}ttj||||ddS)Nrmr?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?rrW)rjrrrr9rDrq)rsr\rErFskcdfRs r3r\zTestSkellam.test_cdfcsm Ic2  S - - - . . EM--ac::FANNNNNNr5cd\}}}ttj|||ddttj|||dddS)N)rr gs1Crrrr )rr9rDrPrq)rsr_rErFs r3test_extreme_mu2zTestSkellam.test_extreme_mu2xse. 3 ))!S#66FFFF ))!S#66FFFFFFr5N)rrrrjr\rKr;r5r3rBrBMsLPPP*OOO*GGGGGr5rBc eZdZdZdZejddZej dddgej d gd ej d gd ej d de ddDe j ddZ dZdS) TestLognormctj5tjdttjgdd}t|gdddddS#1swxYwYdS)Nrsrr|r r )rg~r?ge3E?)rwrxryrzr9r(rirrsris r3rRzTestLognorm.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?rN)rr9r(rrrjrr)rsrsr^sigmas r3rzTestLognorm.test_logcdfs* B ((B%(88 bfRUmmE&9:: < < < ++BrEU+;; ((2u)<== ? ? ? ? ?r5rrc@tjdSr5rrxs r3rzTestLognorm.rngrr5rr]rgr)rrrgr<)rQr rrcg|]}d|v| Srr;)rAes r3rCzTestLognorm.rr5)FTrrrrctjd||||}i} |r|| d<|r|| d<|r|| d<ttj|fi| ddidS)Nra)rrOrfrerrrrrT)r9r(rrrs r3rz'TestLognorm.test_fit_MLE_comp_optimizers}  cYi%,3!@@  #"DJ  #"DL  '&DN &emT < eZdZdZdZdZdZej e ddZ ej e ddZ ej e dd Z d Zejed d Zejd ejjejjgejdddgdZejdddgdZejdddgdZejdgddZejdgddZdS) TestBetactjddd}t|dtjddd}t|tjdS)Nrr r|g;B.)r9rrrrjrrsrs r3rzTestBeta.test_logpdfs\""1a--FN333""1c1--FBF+++++r5c`d\}}tjgd}tj||}t ||dt ||tj||dS)Ni irQr|rgƒ) rjrr9rrrrmrirrsrrr_r2s r3test_logpdf_ticket_1866z TestBeta.test_logpdf_ticket_1866s t H___ % % Jud # # ))+=>>>a"&!"5"566666r5c`gd}tttjj|ddddS)Nr]r|rrr r)rrr)r`rr9rrrs r3test_fit_bad_keyword_argsz"TestBeta.test_fit_bad_keyword_argss= OOi1$ & & & & & &r5c^gd}tttjj|dddS)Nrdr|)fafix_a)r`rr9rrrs r3#test_fit_duplicated_fixed_parameterz,TestBeta.test_fit_duplicated_fixed_parameters0 OOj%*.!3GGGGGGr5zOverflow, see gh-14901reasoncpd\}}}ttj|||ddS)N)g?rQg0xAgx)>)rr9rr)rsrvr1r2s r3test_issue_12635zTestBeta.test_issue_12635s871a q!Q//1FGGGGGr5c>tjgd}tjgd}d}tj||dzd|z }t ||tj||dzd|z }t ||dS)N)g@3@?g^?gNC?)r`rarrr r)rjrr9rrrr)rsinv_R count_listrvinvrs r3test_issue_12794zTestBeta.test_issue_12794s11122Xooo.. jnnQ Q0CDDU###jmmCa*1DEEQr5cd}tjdd}d}d|z |dz||z }}}tj|||}tj|||}t |d|z dS)Nh㈵>r rr)rjrr9rrrqr) rsalpha_2count_nobsrr1r2rqrs r3test_issue_12796zTestBeta.test_issue_12796s1b!!g+vz4&=a1jnnQ1%%jnnS!Q''Q[)))))r5cd\}}ttjd||tjd\}}ttjd||tjd\}}ttjd||dttjd||dd\}}ttjd||dttjd ||ddS) Nrr )rQrr)r rr+ph)rr rT)rr9rrirjr)rsr1r2s r3rzTestBeta.test_endpointss1UZ^^Aq!,,bf5551UZ^^Aq!,,bf5551UZ^^Aq!,,a000UZ^^FAq1115551UZ^^Aq!,,a000UZ^^Ha33Q77777r5zDoes not convert boost warningcd\}}}tjt5tj|||ddddS#1swxYwYdS)N)gףp= ?gvH7B@0B)rwarnsrzr9rr)rsrr1r2s r3test_boost_eval_issue_14606z$TestBeta.test_boost_eval_issue_14606s'1a \. ) ) $ $ JNN1a # # # $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $s"AAAra, b)rz)@)rrzcHd} ||||dS#t$rYdSwxYw)Nr) OverflowError)rsrr1r2rvs r3 test_beta_ppf_with_subnormal_a_bz)TestBeta.test_beta_ppf_with_subnormal_a_bsG   F1aOOOOO    DD s  !!z x, a, b, ref)rrrg>׵NlIq)& .!>rrg'rOcltj|||}t||ddSr)r9rrrrsr_r1r2rrs r3rzTestBeta.test_logcdf3s8""1a++%000000r5)rrrgp}^U)rvrrg 1*cjtj|||}t||ddS)Nr)r9rrrrsr_r1r2rrs r3rzTestBeta.test_logsf;s5   Aq))sE*****r5r))r|r|gο)rr g)r rg&׾k )rrg*)Mcpttj|||dSrvrr9rrHrs r3rqzTestBeta.test_entropyLs2  1a((0022C88888r5za, b, ref, tol))r r`gCpr)r`rg8EOr)gNAgNAg(4Fr)gSAgSAg8TAUr-)rg _Bg[VVuD&r)rLrLgR#Lr)rgrg?r5r)rgr\r)r`rgnQc}4r)r`rg{CEr)r`rL%\r)rrgrr)rrrr)rLr`rrctttj||||dSrr)rsr1r2rrWs r3rzTestBeta.test_extreme_entropyTs8H  1a((0022CcBBBBBBr5N)rrrrrbrerirrskipif MACOS_INTELrmrrrxrxfailrr~rr9rrrrrrrqrr;r5r3r[r[s,,,777&&& HHH  [ ,DEE H HFE H [ ,DEE  FE " [ ,DEE * *FE *888. [w'GHH$$IH$  [X  'GHH [Vnn%EFFGFIH. [^GCEFF11FF1  [^GEGHH++HH+ [[DDDEE 99 EE 9 [   . C C/. C C Cr5r[cxeZdZgdZdZdZejdgddZ ejdedZ d Z ejd egd zd Z ejd d dgdZ dZdZdZdZdZdS) TestBetaPrime) )rY@rFD>?)rrrFm嗽?)rrFr]gPK?)rrrFg%p?)rrFr]g#|/?)rrrgsM <)rrFr$5Є*?)^ 9^;rFr]gompP?)rrrg7j"!9)rrFrz ^J?)rrFr]gܷ"+>)rrrgrNs: )rrFrgK>cd\}}tjgd}tj||}t tj||t| |tj ||dS)Nr_r`) rjrr9r r rGrrrrirras r3rzTestBetaPrime.test_logpdfs t H___ % % OE4 ( ( AHHQKK((,,..///a"&!"5"566666r5ctjddd}t|dd\t jgd}tj|}t t j|tj j fd|D}t||dd dS) NrrQr~rr_r`c@g|]}tj|Sr;)r9r )rArIrrgen_cdfs r3rCz*TestBetaPrime.test_cdf..s+JJJ''%/3t<<JJJr5-=rn) r9r rqrrjrr rGrrF _cdf_singler)rsr_rcdfs_grrrs @@@r3r\zTestBetaPrime.test_cdfs O  3 , ,Q t H___ % %""1eT22 D!!%%''(((%1JJJJJJJJJf15999999r5zp, a, b, expected))r~rrgV)?)rrrgWJB9*=)r8rrgOGJ<)rrl@gΣ01)?rlrg8ǘ`?)>q?rFr]gMDcltj|||}t||ddSr#)r9r rr)rsrvr1r2rXr_s r3rzTestBetaPrime.test_ppfs8 O  1a ( (8%000000r5z x, a, b, pchttj||||ddSr)rr9r r)rsr_r1r2rvs r3test_ppf_gh_17631zTestBetaPrime.test_ppf_gh_17631s1++Aq!44aeDDDDDDr5ctjd}tjd}tjd}ttj|||dddS)NrTr|rr)rjrrr9r _ppf)rsr1r2rvs r3 test__ppfzTestBetaPrime.test__ppfsX HSMM HSMM HSMM,,Q155sGGGGGGr5zx, a, b, expected))rrrr)rrFr]gV[?)rrFr]rchttj||||ddSr#)rr9r rq)rsr_r1r2rXs r3test_cdf_gh_17631zTestBetaPrime.test_cdf_gh_17631s3 ++Aq!44hUKKKKKKr5)rLrFr]g%?)rLrrFgoXr?c|tj|||}|dksJt||ddS)NrTgh㈵>r)r9r rqr)rsr_r1r2rXr2s r3test_cdf_extreme_tailsz$TestBetaPrime.test_cdf_extreme_tailssE O  1a ( (3wwww8$//////r5cgd}gd}gd}gd}tj|||}t||ddS)N)rrrgrFrFrFrFrrrFrFrFrr)rrgr r]r]r]r]rFrFrrrrr)rrꌠ9Y>)Frrrrrrrrrrr)g/:g U/7gKH9g<![a?gw 4?g)J?g5?rrrrg%?gsM  [ B B B111 [\844EE54EHHH [      LL  L [ . / 12200 220444*111000000 " " " " "r5rc 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) NZirQrg CTb?rr`gBΖ?)r9rrirrPs r3rRzTestGamma.test_pdf%sZkoob#To22C---kooa4o00C+++++r5cftjdd}t|ddSr)r9rrrr]s r3rzTestGamma.test_logpdf-s1##Aq))FA&&&&&r5c^gd}tttjj|dddS)Nrdrr)rr)r`rr9rrrs r3rez#TestGamma.test_fit_bad_keyword_args3s. OOi!!8LLLLLLr5ctjtjddddsJtjtjdddd sJdS) Nrr gplC@rrrrag1}t@r)rjiscloser9rrrxs r3rzTestGamma.test_isf7s"z%+//%33+%999 9 9 9z%+//%55+%999 9 9 9 9 9r5cvd}d}d}tj||}t||ddS)NPrgޟ򑁺rr)r9rrrrs r3rzTestGamma.test_logcdfMsC  $##Aq))%000000r5cvd}d}d}tj||}t||ddS)NrrgDmrr)r9rrrrs r3rzTestGamma.test_logsfTsC  % !!!Q''s//////r5rfrTrUc|tj|dz|dzd|}t|dddS)Nr"rrg>S*rr)r9rrrrsrfrrs r3rzTestGamma.test_delta_cdf[sF &&uSy%)Qe&LL6UCCCCCCr5z a, ref, rtol))rgt.r)rgrr)ragX>k-־ @r)r gwM7@r)gNgmCg%og$6@r)roܘ#]@rcdttj|||dSr)rr9rrH)rsr1rrs r3rqzTestGamma.test_entropyis/  ++A..$??????r5r1)r~r rre)r~rrrhTFrr>cHtjd}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)NrrarArgrrrrr r rrr rg)rjrrr9rrrrrrrrrr)rsr1rerfrhrr>rrrrrEthetarBs r3 test_fit_mmzTestGamma.test_fit_mmzsi##$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)rrrrRrrerrrrrrrrqrr;r5r3rr$s,,,''' MMM999,111000 [WsCj11 D D21 D [^BBBCC@@CC@ [S...11 [UNNN33 [Wnnn55 [WtUm44 [Yu 66 [[4-88>>987654654321 >>>r5rcd}tjd|dzz d|dzz dd}t|dddS) Nrg;f?rgr rrdrTgV{q@)r9rrri)jitterZs r3test_pdf_overflow_gh19616rsTF 6FAI-q619}!1MMMAAEE#JJ 122222r5ceZdZdZejdgddZejdgddZejdgdd Z d Z d S) TestDgammactjd}d}|d|}|d|}t j||}t jtj ||dz }t||t j|}t|||ddS)NlOP($r`r )rrrgrr) rjrrnormalrr9dgammarirrr)rsrrr_r1rrrBs r3rRzTestDgamma.test_pdfsi##$788 JJRdJ + + KKRdK + +lq!$$koobfQii++a/S!!!|A Su555555r5zx, a, expected))rr ggrU>)rr g$IC<)irg2Wj<)ryg~)A.=)rr gf?ctj||}t||dtj||}t||dtj| |}t||dtj||}t|| ddSr)r9rrqrrrr)rsr_r1rXrqrrrs r3test_cdf_ppf_sf_isf_tailz#TestDgamma.test_cdf_ppf_sf_isf_tailslq!$$XE2222lx++QU++++ \__aR # #H51111lx++aRe,,,,,,r5r))rgmqn@)?g?)rgx?cdttj||ddSr#rr9rrHrs r3rqzTestDgamma.test_entropys/  ,,Q//5AAAAAAr5))rr)rg>_)r;g5i)r go@)rg4Fa3@)rgrO]@cdttj||ddSrrrs r3test_entropy_entreme_valuesz&TestDgamma.test_entropy_entreme_valuess/"  ,,Q//5AAAAAAr5ctjgd}tj|}t t |D]3}||tj||ksJ4dS)N)r rrr;)rjrr9rrHrr)rsr_r2rs r3test_entropy_array_inputz#TestDgamma.test_entropy_array_inputs~ H''' ( ( L  # #s1vv 6 6AQ45<//!5555555 6 6r5N) rrrrRrrrrrqrrr;r5r3rrs 6 6 6, [-:::;; -- ;; - [X88899 B B 99 B [X:::;; B B;; B66666r5rceZdZdZejdgddZejdgddZdZ ejdgd d Z d Z d S) TestChi2cttjddddttjdddddS)Nrgޞw1D?r.rWrag6:֜?rr9chi2rirxs r3rzTestChi2.test_precisionsjEJNN4668N$& ( ( ( (EJNN3446J$& ( ( ( ( ( (r5rP))gp@rg~#e)g^@r?g tA)rrgzĀ׿cjtj||}t||ddSr)r9rrr)rsr_rrrs r3rzTestChi2.test_logcdfs6""1b))%000000r5))rr?r)rr}gc)rr`g]3cjtj||}t||ddSr)r9rrr)rsr_rrrs r3rzTestChi2.test_logsfs6   B''s//////r5cd}tjd|}t|ddtjd|}t|ddd}tjd |}t|d dtjd |}t|d ddS) Nr<gλm:=6g'bd5)r gƯʉ?)ragn>@)g͔v0@)rg9:3@crttj||ddSr)rr9rrHrs r3rqzTestChi2.test_entropy4s3  2..00#EBBBBBBr5cdttjdddddS)Nrrgr|r.rrxs r3test_regression_ticket_1326z$TestChi2.test_regression_ticket_1326=s*EJNN322C<<<<d3ejejejfgd?d@ggdAZej dBgdCej dDej j!dEejdFd3dGdHfej j"dEejdFd3dGdHfej j!dIejd3dJdGdEfej j"dIejd3dJdGdHfgdKZ#ej dLgdMdNZ$ej jej dLgdOdPZ%dQZ&dRZ'dSS)TTestLevyStableT)autousecdtj_dtj_dtj_tjjtj_dS)z2Setup default parameters for levy_stable generatorS1 piecewiseN)r9rparameterizationcdf_default_methodpdf_default_method _levy_stable _QUAD_EPSquad_epsrxs r3reset_levy_stable_paramsz'TestLevyStable.reset_levy_stable_paramsws<.2*/:,/:,%*%7%A"""r5ctjttjdz }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,pctrrjrrrrrrTr|s r3nolan_pdf_sample_dataz$TestLevyStable.nolan_pdf_sample_datasM6w NN ! < =  v  /C DD r5ctjttjdz }tj|jd}|S)a#Sample data points for cdf computed with Nolan's stablec See - http://fs2.american.edu/jpnolan/www/stable/stable.html There's a known limitation of Nolan's executable for alpha < 0.2. The data table loaded below is generated from Nolan's stablec with the following parameter space: alpha = 0.1, 0.2, ..., 2.0 beta = -1.0, -0.9, ..., 1.0 p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5, and the equivalent for the right tail Ideally, Nolan's output for CDF values should match the percentile from where they have been sampled from. Even more so as we extract percentile x positions from stablec too. However, we note at places Nolan's stablec will produce absolute errors in order of 1e-5. We compare against his calculations here. In future, once we less reliant on Nolan's paper we might switch to comparing directly at percentiles (those x values being produced from some alternative means). Typically inputs for stablec: stablec.exe << 2 # cdf 1 # Nolan S equivalent to S0 in scipy .25,2,.25 # alpha -1,-1,0 # beta -10,10,1 # x 1,0 # gamma, delta 2 # output file z.data/levy_stable/stable-Z1-cdf-sample-data.npyr rr r|s r3nolan_cdf_sample_dataz$TestLevyStable.nolan_cdf_sample_datasNJw NN ! < =  v  /C DD r5cbtjttjdz }|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)rjrrrrr|s r3nolan_loc_scale_sample_dataz*TestLevyStable.nolan_loc_scale_sample_datas1w NN ! ? @   r5 sample_sizer=rEmarksrS0rz alpha,beta))rTr)rTr)rr)r&r|z gamma,deltar rrvc|tj_tj||||}tj||d|j\}} | dksJdS)N)rrrfrerrrF)r9rrrIrrq) rsrrrrrrrlsrrvs r3rJzTestLevyStable.test_rvssp(.>*  d%U   | FF $F 7 7  14xxxxxxr5rr|r ctjdd}d}d}tj||||d}tj|d||||f\}}|d ksJd S) z3Additional test cases for rvs for alpha equal to 1.h:rTr|rrrerfrrr[r~N)rjrrr9rrrI)rsrrrerfr_statrvs r3test_rvs_alpha1zTestLevyStable.test_rvs_alpha1s y!!!   ! !%3e'+ " - -,q-%*D#u$=???a4xxxxxxr5cgd}tj|\}}}}t|dddt |ddt |dd t |d d|gd z}tj|\}}} } t |dt |d t | d d t | dd dS)N)wgrrrrr羼u?r r r r 67',?r!r!r!r!tA}˜.?r"r"r"r"Gz?rr~rf)\(̿rggۧ1?rg9]c?)r"r"r"r"r"rgv?r!)r9rrtrrr rsr_alpha1beta1loc1scale1rsalpha2beta2rrs r3ryzTestLevyStable.test_fits    ',&7&A&A!&D&D#tV148888E4+++FGQ/// '1   999 9&+&7&A&A"&E&E#tVVQUBFFA...D&!,,,,,r5zUnknown problem with fitstart.rjzalpha,beta,delta,gamma)rrrgr)rTrrgrparametrizationc|tj_tj||||dd}tj|}|\}} } } t ||||g|| | | gddS)z7Test that fit agrees with rvs for each parametrization.rrrAr~rN)r9rr,rrtr) rsrrrrrr,rr alpha_obsbeta_obs delta_obs gamma_obss r3 test_fit_rvszTestLevyStable.test_fit_rvss-<) $$ 4U%e$%  ))$//471 8Y  D% ' )Y 7      r5cxtjgd}tj|\}}}}tj| \}}}} t |d|dksJt ||t || t || t | |dS)N r r rrr`r`r`r:r:rarar r)rjrr9rrtrr) rsr_r&r'r(r)r*r+rrs r3test_fit_beta_flipz!TestLevyStable.test_fit_beta_flip8s H??? @ @&+&7&A&A!&D&D#tV&+&7&A&A1"&E&E#tVUAqyyyyFF+++EE6***D4%(((FF+++++r5cVd}tjgd}tj| \}}}}tj| |z\}}} } t ||t ||t | ||zt | |dS)Nr r4)rjrr9rrtr) rsSHIFTr_r&r'r(r)r*r+rrs r3test_fit_delta_shiftz#TestLevyStable.test_fit_delta_shiftDs H??? @ @&+&7&A&A1"&E&E#tV&+&7&A&A1"u*&M&M#tVFF+++E5)))D$,///FF+++++r5cgd}tj|\}}}}|dks Jd||t|ksJdt|d|gd}tj|\}}} } |dks Jd|| t |ksJdt |d| dS) N) r r rrr`r`r`r:r:r:r zExpected alpha < 1, got zExpected loc < z, got ) r r rrr`r`r`r:r:r;zExpected alpha > 1, got zExpected loc > )r9rrtrrr%s r3test_fit_loc_extrapz"TestLevyStable.test_fit_loc_extrapOs 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~~~~~r5z pct_range,alpha_range,beta_range)r~r|r)r]r rg)rrr)r~rFr|r@r)r]r|r rrg)grrr~rr ) r~rFr]rlffffff?r|?rrr@rr]rgrrrct|}tj}|jdko |jdkd|j|j|jg}ddfdgddfd gddfd gdd fd gd dfdgd dfdgg}t |D]\} \} } } | tj_ | || |n|} t5}| tdtj | 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)Npctrrrr|rrrr~rr~rFr@rQr]rlr)r|rrr=r>)gٿ333333ӿr~rr|rFrTr]rQr~r)rrrTr!r)rjisinrr alpha_range beta_range pct_ranges r3rPz7TestLevyStable.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,EHr5rrctj|dtj|dztj|dz|ddkz|ddkzS)NrErrrQrTrjrHrIs r3rPz7TestLevyStable.test_pdf_nolan_samples..sqGAeHi00GAgJ 445GAfIz223wZ#%'wZ2% 'r5c|ddk ztj|dzdvztj|dzS)NrrTrErrN)rrJrK is_linux_32rLs r3rPz7TestLevyStable.test_pdf_nolan_samples..s_wZ2%$_&GAeHi001;&(GAfIz22 3r5g& .=ctj|dtj|dztj|dz|ddkzS)NrErrrQrNrIs r3rPz7TestLevyStable.test_pdf_nolan_samples..s^GAeHi00GAgJ 445GAfIz223wZ3&(r5 fft-simpsonr;c|ddktj|dztj|dztj|dzS)Nrr&rErrNrIs r3rPz7TestLevyStable.test_pdf_nolan_samples..s^wZ3&GAeHi001GAgJ 445GAfIz223r5rvctj|dtj|dztj|dz|ddkz|ddkzS)NrErrr r&rNrIs r3rPz7TestLevyStable.test_pdf_nolan_samples..spGAeHi00GAgJ 445GAfIz223wZ!^%wZ#% 'r5Nz2Density calculations experimental for FFT method.*r_rrr rrfrerrcalcabserrrelerrrvrYz pdf test  failed with method 'z ' [platform: z]  Ferr_msgverbose)platformunamesystemmachinejoin processorrjr9rrr recordrzrirjrrrisnanrrr)rsr rLrJrKrr` platform_desctestsixdefault_methodr filter_funcsubdatasuprvsubdata2failuresmessagerPs ``` @r3test_pdf_nolan_samplesz%TestLevyStable.test_pdf_nolan_samples[s4%  lg-I%-62I  \5=%/ :<< tJJJJJJL ^U%%%%%% U%%%%%%% W'''''' t&&&&&& t&&&&&& kC L"+5!1!1* *  B3AE  0 + 7;;t,,=A "$$%  "H%))CLG$FO *[h///  0444F1ws|#344F1ws|#344rvgcl7K7KK  H               $H%-(1++ WWWWW"/WW4.PsGAeHi00GAgJ 445GAfIz223 wZ2-GAfI/A/A/ABBCuX-/ wZ2-GAfI??@uX-/  r5rFctj|dtj|dztj|dz|ddktj|dgdz|ddkzz|ddktj|dgdz|ddkzzSrtrNrIs r3rPz7TestLevyStable.test_cdf_nolan_samples..esGAeHi00GAgJ 445GAfIz2237r)& +=+=+=>>?5T)+ 7r)& ???;;<5T)+ r5rRr;ctj|dtj|dztj|dz|ddkzS)NrErr333333?rNrIs r3rPz7TestLevyStable.test_cdf_nolan_samples..ws^GAeHi00GAgJ 445GAfIz223wZ#%'r5rctj|dtj|dztj|dz|ddkz|ddkzS)NrErrrrxrNrIs r3rPz7TestLevyStable.test_cdf_nolan_samples..qGAeHi00GAgJ 445GAfIz223wZ#%'wZ3& (r5rctj|dtj|dztj|dz|ddkz|ddkzS)NrErrrrrNrIs r3rPz7TestLevyStable.test_cdf_nolan_samples..rzr5r~ctj|dtj|dztj|dz|ddkz|ddkzS)NrErrrTrrNrIs r3rPz7TestLevyStable.test_cdf_nolan_samples..rzr5Nz[Cumulative density calculations experimental for FFT method. Use piecewise method instead.*r_rrr rrUrrrVrvrYz cdf test rZz' r[Fr\)rjr9rrr rerzrqrjrrrrfrrr)rsrrLrJrKrrhrirjrrkrlrmrvrnrorps ``` r3test_cdf_nolan_samplesz%TestLevyStable.test_cdf_nolan_samples3s2%U%%%%%% ,T$$$$$$ &t&&&&&& t&&&&&& t&&&&&& t&&&&&& GL \"+5!1!1( (  B3AE  0 + 7;;t,,=A "$$#  "@ %))CLG$FO *[h///  0444F1ws|#344F1ws|#344rvgcl7K7KK  H               $H%-(1++ArAAAA&n2AA6>AACL#! ;# # # # # # # # # # # # # # #  ( ( s9 A'G2A(E& G&E* *G-E* .AGG G rrrrirqctj}|jdkodtjdv}|r|dkrt jd|}dt j_dt j_ ||d|k}d|t j_ |d vsJ|dkrt jj nt jj }||d |d |d d d} t| ||ddS)zGTests for pdf and cdf where loc, scale are different from 0, 1 r@32bitrriz4Test unstable on some platforms; see gh-17839, 17859rrS)rirqr_rrrgrrUr;N)r_r`ra architecturerrr9rrrrrirqr) rsrrrr`rPrrlrrNs r3test_location_scalez"TestLevyStable.test_location_scales  lg-W'X=R=T=TUV=W2W   P45== KN O O O*0;,/:,tG}-.-8[[*~%%%%%)U]]E  ! !8I8M X CL''*GFO1!    GDM400000r5zmethod,decimal_placesrCrrc tjgd}tjgd}tjgd}tjd5t5}|t d|t j_t j |d|dd }t||||d d d n #1swxYwYd d d d S#1swxYwYd S) z sample points extracted from Tables and Graphs of Stable Probability Density Functions - Donald R Holt - 1973 - p 187. )rrrrr r r r rgrgrgrgrrrrrrrr)gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g ?gDioɴ?g r?gH?g+?gHPs?gX?g&?g 0*?gv/?ga2U0*?)rrlr|r rrlr|r rrlr|r rrlr|r rrlr|r rrzDensity calculation unstable.*)categoryrpr rrUN) rjrrr rSrzr9rrrir)rsrdecimal_placesxsdensitybetasrmris r3'test_pdf_alpha_equals_one_beta_non_zeroz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerosX H H H  (           [X & & &  (9(;(; s JJ'8    4:E  0#''AuA1'EEC Wnf                                    s7C/'A$C C/C C/C C//C36C3zparams,expected)r#r$rr )rgrr`r)r`r9rrctj|d|d|d|dd}t||dS)Nrr rgrrrG)r9rr)rsrrXobserveds r3rzTestLevyStable.test_stats sU$** 1IvayfQivay+   Hh/////r5r)rlr|rzfunction,beta,points,expectedrTrr`rrrcd|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. rr rrN)rrjr#r)rsrrrrrXs r3!test_distribution_outside_supportz0TestLevyStable.test_distribution_outside_supportseP5}}}}1}}}}}} HV5t 4 4 4 GCKK * *     r5zx,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=rNr9rrrrirsr_rrrXs r3test_x_equal_zetaz TestLevyStable.test_x_equal_zetaIsJZ&-"   ! !!5t ! < <      r5) )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 r3test_x_near_zetazTestLevyStable.test_x_near_zeta}sJD&-"   ! !!5t ! < <      r5c tjj}tdddd}tj}t jd i|}d|_d|_|jd i|d|d d }|d|d  }tj||krJd|_d|_|jd i|d|d d }|d|d  }t||t||dS) Nr&r]rrTrrrerfrrr` rr;) rjrrrr9rrrrr rsrrunfrozenfrozen unfrozen_afrozen_a unfrozen_bfrozen_bs r3$test_frozen_parameterization_gh20821z3TestLevyStable.test_frozen_parameterization_gh20821s5i#Ccs#>>>$",,V,,$(!"&!X\QQFQ##i..QQQQ ::2CC NN:CC6(j011111$(!"&!X\QQFQ##i..QQQQ ::2CC NN:CCXz***Z*****r5ctjj}tdddd}tj}d|_t jd i|}|jd i|d|dd }|d|d }t||d |_t jd i|}|jd i|d|dd }|d|d }t||dS) Nr&r]rrTrrr`rrrr;) rjrrrr9rrrrrs r3%test_frozen_parameterization_gh20821bz4TestLevyStable.test_frozen_parameterization_gh20821bs i#Ccs#>>>$$(!",,V,,!X\QQFQ##i..QQQQ ::2CC NN:CCXz***$(!",,V,,!X\QQFQ##i..QQQQ ::2CC NN:CCXz*****r5N)(rrrrrrr rrrrrrrJrrryrr2r5r8r<rjrYrqr}rrrrrr9rrqrirrrrrr;r5r3rrvsV^D!!!BB"!B ^^B ^))^)V ^  ^  [ [ FL  lfl4v{7GHHH   [/$>> [CCC []VV,<==>=?> $ [ [Vc1X..  /. ---0 [>?? [    [D$<   @?   , , , , , , G G G [ [* FL     FL(((###(((k&     FLDDD CB'' B2&&k'    - *@@+,@D [* FL     FL(((###(((k&     FLDDD CB'' B2&&k'    - *zz+*zx [Wq!f-- [VeU^441154.-1@ [ AJ !  @ [ !RVRVRV!< =  / 000 [W&7&7&788 ['!% CB''  !% CB''  !% Ar2&&  !% Ar2&&  ' :  ;98<  [&   )8  98 0 [ [    !" 0+++,+++++r5rceZdZdZdZdS)TestArrayArgumentcDtjddSr5r6rxs r3r7zTestArrayArgument.setup_methodr8r5ctjtjdtjdd}t |jddS)Nrrr)r9rrrjrrrrBrsrs r3test_noexceptionz"TestArrayArgument.test_noexceptionsKjnn")A,,rwqzz")++SY(((((r5N)rrrr7rr;r5r3rrs2)))))r5rceZdZdZdZdS) TestDocstringctjj2tdtjjvtjj4tdtjjvdSdS)Nr+r)r9r+r r lowerrrxs r3test_docstringszTestDocstring.test_docstringssn > ! - J%."8">">"@"@@ A A A ? " . K5?#:#@#@#B#BB C C C C C / .r5cRtjtjdSrv)r9rFrErxs r3test_no_name_argzTestDocstring.test_no_name_args&  r5N)rrrrrr;r5r3rrs5DDDr5rctgd}t|dk|d\}}t|gdt|dgtddk|d\}}t||t|dgtj|zt|dk|d\}}t||t|dgtj|zdS)N)r rrgr rgrrr rg)rrgrgrrr)rrrrjrr1r2rs r3test_args_reducers ###$$A a!eQ " "DAqq///***q1# a!eQ " "DAqq!q1# *+++ a!eQ " "DAqq!q1# *+++++r5cReZdZgdZdZgdZejde dZ dZ dZ dZ d Zd Zd Zd Zejjejd ddgdZejd ddgdZdS) TestFitMethod)ncfrLrM irwinhallcDtjddSr5r6rxs r3r7zTestFitMethod.setup_methodr8r5)rgrrrz dist,argsct||jvrtj|dtjdddddtjg}tjdddddtjg}tt|}tt|j |dtt|j |dd S) r z fit known to fail or deprecatedrrrrrr r{N) fitSkipNonFiniterrrjrrrr.r9r`rr)rsrBr0r_r2distfuncs r3!test_fit_w_non_finite_data_valuesz/TestFitMethod.test_fit_w_non_finite_data_valuess 4( ( ( K4AAA B B B HfffffbfE F F HfffffbfE F F5$''j(,!<<<<j(,!<<<<< u [X & & & @ @ !!$Dr!::AWrvayy26"::'=&A%G%G%I%IJJN BHU]%6%6qq%6%L%LMM+Q3$ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @sB;C==DDc tjdd}tj|\}}t |dt |tjdtj|d\}}t|dt|tjdtj|d\}}t |dt|ddS)Nr r3rrgrr{)rjrr9rrrrrrsr_rerfs r3test_fix_fit_normzTestFitMethod.test_fix_fit_norms IaOOZ^^A&& UC###E271::...Z^^AA^.. US!UBGAJJ'''Z^^Aa^00 UC###UAr5ctjdd}tj|}d}tj||\}}}tj||z }ttj|tj |z |dt||t|||z dd}d}tj|||\}}}t||t||t|||z dd }d}tj|||\}}}t||t||t|||z dd}d } tj||| \}}}t||t|| |tj| z } ttj || dS) Nr r3rrrrWrrrrgrB) rjrrrr9rrrrdigammar) rsr_meanlogrr1rerfrOrrrs r3test_fix_fit_gammaz TestFitMethod.test_fix_fit_gamma%s IaOO&)).."" 55 3 F16688  w &BF1II(:(::AqIIIIS$E16688A:q9999  bt<< 3QS$E16688A:q9999  bt<< 3QS$E16688A:q9999 VDD 3S$UF### bfVnn $GOA..22222r5c d}tjgd}tj|dd\}}}}t |dt |dt ||||ddgdtjgd}tj|ddd \}}}}t |dt |dt |d||||\}}t |dd d|z } tj| ddd \} } } } t | dt | dt | d|| | | \}}t |dd t| |tttjj|d dtjgd }tttjj|ddtttjj|dddtttjj|dddtttjj|dddddS)Ncht|}tj|}tjd|z }t j||z}||| t j|zzz ||| t j|zzz g}|Sr)rrjrrmrpsi)r1r2r_rus1r&psiabrs r3mlefuncz0TestFitMethod.test_fix_fit_beta..mlefuncNsAAB!""BKA&&Eufw{1~~566ufw{1~~5668DKr5)ryrlr|rr rBrvrrg)rrrr;)r rrr|rO)rrr)rrr r)rr rr) rjrr9rrrrrr`r)rsrr_r1r2rerfdadbrsrb2rrr2s r3test_fix_fit_betazTestFitMethod.test_fix_fit_betaKs    H''' ( ( :>>!!A>>>1c5S!UA1a((1a&t<<<< H''' ( ( :>>!!>DD1c5QS!UAAq!!BAD))))U$z~~bQQq~IIBfRT1VQR$$BAD))))B""" j%*.!#aHHHH HZZZ j%*.!!AFFFFj%*.!!A!LLLLj%*.!!A!LLLL j%*.!aQ ( ( ( ( ( (r5ctjgd}tj|\}}t |dt |dtj|d\}}t |dt |dtj|d\}}t |dt |ddS)N)rgrgrrrrrrrgrr{rrr)rjrr9rgrrrs r3test_expon_fitzTestFitMethod.test_expon_fits H--- . .[__Q'' US!UA[__Qq_11 US!UA[__QQ_// US!UAr5c tjgd}tj|dz }tj|d\}}}t ||dt|dt |tj | dtj|dd\}}}t |tj |tjdz dz dt|dt|dtj|dd \}}}t|d t|dt |tj | ddS) N)rrr`r?rr rrrr3rBrgr)rfix_s) rjrrr9r(rrr{rrrr)rsr_lnxm1rBrerfs r3test_lognorm_fitzTestFitMethod.test_lognorm_fits H--- . .q1u !M--aa-88sEuyy{{7777S!rvejjll33%@@@@!M--aa-BBsErw):Q(>'D'D'F'FGG" $ $ $ $S!UA!M--aat-DDsEUD!!!S!rvejjll33%@@@@@@r5ctjgd}tj|\}}t ||t |tj|tj|d\}}t |dt ||tj|d\}}t |dt |dtttjj|dtttjj|ddS)N)rTrrorrrr`r{rrU) rjrr9rrrrrrr`rrs r3test_uniform_fitzTestFitMethod.test_uniform_fits# H))) * *]&&q)) US!%%''"""UBF1II&&&]&&qq&11 US!UAEEGG$$$]&&q&44 US!UBj%-"3QSAAAAj%-"3QsCCCCCCr5rMLEMMc `d\}}tj||dd}tj|d|}tj|d|}t ||dd tj|d| }t ||dd tj|d | }tj|d | }t ||dd tj|d |}t ||dd t t tjj|dd|t t tjj|dddd|tj|ddd|} | \} } } } t| | | ggdd}tj|d}tj|||\} } } t| |dS)N)rrrarrr)rr)rgrrrn)rhrr)r r)rr)rrr rg)rgrrrr)rgr rrr)rgrrr)rrr r;) r9rrrrr`rrr)rsrr1r2r_res_1res_2res_3res_4res_5aabbrssrs r3 test_fshapeszTestFitMethod.test_fshapess 1 JNN1acN = = qR77 qR77u5u==== q6::u5u==== qR77 qR77u5u==== q6::u5u==== j%*.!aOOOO j%*.!aQv 7 7 7 7  qRa&IIBBb"b\:::... {qs++[__Ta_?? BRr5ctj}|dd}td}t t |j|fi|d|idS)Nrgra)rri) enikibenikir)r9rrrr`rr)rsrrBrr/s r3test_extra_paramszTestFitMethod.test_extra_paramss]xx!#x&&t$$$i4FF3FFvFFFFFFr5N)rrrrr7rrrrrrrrrrrrrrrrr;r5r3rrsW 1 1 1DA@@ [[(33==43=@@@   $3$3$3L5(5(5(n   AAA(DDD$ [ [Xt}55$$65$L [Xt}55GG65GGGr5rcDeZdZdZdZdZdZdZdZdZ dZ d Z d S) TestFrozencDtjddSr5r6rxs r3r7zTestFrozen.setup_methodr8r5ctj}tjdd}|d}|ddd}t|||d}|ddd}t|||d}|ddd}t|||d}|ddd}t|||d}|ddd}t|||}|dd}t||| }| dd}t||| }| dd}t||| }| dd}t||| }| dd}t||| d}| ddd}t||t|j|jt|j|jdS)Nrrrdrrlrg)r9rrirrqrrrrHrrAr{rHrr1r2)rsrBrresult_frs r3rzTestFrozen.test_normszC000::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&::d##$D44Xv&&&99T??4s33Xv&&&==??S11Xv&&&;;==t3//Xv&&&::<<d#..Xv&&&::<<d#..Xv&&&>>##$c22Xv&&&==##QD44Xv&&&VXtv&&&VXtv&&&&&r5cd}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)Nrrrlrrg)r9rrirrqrrrrHrrAr{rHrr1rBr2)rsr1rBrrrs r3 test_gammazTestFrozen.test_gamma$sa {Q::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&::d##$""Xv&&&99T??q!!Xv&&&==??QXv&&&;;==1Xv&&&::<<!Xv&&&::<<!Xv&&&>>##aXv&&&==##Q""Xv&&&VXv{}---VXv{}-----r5ctjd}|d}|d|d}t||dS)Nr rgrr)r9r(rr)rsrm1rs r3test_regression_ticket_1293z&TestFrozen.test_regression_ticket_1293Xsaq!! ]]1   V $$$]]1   Rr5cld}tj|}|j|\}}t ||gddgd}tjd|t |j|dt jgd}tj|}|j|\}}t ||gddgd}tjd|t |jj|jj ftj|tjd}t|j|judD]}t j |}tj|}|j|j }}t |dtt j |t j d}tj|\}}t||gdd gdS) Nr!rrrr]rrrr|)r9rrBrrrirjrr1r2r rrr)rsrrr1r2rv1s r3rzTestFrozen.test_abgs  _q ! ! !w##A&&1aVb#Y'''  A###RW))!,,q"&k:::  _q ! ! !w##A&&1aVb#Y'''  Aq!!!bgi+U_-I-I!-L-LMMMo$$$'((( / /A 1 A1%%%B4qA B    BKNN # # # 3A?//22DAq QFRI . . . . / /r5cTtttjddS)N rv_frozen)r r0r9r:rxs r3test_rv_frozen_in_namespacez&TestFrozen.test_rv_frozen_in_namespaces#+[99:::::r5ctj}tt|dd|_t |jtj dtj d}| d|dS)Nr*rrr) r9rr r0rr get_staterjrrr)rsrrndms r3test_random_statezTestFrozen.test_random_states//000!V(2244Y**2..88:: < < <y$$T**  -----r5ctjdd}tjd}tjgdgdf}|||fD] }d|_|d t j|}|d }t j|}|d }t||| d | d g} t| d | d t| | d | | d dS) Ngdsz@g@e?r)rr rgrrGr^rrr;r|rr ) r9rrrErrpickledumpsloadsrrrq) rsrpoissrWdistfnrOr0 unpickledr1medianss r3 test_picklingzTestFrozen.test_picklings[z,.ABB b!!"<<<+?+?+?+ABBBUF+ 4 4F"&F  JJAJ    V$$A##B QIA&&B R zz# c(:(:;G WQZ 0 0 0 GAJ//"wqz22 4 4 4 4 4 4r5c d}tjddd}tjdd5||ddd }tj|d ddddd }dddn #1swxYwYt ||tjdd }||}tj|dd}t ||dS)Nc|Srvr;rs r3rz$TestFrozen.test_expect..funcsHr5rgrrrr)rdivider T)rub conditionalrgr0rerfrr r r)rr0re)r9rrjrrrr)rsrgmgm_val gamma_valrvp_val poisson_vals r3 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) rrrr7rrrrr r r r" r;r5r3rrs1'1'1'f2.2.2.h   */*/*/X;;; . . .4440,,,,,r5rcbeZdZdZdZdZdZdZdZdZ 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)Nrr;rs r3rPz&TestExpect.test_norm..s1qs r5rrgrdrr.rWc|Srvr;rs r3rPz&TestExpect.test_norm..sr5rFr@cdSrr;rs r3rPz&TestExpect.test_norm..Qr5rerfrr rcdSrr;rs r3rPz&TestExpect.test_norm..ar5Trerfrr r rT)r9rrrr)rsrrrr prob90prob90cs r3rzTestExpect.test_norms J  33!  D DAq"---- J  mm!  < <Aq"---- Z^^Daq^ 1 1 Z^^Daq^ 1 1"";;AQ2""MMFC4444*##KKQaB204$66GR444444r5c Rtjdddd}t|ddtjd dd d }t|d dtjd dddd}tjddddd}tjddd d ||d}t|ddtjdddd||d}t|dddS)Nc|dz |dz zS)NUUUUUU@r;rs r3rPz&TestExpect.test_beta..s51U7(;r5rrrg)r0rerfqq?rrWc|Srvr;rs r3rPz&TestExpect.test_beta..sr5rUrr2 r@r`rdrFcdS)NrTr;rs r3rPz&TestExpect.test_beta..sRr5)r`r`Fr rcdSrr;rs r3rPz&TestExpect.test_beta..r, r5TrT)r9rrrr)rsrrr rr. r/ s r3 test_betazTestExpect.test_betas= J  ;;'"#1  . .Avr2222 J  kkRr  J JAub1111 Z^^D"baq^ 9 9 Z^^D"baq^ 9 9""<.r) r5)rr`rr rrWc|dz dzSNrrgr;rs r3rPz+TestExpect.test_hypergeom..sadQYr5r.c|dz dzSr; r;rs r3rPz+TestExpect.test_hypergeom..sQrTAIr5r)r0rerr r cdSrr;rs r3rPz+TestExpect.test_hypergeom.. sqr5r3rVcdSrr;rs r3rPz+TestExpect.test_hypergeom..s1r5T)r0rerr r cdSrr;rs r3rPz+TestExpect.test_hypergeom..s!r5r)r0rr )r9rrrrPrm) rsm_truev_truerrv_bounds prob_true prob_boundsprob_bcprob_bs r3test_hypergeomzTestExpect.test_hypergeoms..r2qb.AA O " ";;[b " I IAvr2222 O " "#6#6[') # + +Avr2222?))*=*=/:.0Q2*?? Hfb9999eo))1b'2r1!)DDHHJJJ o,,[[{13b-BB KB????/((;B,-"$)HHGQ3333'' ++,(44FAr222222r5c$tjdddd}dtjddz }t ||d tjd ddd }t |dd dS) NcdSrr;rs r3rPz)TestExpect.test_poisson..sQr5r rF)r0rr r rgr.rWcdSrr;rs r3rPz)TestExpect.test_poisson..!sr5T)r9rrrqr)rsrD prob_b_trueprob_lbs r3 test_poissonzTestExpect.test_poissonsm**;;Ta7<+>>  ))!Q/// KbAAAA-&&{{!37'99GQ333333r5ctj}|d}|d|d}t||ddS)N)rr[)r|r.rW)r9genhalflogisticrr)rshalflogr/r3s r3test_genhalflogisticzTestExpect.test_genhalflogistic%sa'~~6~**F###~~6~**D$333333r5c ttjtjddttjtjddttjtjddttjtjdddS)Nr|Gz?cdSrr;rs r3rPz/TestExpect.test_rice_overflow..4r5)rS r[cdSrr;rs r3rPz/TestExpect.test_rice_overflow..5rU r5cdSNrr;rs r3rPz/TestExpect.test_rice_overflow..6rU r5)r rjrGr9ricerirrxs r3test_rice_overflowzTestExpect.test_rice_overflow/s  EJNN35566777 EJ--kk-HHIIJJJ EJ--kk-HHIIJJJ EJ--kk-HHIIJJJJJr5c(d\}}tjd|f}t|||dz z t jd|z z dtjd|f|}t|||zddS) N)r~rc|Srvr;r\s r3rPz(TestExpect.test_logser..;r, r5r[rTrrc|Srvr;r] s r3rPz(TestExpect.test_logser..Ar, r5r )r9rrrrjr)rsrvreres_0res_ls r3 test_logserzTestExpect.test_logser8s3 ##KKqd#;;QV rvb1f~~5E C C C C ##KKqd#DDus{777777r5cd\}}tjd||f}tjd||f}t|||z dt||dzz ||zddS)N)rr$c|Srvr;rs r3rPz)TestExpect.test_skellam..HAr5r[c |dzSrr;rs r3rPz)TestExpect.test_skellam..Irr5rrrg)r9rDrr)rsrp2rrs r3 test_skellamzTestExpect.test_skellamDsB ] ! !++RH ! = = ] ! !..Bx ! @ @BG%0000RU BG%888888r5c d\}}tjd||f}t|t dt ||D||z z ddS)N)rqc|Srvr;rs r3rPz)TestExpect.test_randint..Qr) r5c3K|]}|VdSrvr;rArs r3rz*TestExpect.test_randint..Ss"55!A555555r5rr)r9rArrrmr)rsr0r1rs r3 test_randintzTestExpect.test_randintMsBm"";;R9955uR}}55555bA O O O O O Or5cTtttjjdddS)Nc |dzSrr;rs r3rPz&TestExpect.test_zipf..Xs q!tr5r )r rzr9rrrrxs r3 test_zipfzTestExpect.test_zipfUs.^UZ%6#^T + + + + +r5ctjdd}tjddddd}t||d dS) NcdSrr;rs r3rPz/TestExpect.test_discrete_kwds..\rd r5r r[cdSrr;rs r3rPz/TestExpect.test_discrete_kwds..]rd r5r r-)r0maxcount chunksize tolerancer.rW)r9rrr)rsn0n1s r3test_discrete_kwdszTestExpect.test_discrete_kwdsZsd ] ! !++D ! 9 9 ] ! !++D+/2"OOBB//////r5cd}dD]=}tjd|}t|||d>dS)NcH|dzd|dzzzd|dzzzd|dzzz|zS)Nrr`rrrr?rgr;rs r3 poiss_moment5z-TestExpect.test_moment..poiss_moment5ds8q52b!e8#bQh.BE9B> >r5)rrrrr)r9rrr)rsr} r^m5s r3 test_momentzTestExpect.test_momentase ? ? ? ? ?B%%a,,B B b 1 1 > > > > > ? ?r5cttjdddttjdddttjdddttjdd ttjd d dS) NrLrTrdr}r`r])r[r Ur)rr9rrrrbrxs r3test_challenging_cases_gh8928z(TestExpect.test_challenging_cases_gh8928ks  ))b)<>$22!IOOD!44 #56H!I(*@*C" $ $ $ $)+A" $ $ $ $9>>&!,,IOOFA.. ,.@A."3%@@@@ >======r5c ~ttjddt dddS)Nrgir)rr9r rqrrxs r3test_cdf_large_nczTestNct.test_cdf_large_ncs0 aE%LL991=====r5zx, df, nc, expected)rr`rugAs69)rmrrugV1chttj||||ddSr)rr9r ri)rsr_rr rXs r3test_pdf_large_nczTestNct.test_pdf_large_ncs1  aR00(GGGGGGr5N) rrrr r r r r r rrrr r;r5r3r r sCCC222$$$    >>>,>>>6 [2.+5   HH   HHHr5r c&eZdZdZdZdZdZdS)TestRecipInvGausscVtjdd}|dksJdS)Nrrr)r9 recipinvgaussrirs r3test_pdf_endpointz#TestRecipInvGauss.test_pdf_endpoints+   # #As + +Cxxxxxxr5cltjdd}|tj ksJdS)Nrr)r9r rrjrrks r3test_logpdf_endpointz&TestRecipInvGauss.test_logpdf_endpoints/"))!S11wr5cntjdd}d}t||ddS)NrFr|g9V9s;rr)r9r rqrrsrvrXs r3test_cdf_small_xz"TestRecipInvGauss.test_cdf_small_xs<   # #D# . .(8%000000r5cltjdd}d}t||ddS)Nrr|glH>> EJNN1N334488::;;; EJ--a2-6677;;==>>>  EJNN1N334488::;;;z622 D!!%%''(((  q!,,ejnnQ.B.BQ ( ( ( ( ( (r5ctjj}t|djdt|ddjddS)Nrr r )rr)r2r)r9rY rrrrBrs r3 test_rice_rvszTestRice.test_rice_rvs%sOjnSS2YYY^Q'''SS2F+++16:::::r5ctjtjdddtjddd}gd}t ||tjddd}tj|dd}gd }t ||tjjd tjdd d}gd }t ||dS) Nr`)g/ Ƹ?g[jNJ\?g ?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?r]r g@_@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@)r9rY rqrjrrrr8)rsrqcdf_exp probabilitiesrppf_exps r3test_rice_gh9836zTestRice.test_rice_gh9836*sjnnRYr333RYr35K5KLL OOO W%%% #q#.. jnn]En;; LLL W%%%k""3 "c2(>(>?? ;;; W%%%%%r5N)rrrr r r r;r5r3r r sA(((*;;; '&'&'&'&'&r5r c eZdZdZdZdZdS) TestErlangcDtjddSr5r6rxs r3r7zTestErlang.setup_methodUr8r5c tj5tjdtt tt jjddddgd}t j|d}t j |d}t||d ddddS#1swxYwYdS) Nrsrrr rr)r|rTrrrrr) rwrxryrzr`r9erlangrrrr)rsr result_erlang result_gammas r3test_erlang_runtimewarningz%TestErlang.test_erlang_runtimewarningXs  $ & & D D  !'> : : : .,*CQaa I I I I (''D!L,,Ta,88M ;??4A?66L M.scale_mles/FD4KA-..!c$ii-@RG Gr5rrr{)r9r+rrr)rsrr<rr scale_expectrerfs r3ryzTestRayleigh.test_fit}s~!!sy!II H H H!yw// ^''7';; US'"""UL)))^''R'88 UUB ^''-- UUIIdC0011111r5rS r~g̡=E?g@1d?c~tjd||}ttj|dS)Nr"rn)r9r+rr)rsrr<rs r3 test_fit_comparison_super_methodz-TestRayleigh.test_fit_comparison_super_methods8 ~!!sy!II%end;;;;;r5c8ttjdSrv)rr9r+rxs r3rzTestRayleigh.test_fit_warningssEN+++++r5ctjd}d\}}}tj||||}tj|\}}|tj|ksJtj||\}}|tj|ksJ||ksJdS)Ni)r=rrrr{)rjrrr9r+rrr) rsrrerfrrrrrs r3test_fit_gh17088zTestRayleigh.test_fit_gh17088si##C(('UDn  e$S II^'',, $$$$"^//E/BB$$$$E!!!!!!r5N) rrrr7rrrrrryr rr r;r5r3r r ps"""000""" [03K3K3MNN22NN2. [0D$<4> 3K3MNN<<NN< ,,, " " " " "r5r cPeZdZdZdZdZejdgddZ ejdgdd Z ejdd d gd Z ejdd dgdZ dS) TestExponWeibcd}d}d}tj|||}tj|||}t ||gddgdS)Nr]rTrg:23W+g~`9k)r9 exponweibrirr)rsr_r1rrvrs r3test_pdf_logpdfzTestExponWeib.test_pdf_logpdfss    O  1a ( (%%aA..D /1DE G G G G Gr5c~tjddd}d}d}tj|||}tj||}t ||tj|||}tj||}t ||dS)Nrrrr ra)rjrr9r ri weibull_minrrrsr_r1rrvrXrs r3 test_a_is_1zTestExponWeib.test_a_is_1s KB " "   O  1a ( ($((A..8$$$%%aA..$++Aq11h'''''r5cztjddd}d}d}tj|||}tj|}t ||tj|||}tj|}t ||dS)Nrr r`)rjrr9r rirgrrr s r3test_a_is_1_c_is_1z TestExponWeib.test_a_is_1_c_is_1s KAr " "   O  1a ( (;??1%%8$$$%%aA..;%%a((h'''''r5z x, a, c, ref))r rrg=J ?)r=rrg$+PR>)r!rrg ><)r"rrggX.X:)r"?rgRy9)rr rg'vR0=)g_QPrrgQ: [ 5 5 5  --  -* [ 4 4 4...  [^AGIJJ11JJ1  [^IFHII00II000r5r ceZdZdZdZdS)TestFatigueLifecjtjdd}t|dddS)Nr{rX9rr)r9r!rrrs r3 test_sf_tailzTestFatigueLife.test_sf_tail(s8    , ,0u======r5cnd}tj|d}t|dddS)Nr rr{rr)r9r!rr)rsrvrs r3 test_isf_tailzTestFatigueLife.test_isf_tail6s: !   ! !!S ) )5u------r5N)rrrr r r;r5r3r r &s2 > > >.....r5r ceZdZdZdZejdddgdZdZ ejdd d gd Z d S) TestWeibullcftjdd}t|ddSr)r9r rrr s r3rzTestWeibull.test_logpdf?s0   $ $Q * *Qr5cd}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) Nrrrrrrr:rgrrXg& .gCe)r9r rirrjrrrrqrrrrr weibull_max) rsr_r1r2rvr7rlcrOrs r3test_with_maxima_distribz$TestWeibull.test_with_maxima_distribDs.      ! !!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#IJJKKKKKr5rfrTr]cxtj|dz|dzd|}t|ddS)Nrrrrg>)r9r rrrs r3rzTestWeibull.test_delta_cdfsI"!,,U3Ya38-::566666r5ctjd}d\}}}tj|||}|d|}tj|dd\}}} tj|dd\} } } || cxkrdksnJ|| ksJtj|ddd \} }}|dksJtj| ||}|d }tj|tj|f}t||dS) Nl>)rgr;r|rarrrrrrrrr) rjrrr9r rrrrBr)rsrrrerfrBrc2rrc3rrc4rrrrrs r3 test_fit_minzTestWeibull.test_fit_minsTi##$788# 3 C//hhCch22!,00c0BBD& ,00c0BBD&t    q      Rxxxx!,00a$0OOD&{{{{!"dF33kk$k''gcllEJsOO+S!!!!!r5r,)r=r r)rrgq뮕qH)cttj|||dttj|||ddSrT)rr9r rrr0s r3rzTestWeibull.test_sf_isfsZ ),,Q22CeDDDD)--c155quEEEEEEr5N) rrrrr rrrrr rr;r5r3r r =s RLRLRLh [WsCj1177217("""< [[+J,D+EFFFFFFFFFr5r ceZdZdZdZdS) TestDweibullcBtjd}d|ddz}tj|}tj|tjdz }t||ddS)Nq>~).r`rar r|rr) rjrrrr9dweibullrHr rr)rsrrrrs r3rqzTestDweibull.test_entropysi##$788  2 .. .n$$Q''''**RVC[[8Su------r5cPtjd}d|ddz}d|z}t j||}dt j||z}t||ddS)Nr r`r r r|rr) rjrrrrr9r rr r)rsrrr_rrs r3rzTestDweibull.test_sfsi##$788   ,, ,  n1%%E%((A...Su------r5N)rrrrqrr;r5r3r r s2 . . ......r5r cDeZdZdZdZdZdZdZdZdZ dZ d Z d S) TestTruncWeibullcrtjddgddd}t|ddgdS)Nr]rg)\(?gףp= ?r)r9truncweibull_minrirr s r3test_pdf_boundsz TestTruncWeibull.test_pdf_boundss<  " & &Sz3d C CQc #####r5ctjdddtj}t |dtjdddd}t |ddS)NrrTrrg~?)r9r rrjrrrr s r3rzTestTruncWeibull.test_logpdfse  " ) )#sC @ @Q  " ) )#sC = =./////r5crtjddgddd}t|ddgdS)NrrTrr])r9r rrr s r3test_ppf_boundsz TestTruncWeibull.test_ppf_boundss<  " & &Sz3S A AQc #####r5cgd}tj|ddd}tj|ddd}t ||dSN)rr]rlr|rrrTrrr)r9r rrqrrsrr_q_outs r3test_cdf_to_ppfz TestTruncWeibull.test_cdf_to_ppfs[ 0 0 0  " & &q"b" 5 5&**1b"b995!!!!!r5cgd}tj|ddd}tj|ddd}t ||dSr )r9r rrrr s r3test_sf_to_isfzTestTruncWeibull.test_sf_to_isfs[ 0 0 0  " & &q"b" 5 5&))!RR885!!!!!r5c d d d fdtjd }t|dtjd }t fd \}}t ||tjd }t fd  \}}t ||tjd }t fd  \}}t ||tjd } t fd  \} }t | | dS)NrrTrcT||ztj|zSrv)r9r ri)r_rur1r2rs r3xnpdfz)TestTruncWeibull.test_munp..xnpdfs)a4.221aA>>> >r5rr c|dSrr;r_r s r3rPz,TestTruncWeibull.test_munp..a r5rgc|dSrr;r s r3rPz,TestTruncWeibull.test_munp..r r5rc|dSrX r;r s r3rPz,TestTruncWeibull.test_munp.. r r5rc|dS)Nrr;r s r3rPz,TestTruncWeibull.test_munp..$r r5)r9r rrrr)rsrr m1_expectedrr m2_expectedm3 m3_expectedr m4_expectedr1r2rr s @@@@r3 test_munpzTestTruncWeibull.test_munp s    ? ? ? ? ? ? ? # * *1aA 6 6R  # * *1aA 6 63333Q:: QK(((  # * *1aA 6 63333Q:: QK(((  # * *1aA 6 63333Q:: QK(((  # * *1aA 6 63333Q:: QK(((((r5c ^d}d}d}tjdtjdtjdtjdz zz }tj||||}t|dtj||||}t|tjd tj d|||}t||tj ||||}t|dtj ||||} t| tjd tj d|||} t| |dS)NrTrrr r|r%) rjrrrr9r rqrrrrrr) rsr1r2rx_medrqr rrrrs r3test_reference_valuesz&TestTruncWeibull.test_reference_values'so   BF3"rvbzz/0B)C)C#CDDDEE$((1a88S!!!  # * *5!Q : :RVBZZK((($((aA66U###  # & &uaA 6 6C    # ) )%Aq 9 9RVBZZK((($((aA66U#####r5c*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) Nrrrrrr:rgrr) rjrr9r rir rrrqrrrr)rsr_rr1r2rfrvp_truncr7lp_truncrq cdf_truncr lc_truncrOs_truncrls_truncs r3test_compare_weibull_minz)TestTruncWeibull.test_compare_weibull_min?se    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!!!!!r5cd\}}}tj||d}tj||||}tj||||}tj||tj||z }tj|||z }tj||tj||z |z } tj||tj|| dS)N)rrlrra) rjrYr9r rirqr rr) rsrr1r2r_rrxrrrzs r3test_compare_weibull_min2z*TestTruncWeibull.test_compare_weibull_min2hs"1a K1c " "%))!Q155%))!Q155 $$Q**U->-B-B1a-H-HH $$Q**T1!%%a++e.?.C.CAq.I.II4O ""4... ""4.....r5N) rrrr rr r r r r r" r$ r;r5r3r r s$$$ 000$$$ """ """ )))6$$$0'"'"'"R/////r5r cfeZdZdZdZejdgddZdS) TestRdistctj}gd}t|||dd|ddS)Nrg@rrW)r9rdistrrqr)rsr rXs r3test_rdist_cdf_gh1285zTestRdist.test_rdist_cdf_gh1285zsX$$$FJJvzz&%'@'@%HH"A / / / / / /r5c tjddd}d}tdtj|dz |dz |dzdz ztj||dS)NgGzrr`g@r|rgr )rjrYrr9rrir( )rsr_rs r3test_rdist_betazTestRdist.test_rdist_betas KtR ( ( C 1Q3! 4 4 8 8!a% C CC!KNN..q11 3 3 3 3 3r5r,))rig?)r]g;|bZ?)r|ig79)riUg޻S/cfttj|||ddSrT)rr9r( rr0s r3 test_rdist_sfzTestRdist.test_rdist_sfs/  q!,,c>>>>>>r5N) rrrr) r+ rrrr. r;r5r3r& r& yst///333 [   ?????r5r& c~eZdZdZdZdZdZdZdZe j dgdd Z d S) TestTrapezoidcVgd}|D]}d|dg}ttj|||tj||ttj|||tj||dS)N)rr~r|r rr )rr9rritriangrq)rsmodesmoder_s r3test_reduces_to_triangz$TestTrapezoid.test_reduces_to_triangs    ; ;DD! A  3 3AtT B B % 0 0D 9 9 ; ; ;  3 3AtT B B % 0 0D 9 9 ; ; ; ;  ; ;r5cbtjddd}ttj|ddtj|ttj|ddtj|dS)Nrr r`)rjrYrr9rrirrqrs r3test_reduces_to_uniformz%TestTrapezoid.test_reduces_to_uniforms K1b ! !EO//1a88%-:K:KA:N:NOOOEO//1a88%-:K:KA:N:NOOOOOr5cnttjddddttjddddttjddddttjddddttjd ddd ttjdddd ttjd ddd ttjd ddd ttjddddttjddddttjd dddttjdddddS)Nrrgr r|rrrQrTr]g?rrr ryg?)rr9rrirqrxs r3 test_caseszTestTrapezoid.test_casessEO//1a88!<<<EO//1a88!<<<EO//Q<</ 1 1 1EO//S#>>/ 1 1 1 EO//S#>>FFFEO//S#>>EEEEO//S#>>FFFEO//S#>>HHHEO//S#>>FFFEO//S#>>DDDEO//S#>>HHHEO//S#>>DDDDDr5c d\ z z z z z z z f\}}}}d z z z z fd}|d}|d|dzz }d z z z z z z z z tjd z z z zz}ttj|||||dttj|||||dttj|||||dttjddd d d dttjddd d ddttjddd d d ddS) N)rrrgrrgc|dzz|dzzz z z |dzz|dzzz z z z z|dzz |dzz S)Nrgr r;)rur1r2rdrps r3rz6TestTrapezoid.test_moments_and_entropy..momentsn!ac(Q1X-!A#6!Hq1Q3x/AaC89:qSqS" #r5r r|rrWrrr3rr)rjrrr9rrrArH)rsrrf rerfrrrArHr1r2rr< rps @@@@@r3test_moments_and_entropyz&TestTrapezoid.test_moments_and_entropys" 1acac]QqSQqSM1acABU 1QqM # # # # # # # # # vayyfQii$'!1Qq/QqSU1W-sac!eAg0G0GGEO00ReDD " . . . .EO//BUCC - - - -EO33BCGG#R 1 1 1 1 EO00Ar1==r2NNNNEO00Ar1==q"MMMMEO//1b!<>>>>>r5c(tjddd}tjd5tj|dd}dddn #1swxYwYt|tj|dS)Nrr r`z`trapz.pdf` is deprecatedr ) rjrYrdeprecated_callr9rIrirr)rsr_rs r3 test_trapzzTestTrapezoid.test_trapzs K1b ! !  #*E F F F . .[__Q1--F . . . . . . . . . . . . . . .FEM$5$5a$8$899999s"AA!Ar)rirrqrrrrrcd\}}ttj|d||}tjd|d5ttj|d||}dddn #1swxYwY||ksJdS)N)rQrr z`trapz.z` is deprecatedr )r.r9rrrI rI)rsrrr< rXrs r3test_trapz_deprecationz$TestTrapezoid.test_trapz_deprecations1375?F33Aq!<<  #3F333    ; ;2WU[&11!Q::F ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;!!!!!!s&A66A:=A:N) rrrr5 r7 r9 r= rG rJ rrrrL r;r5r3r0 r0 s;;;PPP EEE(MMM6???4::: [X(E(E(EFF""FF"""r5r0 ceZdZdZdS) TestTriangctjd5ttjdddttjdddttjdddttjdddttjdddttjddd ttjdddttjddd ttjdddttjdddttjddd ttjdddddddS#1swxYwYdS) Nraiserrrr|rTr rrgrrl)rjrrr9r2 rirqrxs r3test_edge_caseszTestTriang.test_edge_casess [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)rrrrQ r;r5r3rN rN s#66666r5rN ceZdZejdddgdZejdgddZdZd Z d S) TestMaxwellr)rgCR5&.)r~g7q?cdttj||ddSr#)rr9maxwellrr:s r3rzTestMaxwell.test_sf s/  ((++Su======r5rV))rg1!@)g?g?)g>>>>>r5cld}tjd}t||ddS)Ngi6urrr)r9rU rr)rsrrs r3rzTestMaxwell.test_logcdf0s7%%%a((%000000r5cld}tjd}t||ddS)Ng_OԺr-rr)r9rU rr)rsrrs r3rzTestMaxwell.test_logsf6s7% ##D))s//////r5N) rrrrrrrrrrr;r5r3rS rS s  [X::<==>>==>  [X:::;;?? ;;?111 00000r5rS ceZdZdZdZdS) TestMielkecd\}}ttj||dtjttj|ddtjt t jtj|dddS)N)g rh@gv?r rTr0)rr9mielkerrjrr rG)rsr\rOs r3r*zTestMielke.test_moments>s1U\!Q''..q1126:::U\!S))0033RV<<< ELD1188;;<<=====r5ctjddd}d\}}ttj||||z tj|||dS)Nr~rar=)g@gHzG@)rjrYrr9burrrir\ )rsr_r\rOs r3test_burr_equivalencez TestMielke.test_burr_equivalenceEs^ Kc2 & &1 q!QqS115<3C3CAq!3L3LMMMMMr5N)rrrr*r_ r;r5r3rZ rZ =s7>>>NNNNNr5rZ c&eZdZdZdZdZdZdS)TestBurrc ntjddgtjddgtjddgtjddgtjddgtjddgtjd d gg}d |D}d |D}t ||d |D}d|D}t ||dS)Nr r )r|rg)r r )rgr|rr|rT)r rgrc<g|]\}}}|j|jg|RSr;rrs r3rCz0TestBurr.test_endpoints_7491..Xrr5cg|]\}}}| Sr;r;rs r3rCz0TestBurr.test_endpoints_7491..Yrr5c<g|]\}}}|j|jg|RSr;)rr1rs r3rCz0TestBurr.test_endpoints_7491..\s4@@@<2uayry&&&&@@@r5c>g|]\}}}tj|Sr;)rjrrs r3rCz0TestBurr.test_endpoints_7491..]s)FFF)=UI26)$$FFFr5)r9fiskr^ burr12r)rsrrrs r3test_endpoints_7491zTestBurr.test_endpoints_7491LsZq ! Z1 % Z # Z1 % \8S ) \63 ' \63 ')>====>>>>>!#w///@@4@@@FFFFF!#w/////r5cd\}}tj||\}}d\}}t||t||dS)N)rUr)g4U?g&MI?)r9r^ r)rsrr< rvariancemean_hc variance_hcs r3test_burr_stats_9544zTestBurr.test_burr_stats_9544`s_1Aq))//11h Gg&&&+.....r5cd\}}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)r|r)rrr)rr)r;r)r9r)r9r^ r rjrfrGrr) rsrr< rrl e1e2e3e4s r3test_burr_nan_mean_var_9544z$TestBurr.test_burr_nan_mean_var_9544ksb1Aq))//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     r5cd\}}gd}gd}ttj||||ddS)N)rUr)r]rrr7)g+&?gI$_@gKT@gؗVArr)rr9r^ r)rsrr< rrs r3 test_burr_isfzTestBurr.test_burr_isfsV1 & & &### q!Q//5AAAAAAr5N)rrrrj ro ru rw r;r5r3ra ra KsV000( / / /(!(!(!TBBBBBr5ra ceZdZejdddgdZdZejdgddZd S) TestBurr12zscale, expected)rTgd~)r;gR톇T crtjdddd|}t||ddS)NgjAgjArrrrr)r9ri rr)rsrfrXrrs r3rzTestBurr12.test_delta_cdfs?( ''S!Qe'DDxe444444r5c d\}}tjdz }dtjdzdz z }tjdzd|dzzz }tj}||||g}tj||d }t ||d dS) Nrtrr rgrurrt rrrr)rjrkrr9ri r) rsrr< rrArBrrrs r3test_moments_edgezTestBurr12.test_moments_edges 1uQw"%(2+ouaxCH%6S$)l1a  &&v..Su------r5z p, c, d, ref))rrr|ggx4/@)gҶOɃ;rr|gI8aS@)rrl#gj\/@)g#aMR/rlr} g!GAcltj|||}t||ddSr#)r9ri rr)rsrvrr< rr_s r3test_isf_near_zerozTestBurr12.test_isf_near_zeros8 L  Q1 % %3U++++++r5N) rrrrrrrr| r r;r5r3ry ry s [.<;=>>55>>5( . . .  [ 0 0 0,,,,,r5ry 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@)r@rrr rr`rx)rgrr.r)r]ri)#gupm1f?)r r`rg?<-=A?gv"?rgd暕?ga-A?c|jD]>\}}|\}}}tj|||}t ||d?dS)Nrr)rr9studentized_rangerqr)rspvkr p_expectedrr\res_ps r3test_cdf_against_tablesz,TestStudentizedRange.test_cdf_against_tables s_i : :FC" J1+//1a88E E:D 9 9 9 9 9 : :r5c|jD]>\}}|\}}}tj|||}t ||d?dS)Nrr)rr9r rr)rsr q_expectedrvrr\res_qs r3test_ppf_against_tablesz,TestStudentizedRange.test_ppf_against_tables s^#y : :OCGAq!+//1a88E E:D 9 9 9 9 9 : :r5z&data/studentized_range_mpmath_ref.jsonN case_resultcdf_datac|d}|d}|d|d|df}tjj|}t|||d|ddS Nsrc_case mp_resultrr\r expected_atol expected_rtolrn)r9r rqrrsr r r qkvrs r3test_cdf_against_mpz(TestStudentizedRange.test_cdf_against_mp sz* , smXc]HSM9%)3/Y%o6%o6 8 8 8 8 8 8r5pdf_datac|d}|d}|d|d|df}tjj|}t|||d|ddSr )r9r rirr s r3test_pdf_against_mpz(TestStudentizedRange.test_pdf_against_mp r r5z+intermittent RuntimeWarning: invalid value. moment_datac|d}|d}|d|d|df}tjd5tjj|}dddn #1swxYwYt |||d|d  dS) Nr r rr\rrrr r rn)rjrr9r rr)rsr r r mkvrs r3test_moment_against_mpz+TestStudentizedRange.test_moment_against_mp) 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)Nrr`rr[r )rr9r rirjrr)rsr\rrs r3test_pdf_integrationz)TestStudentizedRange.test_pdf_integration: sG15*.26AGGGA"""""r5cd\}}tjddd}tj|||dd}tj|||}t ||}t||ddS) Nr rr`r~)stepr rr)rjrr9r rqrirr)rsr\rr_y_cdf y_pdf_rawy_pdf_cumulatives r3test_pdf_against_cdfz)TestStudentizedRange.test_pdf_against_cdfA s1 Ia$ ' ' ''++Aq!44QRR8+//1a88 / 1== (%d;;;;;;r5 r_case_resultc|\}}}}tjd5tj|||}dddn #1swxYwYt ||dS)Nrr)rjrr9r rqr)rsr rr\rr_resrs r3test_cdf_against_rz'TestStudentizedRange.test_cdf_against_rQ 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) Nrrr rgrrr`rr z...could not be broadcast...r )r`rrV) rjrr9r rrrBrrrrs r3test_moment_vectorizationz.TestStudentizedRange.test_moment_vectorizationY 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<ct5}tjd5|tt jgd\}}}}dddn #1swxYwYdddn #1swxYwYtt j ||dS)Nrrr ) r rjrrSrr9r rtr _argcheck)rsrmr\rrs r3test_fitstart_validz(TestStudentizedRange.test_fitstart_validi sF   GCX)F)F)F G G JJ) * * *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!R8899999s5B AA2& B 2A6 6B 9A6 :B  B B ctjddtj}tjddd}t ||ddtjddtj}tjddd}t ||dddS)Nrr`韆rrn)r9r rirjrrrq)rsr res_finites r3test_infinite_dfz%TestStudentizedRange.test_infinite_dfq s%))!R88,00B>> Zd>>>>%))!R88,00B>> Zd>>>>>>r5cZtjddd}tjddd}tjddd}ttt ||ddt ||ddtjddd}tjddd}tjddd}ttt ||ddt ||dddS)Nrr`rr irvrn)r9r rir`AssertionErrorrrq)rsrr res_sanitys r3test_df_cutoffz#TestStudentizedRange.test_df_cutoff| s%))!R88,00B>> ,00B>> nosJd , , , , JTEEEE%))!R88,00B>> ,00B>> nosJd , , , , JTEEEEEEr5cd\}}}tj|||}t|dd|dksJdS)N)gaRA@riSrrr)r9r rr)rsrr\rrvs r3 test_clippingz"TestStudentizedRange.test_clipping sO.1a  # & &q!Q / /15))))Avvvvvvr5)1rrrq05q01q001rjrwqspsrvskslistrr(rr_datarrrr rr ospathdirnamer path_prefix relative_pathopenrcfilejsonrpregenerated_datarr r xfail_on_32bitr r r r r r r r r r;r5r3r 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::;;;#<<<<<<<<<<<<<<<<<>A H % % %99%-++AB+7788999999999999999a0000 Xem''#1'== > >Fa0000 Xem''d':: ; ;Fa0000 Xem''d';; < >H!444444s4CCCctjdtjd}tj|}d}t||ddS)Ni rar;)g ףp= ?gʡE?r rW)rjrrr9rrrr)rrrXs r3test_regression_ticket_1530r f!scINN6 ,    $ $C \  c " "FH!444444r5ctjdtjd}dD]K}tj||z\}}t||dt|ddLdS)Nrr )r g6ArTrr)rjrrr>r9rrr)r_offsetrerfs r3test_gh_pr_4806r o!sINN4 A'..\%%a&j11 UV#....s-----..r5cttjtjdddS)NrErS)r rjrGr9rr:r;r5r3test_poisson_logpmf_ticket_1436r y!s2 BK ,,T377 8 899999r5cddg}|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)) )rT)r|rrr)r)gUUUUUU?r3 g^cQg333333rrN)r9rr)rZr1 exact_mvskrs r3test_powerlaw_statsr }!s[>, = ?E44 :~##Av#66!$ 333344r5cftjdd}t|ddS)Nrr r)r9rrrrvs r3test_powerlaw_edger !s/ a##ACr5cxtjdd}t|dtjdgd}t|t jddgtjdgd}t|t jdt j gdS)Nrr r)rlrTrrT)r9r@rrrirjrr s r3test_exponpow_edger !s a##AC 1...//ARVS#&''' a!1!1!122ARVS26'*+++++r5chtjddd}t|ddS)Nrr rT)r9gengammarirr s r3test_gengamma_edger !s1 1a##ACr5za, c, ref, tol))g`6Ar g2j!@r)rr ggA@r)rr rr)rr g#@r)g`FArgI~mr)gl$W}Lrg.I#Urcfttj||||dSr)rr9r rH)r1rrrWs r3test_gengamma_extreme_entropyr !s1"EN**1a00#C@@@@@@r5ctjddd}|dksJtjddd}|tj ksJdS)Nrr rr)r9r rirrjr)rvrs r3!test_gengamma_endpoint_with_neg_cr !sV 1a$$A 8888 > Ar * *D BF7??????r5ctjddd}t|dtjddd}t|ddS)NrrSrTg>r`gqq?)r9r rrr s r3test_gengamma_munpr !sZ Rb))A:&&& RR((A6"""""r5ctjgd}tjd5t5}|t d|t dtj |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) rjrrr rSrrzr9rLr)r< rms r3test_ksone_fit_freezer !sK  / / / 0 0A X & & &   C JJ)# $ $ $ JJ~F H H H KOOA                   s5B5AB B5B! !B5$B! %B55B9<B9c rtjttddd }gd}t t j||dt t j|dzj|dt j|dzd z j }tj t j |t j|z }t ||d dS) Nrr r)gDB.g8_$g%`OAgjhwHRgWMB@v`g7VY}igۦx\Arg xg#g/dg3$gegd)gNq{3g يGǓgr 4g37' gfFg?dJgضg2, gm%gӅJgz;pg ɿ{gk2gij<%giVSͶgBR4g Q/Mr-ry+=y|=r) rjrr rrr9rrrealimagrr)r_rXderivderiv_expecteds r3test_norm_logcdfr !s  Dq#q))** + ++A000HEJLL''**H4@@@@EJLL''F 338(NNNNZ  q6z * *5 0 6EVEJ--a005:3D3DQ3G3GGHHNE>666666r5ctjgd}tjgd}tj|}t ||ddS)N)gMb{Gzg{Gztg~jtX)g#]>g~666UZ^^Aryc':':A>>BBB""1biS&9&91==>>>>>>>>>>>>>>>  BK   # # % %&&&  " "MMg~666UZ^^E1b111555 ))%B779KLLLMMMMMMMMMMMMMMMMMMs%BB11B58B5A9FF F zmethod, expectedrqg u%>g ;Q=riggRz\R>rgʎK$/gԆX1rgfHu@ge:@czttj|dddgd}t||ddS)Nr]rrr`)r rrr)r.r9r r)rrXrs r3test_ncx2_zero_ncr& t"sE )WUZ ( (!QB ? ? ?FFH5111111r5ctjddd}tjdd}t ||ddS)Nr`rr )rr r)rrrr)r9r rrr)rrXs r3test_ncx2_zero_nc_rvsr( "sOZ^^raa^ 8 8Fz~~!~44HFH5111111r5cdtjddz}ttjdd|ddS)Nr`rr r rr r)rjrrr9r rq)r s r3test_ncx2_gh12731r+ "sB RYq"   Bb11155555r5ctjgd}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* ) rTrTrTrTrTg?gy[qD?rrrrrrrr)rjrr9r rr)r_nurr sf_expecteds r3test_ncx2_gh8665r/ "st """ # #A %GB qRC ( (B'''K B %000000r5c d}d}tjtjd||tjd||d}tj|||}tj|||ztjd|zd|zz}t||d dS) Ni,irrrr rgrrr) rjrYr9r rrirrr)rr r_ncx2_pdf gauss_approxs r3test_ncx2_gh11777r3 "s B B EJNN5"b11JNN5"b11u > > >Az~~aR((H:>>!R"Wbga"fq2vo.F.FGGLHl666666r5zx, c, expected))rgr g|1q?)rgrgg~?)r|r V<3T1=)7yQCr u lY<)r|gvHGBg^b!*1=)ryrSgS?chtj||}t||ddSNr)r9 foldcauchyrrr_rrXrs r3test_foldcauchy_sfr; "s4    Q " "BB%(((((r5r))rgg?)r|r4 )r5 r6 )g6ްPg8R#/cftj|}t||ddSr8 )r9rNrr)r_rXrs r3test_halfcauchy_sfr= "s2    Q  BB%(((((r5z p, expected))g?g*wӄZ>)333333?gN9?)r|rT)r~g8<,O@)rg:B)gl ׶w/gMb}[Pcdtj|}t||dSrv)r9rNrr)rvrXr_s r3test_halfcauchy_isfr@ "s0 QAAx     r5cxtjdd}t|dddS)Nrr r)r9r/rrq)rs r3test_foldnorm_zerorB "s6  # # #BAr5))rgr gwo {?)rr gGd-P/)r`r?gof?)rr?g Oul";chtj||}t||ddS)Nr)r9r/rrr: s r3test_foldnorm_sfrD #s3   1a BB%(((((r5ctjgddd}tjddgdd}td|D}t||tjgd}tjddg}td |D}t||dS) N)rr|rTr r|rTc3RK|]"}tjtj|fV#dSrvrjrNrrl s r3rz-test_stats_shapes_argcheck..#s/88q"% *888888r5)rgr=rrgr=c3RK|]"}tj|tjfV#dSrvrG rl s r3rz-test_stats_shapes_argcheck..#s/88q"%26 *888888r5)r9r"tuplerr()mv3mv2 mv2_augmenteds r3test_stats_shapes_argcheckrM #s .  3 7 7C .  Sz1c 2 2C88C88888M$$$ -  lll + +C -  q#h ' 'C88C88888M$$$$$r5ceZdZdZdS) _distr_gencdSNr r;rsr_r1s r3_pdfz_distr_gen._pdf(#srr5NrrrrS r;r5r3rO rO '#s#r5rO ceZdZdZdS) _distr2_gencd|z|zSrQ r;rR s r3_cdfz_distr2_gen._cdf-#Avzr5N)rrrrX r;r5r3rV rV ,#s#r5rV ceZdZdZdZdS) _distr3_genc ||zSrvr;rsr_r1r2s r3rS z_distr3_gen._pdf2#s 1u r5cd|z|zSrQ r;rR s r3rX z_distr3_gen._cdf5#sAvzr5NrrrrS rX r;r5r3r[ r[ 1#s2r5r[ ceZdZdZdZdS) _distr6_genc||z|zSrvr;r] s r3rS z_distr6_gen._pdf=#ssQwr5cd|z|zSrQ r;r] s r3rX z_distr6_gen._cdf@#rY r5Nr_ r;r5r3ra ra ;#s2r5ra cteZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdZdS)TestSubclassingExplicitShapescrtdd}t|ddddS)Ndummyr1rrr rur rO rrirs dummy_distrs r3test_correct_shapesz1TestSubclassingExplicitShapes.test_correct_shapesG#s: gc::: [__Q!_,,b11111r5cvtdd}tt|jdfit ddS)Nrg Arh r ru)rO r`rrirrj s r3test_wrong_shapes_1z1TestSubclassingExplicitShapes.test_wrong_shapes_1K#s> gc::: i!AAtayyyAAAAAr5c~tdd}tddd}tt|jdfi|dS)Nrg za, b, crh r rgrr)rO rr`rri)rsrk r/s r3test_wrong_shapes_2z1TestSubclassingExplicitShapes.test_wrong_shapes_2O#sJ gi@@@ Q!q!!!i!;;s;;;;;r5cXtdd}tttfi|dS)Nrg r rh )rr`rrO rsr/s r3test_shapes_stringz0TestSubclassingExplicitShapes.test_shapes_stringT#s2+++i33s33333r5cXtdd}tttfi|dS)Nrg z(!)rh rr` SyntaxErrorrO rs s r3test_shapes_identifiers_1z7TestSubclassingExplicitShapes.test_shapes_identifiers_1Y#s2...k:5555555r5cXtdd}tttfi|dS)Nrg 4chanrh rv rs s r3test_shapes_identifiers_2z7TestSubclassingExplicitShapes.test_shapes_identifiers_2^#2000k:5555555r5cXtdd}tttfi|dS)Nrg zm(fti)rh rv rs s r3test_shapes_identifiers_3z7TestSubclassingExplicitShapes.test_shapes_identifiers_3b#s2111k:5555555r5cXtdd}tttfi|dS)Nrg za=2rh rv rs s r3"test_shapes_identifiers_nodefaultsz@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaultsf#s2...k:5555555r5cXtdd}tttfi|dS)Nrg z*argsrh rv rs s r3test_shapes_argsz.TestSubclassingExplicitShapes.test_shapes_argsj#r| r5cXtdd}tttfi|dS)Nrg z**kwargsrh rv rs s r3test_shapes_kwargsz0TestSubclassingExplicitShapes.test_shapes_kwargsn#s2 333k:5555555r5cXtdd}tttfi|dS)Nrg za, b, c, lambdarh rv rs s r3test_shapes_keywordsz2TestSubclassingExplicitShapes.test_shapes_keywordsr#s3(9:::k:5555555r5cGddtj}|d}t|ddtjddzdS)NceZdZdZdS)FTestSubclassingExplicitShapes.test_shapes_signature.._dist_gencFtj||zSrvr9rrS rR s r3rS zKTestSubclassingExplicitShapes.test_shapes_signature.._dist_gen._pdfz#zq))A--r5NrT r;r5r3 _dist_genr y## . . . . .r5r r1rr|rgrur9rFrrirrsr rBs r3test_shapes_signaturez3TestSubclassingExplicitShapes.test_shapes_signaturew#s| . . . . .+ . . .y$$$TXXcQX'')<)?????r5cGddtj}|d}tt|jdfit dddS) NceZdZdZdS)STestSubclassingExplicitShapes.test_shapes_signature_inconsistent.._dist_gencFtj||zSrvr rR s r3rS zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.._dist_gen._pdf#r r5NrT r;r5r3r r #r r5r rr r|r rgr)r9rFr`rrirr s r3"test_shapes_signature_inconsistentz@TestSubclassingExplicitShapes.test_shapes_signature_inconsistent#so . . . . .+ . . .y'''i3AA$a...AAAAAr5cGddtj}|d}t|ddtjddzt|ddtjddzt t |jdfitddS) NceZdZdZdS)?TestSubclassingExplicitShapes.test_star_args.._dist_gencV|d}tj||zSNrr )rsr_r0 extra_kwargs r3rS zDTestSubclassingExplicitShapes.test_star_args.._dist_gen._pdf#s$"1g zq))K77r5NrT r;r5r3r r #s# 8 8 8 8 8r5r r r r|!r )xxx)r9rFrrirr`rrr s r3test_star_argsz,TestSubclassingExplicitShapes.test_star_args#s 8 8 8 8 8+ 8 8 8 y ...TXXcrX22EJNN34G4G4JKKKTXXc2&& s(;(;B(>???i3??$2,,,?????r5cpGddtj}|d}t|dddtjddzdzt|dddtjddzdzdS) NceZdZdZdS)ATestSubclassingExplicitShapes.test_star_args_2.._dist_genc\|d}tj||z|zSr r )rsr_r r0r s r3rS zFTestSubclassingExplicitShapes.test_star_args_2.._dist_gen._pdf#s)"1g zq))K7&@@r5NrT r;r5r3r r #s( A A A A Ar5r zoffset, extra_kwargr r|or )r r r r s r3test_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 3r5cGddtj}|d}t|ddtjddS)NceZdZdZdS)BTestSubclassingExplicitShapes.test_extra_kwarg.._distr_gencr|dd}tj||zS)Nr r )popr9rrS )rsr_r0kwargsr s r3rS zGTestSubclassingExplicitShapes.test_extra_kwarg.._distr_gen._pdf#s0%jj:: zq))K77r5NrT r;r5r3rO r #s# 8 8 8 8 8r5rO r r r rr r )rsrO rBs r3test_extra_kwargz.TestSubclassingExplicitShapes.test_extra_kwarg#sw 8 8 8 8 8, 8 8 8z///TXXaQX//1B1BCCCCCr5cGddtj}|d}t|dtjddS)NceZdZdZdS)ITestSubclassingExplicitShapes.test_shapes_empty_string.._dist_genc@tj|Srv)r9rrirs r3rS zNTestSubclassingExplicitShapes.test_shapes_empty_string.._dist_gen._pdf#sz~~a(((r5NrT r;r5r3r r #s# ) ) ) ) )r5r r r|r r s r3test_shapes_empty_stringz6TestSubclassingExplicitShapes.test_shapes_empty_string#sq ) ) ) ) )+ ) ) )y###TXXc]]EJNN3$7$788888r5N)rrrrl ro rq rt rx r{ r~ r r r r r r r r r r r;r5r3re re D#s"222BBB<<< 444 666 666666666666666666 @@@BBB @ @ @ 3 3 3 D D D99999r5re ceZdZdZdZejeddZ ejeddZ dZ dZ d Z d Zd S) TestSubclassingNoShapescptd}t|ddddS)Nrg rr rur ri rj s r3test_only__pdfz&TestSubclassingNoShapes.test_only__pdf#s8 g... [__Q!_,,b11111r5cptd}t|ddddS)Nrg r r ru)rV rrirj s r3test_only__cdfz&TestSubclassingNoShapes.test_only__cdf#s8!w/// KOOAO33Q77777r5docstring strippedrjctd}t|jdt|jdt jd|j}tt|dkdS)Nrg r r r1zlogpdf\(x, a, loc=0, scale=1\)) rO rnumargsrrefindallr r rrsrk rs r3test_signature_inspectionz1TestSubclassingNoShapes.test_signature_inspection#sr!g... [(!,,,['---j:$,..CA r5ctd}t|jdt|jdt jd|j}tt|dkdS)Nrg r rgrz!logpdf\(x, a, b, loc=0, scale=1\)r ) ra rr rr r r r rr s r3test_signature_inspection_2argsz7TestSubclassingNoShapes.test_signature_inspection_2args#sr"w/// [(!,,,['000j=$,..CA r5c>tttddS)Nrg r )r`rr[ rxs r30test_signature_inspection_2args_incorrect_shapeszHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapes#si7;;;;;;r5cxGddtj}tt|fit ddS)NceZdZddZdS)>TestSubclassingNoShapes.test_defaults_raise.._dist_genr cdSrQ r;rR s r3rS zCTestSubclassingNoShapes.test_defaults_raise.._dist_gen._pdf#rr5N)r rT r;r5r3r r #s(      r5r rg r r9rFr`rrrsr s r3test_defaults_raisez+TestSubclassingNoShapes.test_defaults_raise#Z     +    iAAd.@.@.@AAAAAr5cxGddtj}tt|fit ddS)NceZdZdZdS)>TestSubclassingNoShapes.test_starargs_raise.._dist_gencdSrQ r;)rsr_r1r0s r3rS zCTestSubclassingNoShapes.test_starargs_raise.._dist_gen._pdf#r r5NrT r;r5r3r r ##     r5r rg r r r s r3test_starargs_raisez+TestSubclassingNoShapes.test_starargs_raise#r r5cxGddtj}tt|fit ddS)NceZdZdZdS)._dist_gencdSrQ r;)rsr_r1r s r3rS zATestSubclassingNoShapes.test_kwargs_raise.._dist_gen._pdf#r r5NrT r;r5r3r r #r r5r rg r r r s r3test_kwargs_raisez)TestSubclassingNoShapes.test_kwargs_raise#r r5N)rrrr r rrrDOCSTRINGS_STRIPPEDr r r r r r r;r5r3r r #s222888  [+4HIIJI [+4HIIJI<<<BBBBBBBBBBBr5r r cgd}tjD]l}tt|}t|tjtjzr.|D]+}t tj||j du,mdS)N)z,\s*,z\(\s*,z^\s*:) r9rRr.rDrErFr r searchr )badonesdistnamerBregexs r3rr#s---GM@@uh'' dU.1DD F F @  @ @ %66$>???? @@r5cttjtjdddttjtjddddS)Nr`rrrr]r )rr9rDrrjrr rX r;r5r3test_infinite_inputr $sR ((R88!<<< 377;;;;;r5ctjtjddd}t |ddSr)r9lomaxrrqrr s r3test_lomax_accuracyr $s=  22A66AAvr5ctjtjddd}t |ddSr)r9r<rrqrr s r3test_truncexpon_accuracyr $sC U-11&!<,,Q22A66A3++++++r5ctjd5}tjdtjddtjddtjddtjtj dt|}t|dddddS#1swxYwYdS)zregression test for gh-6219T)realwaysr|rrN) rwrxryr9r,rqrirrrjrrr)rnumber_of_warnings_throwns r3 test_genextreme_give_no_warningsr $s   - - -3h''' R### R### R### ---$'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)Nrr rXrrrgr3rVrr=r)rr rr3rrr) rjrr9r,r euler_gammarkrrzetarr) rrrArBrCref_0ref_1ref_3ref_2s r3test_moments_gh22400r &$s# *U%++S"&!T,BF+SS T TC >D %(Q,C  ?W\!__ ,ruax 7D D 3d #EVHQJEE MMEC1Iu51111QQQTE"""C1Iu51111QQQTE"""""r5cd}tjd}t|d|zdzdtjd}t||dzdtjd}t |dtjd d }t||d zt jd zdzdtjd }t|d |zdzdtjd}t|d|zdzddS)Ngox?rrgr rrrrTrr`rrrrmr)r9r,rHrrrjr)r rps r3test_genextreme_entropyr <$sD$K   &&AAq}q(u5555   ##AA{QU3333   %%AA   R 00AA{1}rvbzz1A5EBBBB   $$AAr+~)6666   %%AAr+~)666666r5cRd}tj|d}t|dtj|d}t||d}tj|d}t|dtj|d}t||d}tj|d}t|dtj|d}t||dS) Nrr{g'b%4gQ@rygؗҜ;rg.l6?)r9r,rrr)r_rOrss r3test_genextreme_sf_isfr S$s 2 A Av&&AA-...    a ( (BB A Au%%AA()))    a ' 'BB A Aq!!AA-...    a # #BBr5cld}tj|dd}t|ddS)NrrgrgH&8>)r9ri rr)probrs r3test_burr12_ppf_small_argr $s9 D|a++HH455555r5cd d}tjgd}tj|d|\}}}t |dd|dksJt |d dd S) a? Test fitting invweibull to data. Here is a the same calculation in R: > library(evd) > library(fitdistrplus) > x = c(1, 1.25, 2, 2.5, 2.8, 3, 3.8, 4, 5, 8, 10, 12, 64, 99) > result = fitdist(x, 'frechet', control=list(reltol=1e-13), + fix.arg=list(loc=0), start=list(shape=2, scale=3)) > result Fitting of the distribution ' frechet ' by maximum likelihood Parameters: estimate Std. Error shape 1.048482 0.2261815 scale 3.099456 0.8292887 Fixed parameters: value loc 0 r;rc,t||||ddS)Nr)r0dispxtolftol)r&)rx0r0r s r3rz&test_invweibull_fit..optimizer$sD"4dUKKKKr5)r rrgrrtrrrrrr`rV@c)rrg`?rtrg [@N)r;r)rjrr9r$rr)rr_rrerfs r3test_invweibull_fitr $s.LLLL HHHIIA$((i(HHMAsEAxd++++ !8888E8$//////r5))rrg7Ըh?)rrgz]r>)rg"@goBڱ9)rrg$=cC;cjtj||}t||ddSr)r9r$rr)r_rrXrDs r3test_invweibull_sfr $s7 ""1a((HHhU333333r5zp, c, expected)r|rg9?)geK@g&4I,)?)decimals)r9rrqrrjround) scipy_val check_vals r3test_ncf_cdf_spotcheckr $sG  b!R..IIIrx A>>>?????r5ctjddd}d|d<dtjj|gR}fd|D}t ||dS)Nrr rr)r]rgrrr c>g|]}tjj|gRSr;)r9rr)rAxipars r3rCz,test_ncf_ppf_issue_17026..$s- . . .b%)- !S ! ! ! . . .r5)rjrYr9rrr)r_rq0r s @r3test_ncf_ppf_issue_17026r $sl Aq#A AaD C a#A . . . .A . . .BArr5c2eZdZdZdZdZdZdZdZdS) TestHistogramcJtjdtjgdd}t j||_tjdddd }tj|d }t j||_ dS) Nr)r rgrgrrrrrrrrrrrrr3r3r3r3rrrrrrrbinsrTrr{rAr=) rjrr histogramr9rGtemplaterr norm_template)rsr% rnorm_histograms r3r7zTestHistogram.setup_method$s tL"@"@"@FGIII *955 z~~#Su3~OOd444"/??r5ctjgd}tjgd}t|j||t |jddt |jddt |jddt |jddtjd d d }t|j|tj |d d ddS)Nrr|rTrrrrr;rr9rU@rrrrr%!@rr6)rrrMrM{Gz?r- Q?r. {Gz?r/ rQrQr/ r/ r. r. r. r. rrr%r. r, rrrrrgr`rTrrdr]r) rjrrrr& rirrYr' r9r)rsrX pdf_valuesr_s r3rRzTestHistogram.test_pdf%sXMMMNNZ!I!I!IJJ  ))&11:>>> DM--c22H===DM--c22H=== DM--c22H===DM--d33X>>> KAr " "*..q11 qc==C I I I I I Ir5c6tjgd}tjgd}t|j||t|j|dd|ddtjddd}t|j|j||tjddd}t|j|j||tjd dd }t|j|tj |dd d dS)Nr* )rrrrrMr- r. ףp= ?Q?{Gz?rr|r(\?RQ?= ףp=?)\(?r rTrTrgrrTrrarrr`rrdr]r) rjrrrr& rqrrYr' r9r)rsrX cdf_valuesr_s r3rzTestHistogram.test_cdf_ppf"%sMMMNNZ!M!M!MNN  ))&11:>>> ))*QrT*:;;VAbD\JJJ KS# & & ))$-*;*;A*>*>??CCC KS# & & ))$-*;*;A*>*>??CCC KAr " "*..q11 qc==C I I I I I Ir5c:d}|j|d}ttj|dkdt tj|dkd|zd t tj|d kd |zd t tj|d kd |zd t tj|dkd|zd t tj|dkd|zd t tj|dkd|zd t tj|dkd|zd t tj|dkd|zd t tj|dkd|zd t tj|dkd|zd t tj|dkd|zd t tj|d kd!|zd t tj|d"kd#|zd t tj|d$kd%|zd t tj|d&kd|zd t tj|d&kd|zd ttj|d&kddS)'Nrr$ rrTrrrMrQrrr- rr. r]r;r2 rr3 r9r4 rUrrFr+ r|rrrr5 rr6 rr7 r%r8 r, r r)r& rrrjrmr)rsr2rWs r3rJzTestHistogram.test_rvs8%s """<<RVFSL))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/////r5ctdD]R}t|j|t jdd|dSdS)NrrTrrFr)rrr' rr9rrrs r3r zTestHistogram.test_munpN%sxq G GA D.44Q77!JsC0077:: G G G G G G Gr5ct|jtjddddS)NrTrrdrFr)rr' rHr9rrxs r3rqzTestHistogram.test_entropyS%sT*2244 **s#*>>T K K K K K Kr5N) rrrr7rRrrJr rqr;r5r3r r $s@@@ III4III,000,GGG KKKKKr5r cddggd}}tj||fd}tj|ddgddg|dksJtj||fd}tj|ddgd |d ksJd }tjt| 5tj||f}|d ksJ dddn #1swxYwYtj|gd f}|dksJdS)Nr )rr rF)rr|rSrTg'^P?gH@z(Bin widths are not constant. Assuming...r r<) r9rGrjrrrirHrr}rz)countsr# rBrps r3test_histogram_non_uniformr? X%sFLLLDF  vtne < < .%sa!Q$h#->)>r5rFrV )rsrrrrvs r3test_rvs_small_chizTestArgus.test_rvs_small_chi%sN KOOCcO ? ?|A>>??1Dr5zchi, expected_mean))r gщi?)r`g.憃?)r}g\paP?)r~g ?)r g,6?cltj|d}t||ddS)Nr rrr)r9rQ rr)rsr expected_meanrs r3rzTestArgus.test_mean%s9 K  S  * *=u555555r5zchi, expected_var, rtol))r gLH'B?r)r`go$?r)r}g =>r-)r~g2W>r-)r gb~P>r-cltj|d}t|||dS)Nr rr)r9rQ rAr)rsr expected_varrrs r3rzTestArgus.test_var%s6 KOOCqO ) )r)rgF=r)rg߹Q#B=r)rvg0ޟ)rWrg=~L]=)rWrgD,G '=cjtj||}t||ddSr)r9rQ rr)rsr_rrXrs r3test_sf_near_1zTestArgus.test_sf_near_1&s4[^^As # #H5111111r5))r|)g+&?gk?gμm/?)rQ)g?CL\f?g^N?g]AͭR?)r])ga>$?g;Lf?gaW?)r~)gx?g43n?gwY?)r)go7🤎?g +-oGn?gIQ9‹Y?)r)g T?gGn?g@̋Y?)rv)gU?g{Gn?giG͋Y?)r)gDU?g{Gn?gH͋Y?ctjgd}ttj|||ddS)Nra rr)rjrrr9rQ rqrb s r3test_cdf_small_chizTestArgus.test_cdf_small_chi &rd r5))r|)g Q)?g6{?r)gB`"۹?)g?g8%?r)r])g388?gV%?r)r~)g*j?gRS%?r)r)g! |?gZ%?r)r)gy[|?gG%?r)rv)g"3|?gW%?r)r)g!3|?gW%?rcltj|d}t|||dS)Nrrr)r9rQ r)rsrrXrrIs r3test_stats_small_chizTestArgus.test_stats_small_chi&s9kT22XD111111r5N)rrrrR rrrrJrY rrr_ rc rf ri rk rm r;r5r3rN rN %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 D222r5rN ceZdZdZdZdZdZej dgddZ ej dgdd Z d Z ej d gd d Z ejdej dgdej dgdej dgddZej dgdej dgddZdS) TestNakagamicnd}d}tj||}t|ddS)NrrgM+)r9nakagamirr)rsr- r_rs r3rzTestNakagami.test_logpdf+&s< ~$$Q++122222r5cd}d}tj||}t|ddtj||}t||ddS)NrrUg"S+:rr)r9rq rrr)rsr- r rrrs r3rzTestNakagami.test_sf_isf<&sm  ^  r2 & &1>>>> ^  B ' 'BU++++++r5cvd}d}d}tj||}t||ddS)Nrr|gU iּrr)r9rq rr)rsr_r- rrs r3rzTestNakagami.test_logcdfO&sC  %&&q"--%000000r5cvd}d}d}tj||}t||ddS)NrFrVgD&`Urr)r9rq rr)rsr_r- rrs r3rzTestNakagami.test_logsfW&sC  %$$Q++s//////r5zm, ref))rg|Bd븿)r|r)r`g/ۿcdttj||ddS)Ng^~z=rrr9rq rHrsrrs r3rqzTestNakagami.test_entropy_&s/ ..q113WEEEEEEr5))rg}Ô%I)rgq_)gScAgB4U)gcAgu1U)rgb >%)rgWҙ\c`ttj||dSrvrv rw s r3test_extreme_nuzTestNakagami.test_extreme_nuq&s* ..q11377777r5ctjtjdsJtjtjdsJdS)Nrr)rjrGr9rq _entropyrxs r3test_entropy_overflowz"TestNakagami.test_entropy_overflowx&sT{5>22599:::::{5>226::;;;;;;;r5znu, ref))rg2H?)rg:U?)rg>cdttj||ddSr)rr9rq r)rsr- rs r3rzTestNakagami.test_mean|&s/ ++B//5AAAAAAr5z+Fit of nakagami not reliable, see gh-10908.rjr- )rrrre)rr`r} rf)rrrc d tj |||d tj \}}}t ||dt ||dt ||d fd} fd} fd} t ||||d d t ||||d d t | |||d d dS) Nra9rr- rerfrrQrcd|zdztjd|z z zd|z|dzz tj|z zzS)Nrr rgrjrm)r- rerfr\s r3 dlogl_dnuz(TestNakagami.test_fit..dlogl_dnu&sRUQY"&GcM):";";;d5!8mbfWs]&;&;;< =r5cdtj|ztd|z zdtjtj|z |z zztj|z |z dzz S)Nr rrg)rjrrrmr- rerfr2r\s r3 dlogl_dlocz)TestNakagami.test_fit..dlogl_dloc&svRVBZZ)Ar*:*::;rvw}&=>>???@fw}59::; .dlogl_dscale&sG!GbL5("fuz)BFGcMa3G,H,HHI Jr5rrr)r9rq rrr) rsr- rerfnu_estloc_est scale_estr r r r2r\s @@r3ryzTestNakagami.test_fit&s[ .$$!+0t%EE%*^%7%7%@%@"----3//// 5s3333 = = = = = < < < < < <  J J J J J J  &'9==qtLLLL 67I>>MMMM VWi@@!$OOOOOOr5cd}d}tj||||d}tj||\}}}t j|} t jt j||z dz} t||dt|| dt|| ddS) Nr|rar r rrgr-r) r9rq rrrjrrrr) rsrerfr- rur\r r r loc_theo scale_theos r3 test_fit_nuzTestNakagami.test_fit_nu&s  .$$!+0t%EE%*^%7%7B%7%G%G"6'??WRWg&7A%=>>?? ....5555 :D999999r5N)rrrrrrrrrrrqry r| rrryr r;r5r3ro ro )&s333",,,&111000 [X % % %&& F F && F [X D D DEE88 EE8<<< [Y>>>??BB ??B [KLL [T???33 [UNNN33 [Wkkk22PP324343MLP8 [UNNN33 [Wkkk22::3243:::r5ro c eZdZdZdZdZdS)TestWrapCauchycLtjddgddgg}tjdgdgg}tj||}|jdksJdtj||fD}t||d dS) NQ?rlr|rrTrrtcTg|]%\}}tj||&Sr;)r9 wrapcauchyrq)rArrrE s r3rCz>TestWrapCauchy.test_cdf_shape_broadcasting..&s?<<<%b")--b"55<<???!a")Brvbebdl/C/C,C"D"DRU"JJKKKKKr5N)rrrr r r\r;r5r3r r &sF > > >,,,LLLLLr5r cGddtj}|d}ttd5|ddddS#1swxYwYdS)NceZdZdZdS)/test_rvs_no_size_error..rvs_no_size_gencdSrr;rxs r3_rvsz4test_rvs_no_size_error..rvs_no_size_gen._rvs&s1r5N)rrrr r;r5r3rvs_no_size_genr &s#     r5r rvs_no_sizer z_rvs\(\) got (an|\d) unexpectedr )r9rFr`rr)r r s r3test_rvs_no_size_errorr &s%-"/}555K y(J K K KsAA!$A!zdistname, 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) $skip_test_support_gh13294_regressionrrr.r9rDrFrr rrjr) r r0rBa0b0r(r)a1b1r1r2s r3test_support_gh13294_regressionr &s8777 0$,000 1 1 1 5( # #D$+,, t99>>!T\4(FB RV $ $ $ RV $ $ $  f2t2T26222BR   R     t|T"1QQr5c\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 )r r r rrr) r9rr rjrrrrrB) r r ex_a0ex_b0r r ex_a1ex_b1rrex_a2ex_b2s r3,test_support_broadcasting_gh13294_regressionr &s Z   mmm < >#u % % +v 5 5 5 5 5 5r5)gn! g:I"<)gQ @gE?cttj||ttj| |dSrv)rr9cosinerqr)r_rXs r3test_cosine_cdf_sfr &'sJEL$$Q''222ELOOQB''22222r5))rvgkM6O)rg0ӭ! )r> g;'u(@cttj||ttj|| dSrv)rr9r rr)rvrXs r3test_cosine_ppf_isfr .'sL EL$$Q''222EL$$Q''(33333r5ctjtj tjg}t |ddS)NgrB)r9r rrjrkr )rs r3test_cosine_logpdf_endpointsr 7's: <   / /Dd./////r5cdtD}dtD}||ksJdtD}dtD}||ksJdS)NcBh|]\}}t|t|Sr;)rDrLrArrs r3 z*test_distr_params_lists..B's:44474'c224$444r5ch|]\}}|Sr;r;r s r3r z*test_distr_params_lists..D'sAAAgdATAAAr5ch|]\}}|Sr;r;r s r3r z*test_distr_params_lists..G's333wtQd333r5ch|]\}}|Sr;r;r s r3r z*test_distr_params_lists..H's999'$999r5)r!r"rr)discrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamess r3test_distr_params_listsr >'s44l444AAAAA !6 6 6 6 633(333N99[999 . . . . . . .r5ctjddtjdddksJtjdddksJdS)Nrr\rwr)rr1r)r9r_statsrrr;r5r3test_moment_order_4r L'sr NAs+++ > qA . .# 5 5 5 5 >  1 % % , , , , , ,r5c 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,gammarr r|s r3ROOT_pdf_sample_dataz'TestRelativisticBW.ROOT_pdf_sample_dataa'sMw NN ! ; <  v  /@ AA r5zrho,gamma,rtol))qVEB@gj+@rR)‰FC@Gz@r)ND@_LU?r*c||d|k|d|kz}|d|d}}t|tj||||dS)Nrhorr_rirr)rr9rel_breitwignerri)rsr r rrrr_ris r3test_pdf_against_ROOTz(TestRelativisticBW.test_pdf_against_ROOTt's$ !% (C /#G,5 7 cDK3 &**1c*??d      r5zrho, 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)rjrrk)ErGammarr\s r3rizFTestRelativisticBW.test_pdf_against_simple_implementation..pdf'sGAqDAqD5!8O455ERWQZZ!#e+e3EBGAqD5L1113AA1q(1a4q=89 9r5rFr@r`rr)rjrYr9r rrir) rsr r rrirvr_rrs r3&test_pdf_against_simple_implementationz9TestRelativisticBW.test_pdf_against_simple_implementation's : : : KdB ' '  ! % %aE % : :#''3e'<<c!SY&&St,,,,,,r5z 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#r)rfrrrrrgrQrr rBr~N)rjrrr9r rrr)rsr rrrrrs r3 test_fit_flocz TestRelativisticBW.test_fit_floc's&#i##D))$(( u4c)  #''1'55QQ(3,TBBBB1v{{{{#''1U'CCA$////AAAu:------r5N)rrrrrr rrr r rrrr r;r5r3r r `'se ^^$ [       [/2 2 2  - -  - [ [ FL"F&+2B    FL!5 0A    FL & 0A       ..  ...r5r cZeZdZejdddgdZdS) TestJohnsonSUr)r rrrg={?g?5mV>gn?g\}\1@)g`fo@g$ں _@rr gvUg Nv>>T!""XE222222r5N)rrrrrrr r;r5r3r r 'sZ [V O J&KLL 33 LL 333r5r c2eZdZdZejdddgejdddgejdddgejdddgdZd S) TestTruncParetocHd\}}tjdd}tj|||}tj||tj||z }t||dS)N)?333333@r r )rjrYr9 truncparetorirrqr)rsr2rr_rrs r3rRzTestTruncPareto.test_pdf's1 KS ! !1%%))!,,l1oo!!!$$u|A':':1'='==S!!!!!r5rTFr>rrctjd}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 r rrdrrrrrr r r ) rjrrr9r rrrrrr)rsrr>rrrr2rrerfrBrrrps r3ryzTestTruncPareto.test_fit'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)rrrrRrrrryr;r5r3r r 's""" [Yu 66 [[4-88 [WtUm44 [WtUm44KK54549876KKKr5r ceZdZdZdS) TestKappa3cdtjddz }tjdd}t ||dS)Nr r|gj@)r9kappa3rqrr)rssf0rys r3rzTestKappa3.test_sf'sK%,""3,,,looc3''S!!!!!r5N)rrrrr;r5r3r r 's#"""""r5r ceZdZejddZejdZejdZdZ dZ dZ dZ dZ d Zd Zd Zd Zd S) TestIrwinHallrr r`cVt|jdddS)Nr)rg?rgQ)r ih10r9rxs r3test_stats_ih10zTestIrwinHall.test_stats_ih10's) TY__V446JKKKKKr5cgd}fdtt|D}t||jd}d}t||dS)N) rgUUUUU9@g0a@igx@gn۶mˠ@g:PAg8)AgSAcJg|]}j|dz Src )r r)rArurss r3rCz3TestIrwinHall.test_moments_ih10.. (s-CCCQ49##AaC((CCCr5r=g2⍚H)rrr r r)rsrHrm50 m50_exacts` r3test_moments_ih10zTestIrwinHall.test_moments_ih10(s~---DCCC%D 2B2BCCCWd+++ir""H S),,,,,r5ctjddd}|j|}|j|}t ||ddSNrr rar`maxulp)rjrYunifriih1r )rsptspdf_unifpdf_ih1s r3test_pdf_ih1_unifzTestIrwinHall.test_pdf_ih1_unif(sXk!Q$$9==%%(,,s##Whr::::::r5ctjd}d}tjdd|}tjdd|}d||dzdzdz ||dzdzd<||}t ||ddS)Nrgr^rr r`r )r9rrjrYrir )rsih2nptsr rXpdf_ih2s r3test_pdf_ih2_trianglez#TestIrwinHall.test_pdf_ih2_triangle(soa  k!Q%%;q!T**%&4!8/2B2B)C%C$(q!!"''#,,Whr::::::r5ctjddd}|j|}|j|}t ||ddSr )rjrYr rqr r )rsr cdf_unifcdf_ih1s r3test_cdf_ih1_unifzTestIrwinHall.test_cdf_ih1_unif)(sVk!Q$$9==%%(,,s##Whr::::::r5ctjdd}tj|}||dz }tjdt |}t||ddS)Nr r`rgr|r )rjrr9rrqrrr )rsruihih_cdfexacts r3r\zTestIrwinHall.test_cdf1(sg Ia   _Q  A #s1vv&&VU2666666r5c2gd}t|jtjd|dt|jdddd}t|jd|ddS) N) rg\xO~>g-P2?g8ʝi?gg{Ȇ?r|g&M?g׈Y?gB?gD l?r rr`r r]g+|s r3test_cdf_ih10_exactz!TestIrwinHall.test_cdf_ih10_exact:(s((( TY]]29R==994KKKKTY]]4002EbQQQQ1TY]]5113rBBBBBBr5cgd}|dg|dddzz }t|jtjd|ddS)N)rg4V>gP3NV?g*8f?gNgX?gjS?rrr`r )r r rirjrrs r3test_pdf_ih10_exactz!TestIrwinHall.test_pdf_ih10_exactJ(s\JII $ttt*,,TY]]29R==994KKKKKKr5c ,t|jtjdd|jtjdz d}t |jd|ddS)Nrr rTr]r`r )rr rrjrrqr )rsrs r3test_sf_ih10_exactz TestIrwinHall.test_sf_ih10_exactQ(st RYr]]33QryQS}}9U9U5UVVV2TY\\$//R@@@@@@r5N)rrrr9rr rr r r r r r r r\r r r r;r5r3r r 's 5=A  D %/!  C 5?2  DLLL - - - ; ; ;;;;;;;777CCC LLLAAAAAr5r ceZdZdZdS)TestDParetoLognormcd\}}}}}tj||||}tj||dtj||ddS)N)rrrorrgg6Z?g@# ?)r9dpareto_lognormrjrrrirq)rsr_rrOr1r2rBs r3test_against_Rz!TestDParetoLognorm.test_against_R[(su, 1aA$Q1a00 ""488A;;0CDDD ""488A;;0CDDDDDr5N)rrrr r;r5r3r r Z(s(EEEEEr5r r))r NNNN)rNNNN)r(NNNN)r NNNN)rNNNNc|\}}}}}tjd}|pd}|pd}|pd}|pd}tt|}t t |}||} tj||} | | | } t| | ||dtj||dz } | | | } t| | ||dS) Nr|iirrrnr r) rjrF r.r9rrrrrr) rr lp1lp2rrlpmrBr dist_frozenrrs r3test_sf_isf_overridesr% o(s &*"Hc3d (3--C +C *C 91D =5D 5( # #D (^^H %F$-K +c3  C ..-- . .CC4d3333 bk#sB'' 'C ..-- . .CC4d333333r5rv)NF(r rwr rr pathlibrr r r_ numpy.testingrrrrrr r r r r rrrr`numpyrjrrnumpy.lib.recfunctionsrr8rscipy._lib._utilrr1rrrr scipy.statsr9!scipy.stats._distn_infrastructurerscipy.stats._constantsrscipy.stats.distributions scipy.specialrrrscipy.stats._distr_paramsrrtest_discrete_basicr!r"scipy.stats._continuous_distnsr#r$scipy.optimizer%r&r' itertoolsr(flagsoptimizer rbrr r4r<rYr[rrrrr1r3r^rrrrrrr5rArhrrrrrrrr+r2rLrQrdrnrrrr-rQr\r_rrrrr r#r9rGroryrrrrrrrrr r,rTrrrrkrrrrrrr-r:r>rBrMr[rrrrrrrrrrrrrr$ r r r r r r r r r r r& r0 rN rS rZ ra ry r r r r rr r r r r r r r r r r r r r r r r r r r! r$ r& r( r+ r/ r3 r; r= r@ rB rD rM rFrO rV r[ ra re r rr r r r r r r r r r r r r r r r r r? rA rN ro r r r r r r r r r r r r r r r r r% r;r5r3r7 s!  ::::::::::::::::::::::::::  ******""""""""444444//////333333333333888888(((((( 0000000000;;;;;;;;>>>>>>>>CCCCCCCC==========i(1,|x'M.>h.>.@.@H.L )6z'B$$$$$ 888   G@G@G@G@G@G@G@G@T4444D....>>>?? 6 6 ?? 699999999>G,G,G,G,G,G,G,G,T********>O,O,O,O,O,O,O,O,d<B<B<B<B<B<B<B<B~D/D/D/D/D/D/D/D/N########>>>>>>>*7D7D7D7D7D7D7D7Dt C C C C C C C CA2A2A2A2A2A2A2A2H44444444DI6I6I6I6I6I6I6I6X********. G G G G G G G GFK"K"K"K"K"K"K"K"\=I=I=I=I=I=I=I=I@`&`&`&`&`&`&`&`&FhDhDhDhDhDhDhDhDVDDDDDDDD,DDDDDDDD,U<U<U<U<U<U<U<Uw>w>w>w>w>w>w>t 3 3 3P6P6P6P6P6P6P6P6fB=B=B=B=B=B=B=B=J&&&&&&&&>$$$$$$$$*W +W +W +W +W +W +W +W +t))))))))         , , , mGmGmGmGmGmGmGmG`e,e,e,e,e,e,e,e,Pw;w;w;w;w;w;w;w;t]H]H]H]H]H]H]H]H@",",",",",",",",JB&B&B&B&B&B&B&B&J666666668;";";";";";";";"|u0u0u0u0u0u0u0u0p.........SFSFSFSFSFSFSFSFl........2J/J/J/J/J/J/J/J/Z ? ? ? ? ? ? ? ?Fh"h"h"h"h"h"h"h"V66666666(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###07772 - - -&&& 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+lA2A2A2A2A2A2A2A2HP:P:P:P:P:P:P:P:fLLLLLLLL8   )?[+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#KL""""""""]A]A]A]A]A]A]A]A@EEEEEEEE*"G"G"GHH 44 HH 444r5