S_fdZddlZddlZddlZddlZddlmZddlZddlZddl Z ddl m Z m Z m Z mZmZmZmZmZmZddlZddlmZddlZddlZddlmZmZddlmZddlmZdd lm Z dd l!m"Z"m#Z#m$Z$m%Z%ddl&m'Z'dd l(m)Z)ddl*Zdd l+m,Z,m-Z-m.Z.dd l/m0Z0m1Z1ddl2m3Z3m4Z4ddl5m6Z6m7Z7ddl8m9Z9m:Z:m;Z;ddlZ[Gd?d@Z\GdAdBZ]GdCdDZ^GdEdFZ_GdGdHZ`GdIdJZaGdKdLZbGdMdNZcGdOdPZdGdQdRZeGdSdTZfGdUdVZgGdWdXZhGdYdZZiGd[d\ZjGd]d^ZkGd_d`ZlGdadbZmGdcddZnGdedfZoGdgdhZpGdidjZqGdkdlZrGdmdnZsGdodpZtGdqdrZuGdsdtZvGdudvZwGdwdxZxGdydzZyGd{d|ZzGd}d~Z{GddZ|GddZ}GddZ~GddZddejddejzz zddejddejzz zddejddejzz zddejddejzz zddejddejzz zg fdejddejzz ddejddejzz zddejddejzz zdz ddejddejzz zdz ddejddejzz zdz g fddejdejzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dddejdejzzz dgfgZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGdd«ZdÄZGdĄdūZGdƄdǫZGdȄdɫZGdʄd˫ZGd̄dͫZGd΄dϫZGdЄdѫZd҄ZGdӄdԫZGdՄd֫ZGdׄdثZGdلdګZGdۄdܫZGd݄dޫZGd߄dZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZGddZdZdZdZejjce@ddZdZdZdZdZdZdZd Zd Zd Zd Zejjd gddZdZdZdZdZdZdZejjdgddZĐdZŐdZƐdZǐdZȐdZɐdZejjdd ej4d!d"gfd#ej4d$d%gfd&ej4d'd(gfd)ej4d*d+gfgd,Zːd-Z̐d.Z͐d/Zΐd0Zejjd1gd2d3Zejjd4gd5d6Zejjd7gd8d9ZҐd:Zejjd1gd;d<ZԐd=ZGd>d?e'jZGd@dAe'jZGdBdCe'jZGdDdEe'jZGdFdGZGdHdIZejjce@dJdKZݐdLZސdMZߐdNZdOZdPZdQZdRZdSZdTZdUZdVZdWZejjd1gdXdYZejjdZd[d\gd]Zejjd^ddgd_fd`dagd_fdbdcgddfgdeZdfZdgZejjcejdhkdidjZGdkdlZdmZGdndoZGdpdqZGdrdsZGdtduZdvZejjdwe4e1zdxZdyZdzZejjd4d{d|gd}Zejjd7gd~dZdZdZdZGddZGddZGddZGddZejjdgddZy(z! Test functions for stats module N)Path) assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_ assert_warnsassert_array_lesssuppress_warnings)raises) typecodesarray)rec_append_fields)special)check_random_state)IntegrationWarningquad trapezoidcumulative_trapezoid) argsreduce)xlogy polygammaentr)distcont invdistcont) distdiscreteinvdistdiscrete) FitDataError _argus_phi)rootfmindifferential_evolution)productdarwinx86_64 tukeylambdapearson3cD||d|}tt|||y)Nz does not have attribute msg)r hasattr)abr,s Dlib/python3.12/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattrr14s( {,QC0 GAqMs#cLttjjdy)Nf_gen)r1scipystats distributionsr2r0test_api_regressionr9:sEKK--w7r2cttjjj}t Dcgc]}|d }}t Dcgc]}|d }}gd}||z|z}ttd|}||k(sJycc}wcc}w)Nr) rv_discrete rv_continuous rv_histogramentropytrapzc8t|jd S)N<)str startswithss r0z.test_distributions_submodule..IsA(9(9#(>$>r2)setr5r6r7__all__rrfilter)actualdist continuousdiscreteotherexpecteds r0test_distributions_submodulerP?s **22 3F&./d$q'/J/$01DQ1H1 !EH$u,H6>IJH X  01s B B c @eZdZejj dgdejj dddejddgdZd Z d Z ejj d gd d Z ejj dgddZ dZ ejj dgddZdZejj ejj dddgejj dgdejj dddgejj dddgdZdZejj d d!dgd"Zd#Zd$Zd%Zy&)' TestVonMisesk)皙?rexrr dcd}d}||dd|||dd|||dd|||dd|||dd|||dd|y)Nctj|||}t|j||j|dtj z|zzy)Nlocscale)r6vonmisesrpdfnppirSLrErVvms r0check_vonmises_pdf_periodiczHTestVonMises.test_vonmises_periodic..check_vonmises_pdf_periodicRs@q2B q 266!q255y1}2E+F Gr2ctj|||}t|j|dz|j|dtj z|zzdzy)Nr[rr^)r6r_rcdfrarbrcs r0check_vonmises_cdf_periodiczHTestVonMises.test_vonmises_periodic..check_vonmises_cdf_periodicVsMq2B q A "qAIM': ;a ? Ar2rrrWr8)selfrSrVrfris r0test_vonmises_periodicz#TestVonMises.test_vonmises_periodicOsd H A $Aq!Q/#Aq!Q/#Aq"a0#Aq!Q/#Aq!Q/#Aq"a0r2cttjjtj ttjj tj yN)rr6 vonmises_liner.rarbr/rjs r0test_vonmises_line_supportz'TestVonMises.test_vonmises_line_supportcs8U((**RUUF3U((**BEE2r2cdtjd}t|jddy)N r?)r6r_rrh)rjres r0test_vonmises_numericalz$TestVonMises.test_vonmises_numericalgs" ^^C BFF1Is+r2zx, kappa, expected_pdf))rT{Gz?g|65?)rT9@g?U?)rTrrg"?)@rugDfI?)rwrvg1<)rwrrc`tjj||}t||dyNV瞯<rtol)r6r_r`r)rjrVkappa expected_pdfr`s r0test_vonmises_pdfzTestVonMises.test_vonmises_pdfus&nn  E*\6r2zkappa, expected_entropy))rgA ?)g,eޞ?)rXgBb9d22)g G)g c^tjj|}t||dyNvIh%<=r|)r6r_r>r)rjr~expected_entropyr>s r0test_vonmises_entropyz"TestVonMises.test_vonmises_entropys%..((/!1>r2cLd}tjj|}tjj|}tjj|}tjdddj |}tjddtj zdj |}tjdddtj zt|z dzj |}t||dt||dy) Ni@}rrr[ random_stater^r{atol) rarandom default_rngr6r_rvsrbabsr)rjseedrng1rng2rng3rvs1rvs2rvs3s r0test_vonmises_rvs_gh4598z%TestVonMises.test_vonmises_rvs_gh4598syy$$T*yy$$T*yy$$T*~~aQa044$4G~~aQruuWA6:::M~~aQ%&ruuWSY%6q%8;;>3D3;Q d/d/r2zx, kappa, expected_logpdf))rTrug EJ?)rTrvgoι?)rTrrg0,)rwrugdty)rwrvgʹw[A)rwrrgc`tjj||}t||dyrz)r6r_logpdfr)rjrVr~expected_logpdfrs r0test_vonmises_logpdfz!TestVonMises.test_vonmises_logpdfs&&&q%0e.r2rr^cyrr8rs r0rFz3TestVonMises.test_vonmises_expect..rr2c2tjd|zS)Ny?)raexprs r0rFz3TestVonMises.test_vonmises_expect..sBFF2a4Lr2 complex_funcN) rarrr6r_expectr issubdtypedtypefloatingrbanglecomplexfloating)rjrngr\r~lbresboundss r0test_vonmises_expectz!TestVonMises.test_vonmises_expectsUii##$78A+UBnnE299+FQ}}SYY 444R!bee)^#9ennE299+OOQ}}SYY 444R!bee)^#9ennE299:PS;ASPQS sag7}}SYY(:(:;;;r2rvs_locr^ rvs_shape)rrXחAfix_locTF fix_shapecF|r|rtjdtjj d}t j j|d||}ddi}|r||d<|r||d<tt j |t j jfi|y) NzNothing to fit.rr)sizer\rfscalerflocf0) pytestskiprarrr6r_r_assert_less_or_close_loglikennlf)rjrrrrrdatakwdss r0test_fit_MLE_comp_optimizerz(TestVonMises.test_fit_MLE_comp_optimizers  KK) *ii##$78~~!!)$G/2"4!} "DL "DJ%ennd&+nn&9&9 C=A Cr2cbgd}tj|}dtjz}tjj ||\}}}|tj tjk(sJttj|tjjd|y)N)g!*Kg4,%OԿgZ۵?g ge_@g-8gPghn?grr^g d?)r5r6r_rrarbros r0test_vonmises_fit_boundsz%TestVonMises.test_vonmises_fit_bounds sT    !WA 6    "%%'9"5!6Q ?r2N)__name__ __module__ __qualname__rmark parametrizerarbrkrprtrrrrrxslowrrrrrrr8r2r0rRrRNs [[S-0 [[S1aC"891:11$3, [[5/0707 [[6;< ? < ? 0  [[8BC=C=<4 [[ [[YA/ [[[-8 [[Yu 6 [[[4-8C9790 C$ O [[Vb!W- (. ( M9 @r2rRc X| |j}|j|fi|}tt|||fi|}|st j ||k7sJ|||}|||}||kst j ||dsJd|vr |d|dk(sJd|vr|d|dk(sJyy)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. Nr{r|rrr)rrsupertyperaanyallclose) rKrfuncmaybe_identicalrmle_analytical numerical_optll_mle_analyticalll_numerical_opts r0rrs |yyTXXd+d+N$t*d/==M vvn 5666^T2M40 !1 1 KK)+;% HJ I ~b!T&\1114b!T(^333r2c ddg}|jr.t|jjd}|gdd|z }tt |t j t|}gd}tjtd5|j|fi|dddtjtd5|jt jgdddtjtd5|jt jgdddtjtd 5|j|d dddtjtd 5|j|gd gt|d z zdddy#1swYxYw#1swYxYw#1swYxYw#1swYvxYw#1swYyxYw)Nrr,)rf1f2rr^r3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:r^) extra_keywordzToo many positional arguments.r)shapeslensplitdictzipraarangerr RuntimeErrorr ValueErrornaninf TypeError)rKparamnshapes all_fixedrs r0assert_fit_warningsr9s X E {{dkk'',- #HW--S #e* 567I D |& '$ ##$ zB D "&& zB D "&& y(D E( Q'( y(H I.-SZ!^,-..$$((..s<F2!F? !G G$G#2F<?G GG #G,rK)alpha betaprime fatiguelifeinvgammainvgauss invweibull johnsonsblevylevy_llognormgibrat powerlognormrayleighwaldctt}||}tt|}t |j |j g|dt|j|j g|tj t |j |jg|dt|j|jg|tj y)zgh-6235rN) r rgetattrr6rr`r.rrrarr/)rKdctargss r0 test_supportr'Ps x.C t9D 5$ D/$/3TVV+d+bffW5/$/3TVV+d+bffW5r2c$eZdZdZdZdZdZy) TestRandIntcBtjjdyNrrarrros r0 setup_methodzTestRandInt.setup_methodc tr2c0tjjddd}tt j |dkt j |dk\ztt |dk(tjjddd}tt j|dk(t|jjtdvtjjdd}t|dk\|dkztt|tjtt| tjddjd }t|jjtdvy) NrrXrr^2 AllInteger.r+r)r6randintrr numpyrrshapercharr isinstance ScalarTypereprrrjvalsvals r0test_rvszTestRandInt.test_rvsfs}}  BS 1 $)$uyy';;<D S !}}  BW 5 D!W,- 9\#::;mmB'sRx() 3 0 01tDIGmmB#''* )L"99:r2ctjdd}tj|dk\|dkzdd}tjj |dd}t ||y)Nr$rr0{Gz?)r8r_wherer6r7pmfr)rjrSoutr?s r0test_pdfzTestRandInt.test_pdfssR HHQrNkk16a"f-z1=}}  Ar*!$,r2ctjddd}tj|}tj|dk\|dk\gd|dz dzd z gd}t j j|dd}t||d y) NrrCrXr0r?@rrv decimal) ralinspacer8floorselectr6r7rhr)rjrVrSrHr?s r0test_cdfzTestRandInt.test_cdfysv KK2s # KKNllAGQ!V,sQsU1Wv4F.GK}}  Ar*!$R8r2N)rrrr-rArIrSr8r2r0r)r)bs ;- 9r2r)cBeZdZdZdZdZdZdZdZdZ dZ d Z y ) TestBinomcBtjjdyr+r,ros r0r-zTestBinom.setup_methodr.r2ctjjddd}tt j |dk\t j |dkztt j |dk(t|jjtdvtjjdd}tt|ttjddjd}tt|tjt|jjtdvyNrWrr2r1rr4r) r6binomrr r8rr9rr:rr;intndarrayr>s r0rAzTestBinom.test_rvss{{r4g6 $!)$uyy'<<= D!W,- 9\#::;kkoob$' 3$%kk"d#''* 3 ./ )L"99:r2ctjjddd}tjjddd}t|dddt|dddy)NrXrrrKr{r}rr6rYrGr)rjvals1vals2s r0test_pmfzTestBinom.test_pmfsJ S!, 3*sQ7sQ7r2ctjdd}tjgd}t t || }|j }t||tjdd}|j }t|dtjdd}|j }t|dy)Nr^rs)?rsrcrxrK) r6rYrarsumrr>rr)rjr/ expected_p expected_hhs r0 test_entropyzTestBinom.test_entropys KK3 XX/0 % J788 IIK:& KK3  IIKQ KK3  IIKQr2cFtj5tjdtt t j ddjdt t j ddjddddy#1swYyxYw)Nerrorr^rnp) warningscatch_warnings simplefilterRuntimeWarningrr6rYrstdros r0 test_warns_p0zTestBinom.test_warns_p0so  $ $ & 9  ! !'> : qA.335q 9 qA.224a 8 9 9 9s A9BB cVd}tjjd|d|k(sJy)Nr333333?rK)qrlrm)r6rYrrjrls r0 test_ppf_p1zTestBinom.test_ppf_p1s( {{S1Q666r2cd}d}tjd}tjj |||}tj j |||z}t ||dy)NglyCgq]\ T3s r0rAzTestBernoulli.test_rvss""4g"6 $!)$uyy';;< D!W,- 9\#::;oo!!$' 3$%ood#''* 3 ./ )L"99:r2ctjd}dtjdzdtjdzz }|j }t ||tjd}|j }t |dtjd}|j }t |dy)NrcпrrxrK)r6rralogr>rr)rjr/rfrgs r0rhzTestBernoulli.test_entropys OOD !266$<'$rvvd|*;; IIK:& OOC  IIKQ OOC  IIKQr2N)rrrr-rArhr8r2r0rrs ; r2rceZdZdZy) TestBradfordcd}tjdd}tjj ||}tjj ||}t ||y)NrT)ralogspacer6bradfordrhrr)rjcrVrvxxs r0 test_cdf_ppfzTestBradford.test_cdf_ppfsM  KKR  NN  q! $ ^^  1 %2r2N)rrrrr8r2r0rrsr2rceZdZdZdZdZdZejjddefdgdZ ejjdgd d Z y ) TestChignT9;g2 >h?@cttjjdd}t||jdy)NrWrr{r|)r6chirr CHI_SF_10_4rjrEs r0test_sfzTestChi.test_sfs( IILLQ 4++%8r2cttjj|jd}t |ddy)NrrWr{r|)r6risfrrrjrVs r0test_isfzTestChi.test_isf s( IIMM$**A .2E*r2df, ref@@)gļBgcAcZttjj||dyN-q=r|)rr6rrrjdfr|s r0 test_meanzTestChi.test_means  r*Cers r0rhzTestChi.test_entropy%s!  " --/5Ar2N) rrrr CHI_MEAN_1000rrrrrrrhr8r2r0rrs{'K$M9+ [[Y"M279= = [[Y;< B < Br2rc$eZdZdZdZdZdZy) TestNBinomcBtjjdyr+r,ros r0r-zTestNBinom.setup_method0r.r2cntjjddd}tt j |dk\tt j |dk(t|jjtdvtjjdd}tt|ttjddjd}tt|tjt|jjtdvyrX) r6nbinomrr r8rr9rr:rr;rZr[r>s r0rAzTestNBinom.test_rvs3s||Dw7 $!)$% D!W,- 9\#::;llr4( 3$%ll2t$((+ 3 ./ )L"99:r2c ,ttjtjj dddtjj dddtjjj ddd}t|dy)Niigp= ף?rr) rrarr6rlogpmfrGr5r)rjr@s r0razTestNBinom.test_pmf>shu||223TBC ((c48 :kk  ''1a0S!r2ctjjgddd}tjtjj gddd}t ||y)N)rrrr333333@?rk)r6rlogcdfrarrhr)rjr?r|s r0test_logcdf_gh16159zTestNBinom.test_logcdf_gh16159FsK||""<3$"?ffU\\%%lcT%BCc"r2N)rrrr-rArarr8r2r0rr/s ;#r2rc eZdZdZej j dZej j dZej j dZ ej j dZ dZ dZ dZ d Zy ) TestGenInvGausscBtjjdyr+r,ros r0r-zTestGenInvGauss.setup_methodNr.r2ctjdd}tj|jdd|j\}}t |dkDdy)Nffffff@?rr皙?Tr6 geninvgausskstestrrhrrjgigrrms r0test_rvs_with_mode_shiftz(TestGenInvGauss.test_rvs_with_mode_shiftQIS)||CGGDGA377K1QXt$r2ctjdd}tj|jdd|j\}}t |dkDdy)NrrrrrrTrrs r0test_rvs_without_mode_shiftz+TestGenInvGauss.test_rvs_without_mode_shiftXsIT*||CGGDGA377K1QXt$r2ctjdd}tj|jdd|j\}}t |dkDdy)NrT皙?rrrrTrrs r0test_rvs_new_methodz#TestGenInvGauss.test_rvs_new_method_rr2c|d}t|dddt|dddt|dddy)Nctj||}|jdd}tj||jddkDS)Nrrrrr)r6rrrrh)rmr/rrs r0 my_ks_checkz4TestGenInvGauss.test_rvs_p_zero..my_ks_checkhsE##Aq)C''t$'7C<<SWW-a047 7r2rrTrr)r)rjrs r0test_rvs_p_zerozTestGenInvGauss.test_rvs_p_zerofs< 8 [C($/[C($/[C($/r2cttjddjdddtjddjddz y)Nr^rWrrrr)rr6rrros r0test_rvs_negative_pz#TestGenInvGauss.test_rvs_negative_pqsP!!$*..BT.JE%%c1-11r1MM Or2ctjjdddd}ttj|ddgddkDd d t j d dd }}tjj|dd|z | }t|tj|j|tjj|dd|z | }t|tj|j|y)Nrrrr)rrmr/rrr&333333?TrXrurW)rmr/r]) r6rrrrrarPr`rrrh)rjigmurVpdf_igcdf_igs r0 test_invgausszTestGenInvGauss.test_invgaussws    " " " MU\\"js;A>EtLR[[q"-A""&&qDAF"&Er 2 6 6q 9:""&&qDAF"&Er 2 6 6q 9:r2ctjgd}tjddd}t|tj j |ddy)N) g;g8y8?g\}Z?ghܲ0|?gRq?rurrWrsr)rarrPrr6rr`)rjvals_RrVs r0 test_pdf_RzTestGenInvGauss.test_pdf_RsJ,- KKa $ 1 1 5 5aa @Ar2cttjjddddttjjddddy)Nrrsg>Ar3r^)rr6rr`ros r0 test_pdf_zerozTestGenInvGauss.test_pdf_zerosBU&&**1c37; U&&**3A6:r2N)rrrr-rrslowrrrrrrrrr8r2r0rrMs [[%%  [[%%  [[%%  [[00O ; B;r2rceZdZdZdZdZejjdgddZ ejjdgddZ d Z d Z d Z d Zd ZdZy)TestGenHyperboliccBtjjdyr+r,ros r0r-zTestGenHyperbolic.setup_methodr.r2ctjgd}d\}}}d\}}|||z||zf}tj|||d}tjddd} t |j | |dd y) N) gF^T=g{X'=gNunƢsy>g7!t?gɫzI?g̸?g?gq 6.?gmPZz?g:PgN?r^r^rrsrr[rWrrrr})rarr6 genhyperbolicrPrr` rjrlmbdarbetardeltar&ghrVs r0 test_pdf_rzTestGenHyperbolic.test_pdf_rs~ %ud EuU{DJ/  $Be < KKR $q 6>r2ctjgd}d\}}}d\}}|||z||zf}tj|||d}tjddd} t |j | |dd y) N) g=R0W<=gEB=g#Nb>g_PG>g! 1Or?gUM?g u./?gfy?gl5\?gkV?rrr[rrWrư>r)rarr6rrPrrhrs r0 test_cdf_rzTestGenHyperbolic.test_cdf_rs~ %ud EuU{DJ/  $Be < KKR $q 6=r2zx, p, a, b, loc, scale, ref) )r^rrrsrg8ɹvF(;)rrWrrcrrg[ Ϡ?)rrWrg?rrg✝`D;)r?r):?rrg dL;)rrrrrrgzK^7?)rrrrrgj?)rrrrrga=vG:)rrrrrg?)(rrrrrg1bV?)<rrrrrg?cjtjj||||||}t||dyNr[dy=r|)r6rrhr) rjrVrmr.r/r\r]r|rhs r0test_cdf_mpmathz!TestGenHyperbolic.test_cdf_mpmaths3!!%%aAqc%GSu-r2))rrrMrrrgC!,?)rr@@rrg,Ћf?)rrr r rrrK)r^rrrsrgm"چ >),rWrrcrrg:;)rrrrrrgw=)Krrrrrg3Z0&K4 [[% < . . [[% @ - -=. %$"*r2rceZdZejj dddgdZejj dddgdZy ) TestHypSecantz x, reference)r0gA0=)r3g!b;c^tjj|}t||dyN+g @X>g}e?g{)߳?gwH?irr5rrsr.r/& .>r)rarr6r*rhr)rjr_cdfx_testvals_cdfs r0 test_cdf_RzTestNormInvGauss.test_cdf_RzsO <=,-%%))&A)=%d3r2ctjgd}tjgd}tjj |dd}t ||dy)N)gp϶>g\H55$?geСt&?go NiH?g]u>r9rrsr<r=r)rarr6r*r`r)rjr_pdfr?vals_pdfs r0rzTestNormInvGauss.test_pdf_RsM<=,-%%))&A)=%d3r2zx, a, b, sf, rtol))rrr!7?r)r rr?=r)rrrgy5`?r)rWrrgMLC9r=ctjj|||}t|||tjj |||}t|||yNr|r6r*rrr)rjrVr.r/rr}rErs r0test_sf_isf_mpmathz#TestNormInvGauss.test_sf_isf_mpmathsP    ! !!Q *2D)    " "2q! ,14(r2cddg}ddg}d}ddg}tjj|||}t||dd tjj |||}t||d y) Nrr rrrErFrrzr]rr|rI)rjrVr.r/rrErs r0test_sf_isf_mpmath_vectorizedz.TestNormInvGauss.test_sf_isf_mpmath_vectorizedsr H F  "8 9    ! !!Q *2E6    " "2q! ,14(r2ctjdd}tjddd}|j |}|j |}t ||y)Nrrrr^)r6r*rar rrr)rjdstrVrrs r0 test_gh8718zTestNormInvGauss.test_gh8718sJ  A& IIaQ  VVAYggbkQr2c(d\}}tj|dz|dzz }||z |dz|dzz d|z|tj|zz ddd|dzz|dzz zz|z f}t|tjj||dy) Nrrsr^r@rrmvskmoments)rarrr6r*)rjr.r/gammav_statss r0 test_statszTestNormInvGauss.test_statss11q!t $u9adUAXosQw!bggen:L/M!a!Q$hAo-.68We0066q!V6LMr2cd\}}tjgd}tjj |||}t |tjj |||y)NrQMbP?rsr)rarr6r*rrrh)rjr.r/r?r?s r0test_ppfzTestNormInvGauss.test_ppfsS1-.!!%%fa3 2 2 6 6tQ BCr2N)rrrr-rArrrrrJrLrOrXr\r8r2r0r6r6vsU 44 [[0JK ) K ) ) NDr2r6cHeZdZdZdZdZdZdZdZdZ dZ d Z d Z y ) TestGeomcBtjjdyr+r,ros r0r-zTestGeom.setup_methodr.r2chtjjdd}tt j |dk\tt j |dk(t|jjtdvtjjd}tt|ttjdjd}tt|tjt|jjtdvy)Nrr2r1rr4r) r6geomrr r8rr9rr:rr;rZr[r>s r0rAzTestGeom.test_rvsszz~~d~1 $!)$% D!W,- 9\#::;jjnnT" 3$%jj""1% 3 ./ )L"99:r2cttjjd}tjj tj dd|}|jtjk(sJtj|tjtjjkDsJy)NlA:irr) rarrr6rarrrint64riinfoint32max)rjrrs r0 test_rvs_9313zTestGeom.test_rvs_9313sxii##O4jjnnRVVC[qsnCyyBHH$$$vvcBHHRXX.222333r2cdtjjgdd}t|gdy)Nrrs)rsrcr)r6rarGrrjr?s r0razTestGeom.test_pmfs!zz~~i-!$(:;r2c(tjtjj gdd}tjj gdd}t ||ddtjj dd}t|dy)Nrrsr{rr]rrx)rarr6rarGrrr)rjr_r`r@s r0 test_logpmfzTestGeom.test_logpmfseuzz~~i56 !!)S1u5q9jj1%S#r2ctjjgdd}tjjgdd}t gd}t ||t |d|z y)Nrrsrsr?r)r6rarhrrrrjr?vals_sfrOs r0 test_cdf_sfzTestGeom.test_cdf_sfsMzz~~i-**-- 3/+,!$1!'1X:6r2c$tjjgdd}tjjgdd}t gd}t |t j|t |t j| y)Nrrsrm) r6rarlogsfrrrarlog1pros r0test_logcdf_logsfzTestGeom.test_logcdf_logsfsazz  C0**""9c2+,!$x(89!'288XI+>?r2cztjjgdd}tgd}t ||y)Nrmrs)rKrwrR)r6rarrrrjr?rOs r0r\zTestGeom.test_ppfs+zz~~0#6)!$1r2c\ttjjddddy)N#B ;rK+=r)rr6rarros r0test_ppf_underflowzTestGeom.test_ppf_underflows ue4cFr2cftjdj}t|ddy)Ng<,Ԛ?g۩@r{r|)r6rar>r)rjrgs r0test_entropy_gh18226zTestGeom.test_entropy_gh18226s( JJv  & & (,59r2N) rrrr-rArgrarkrqrur\r{r}r8r2r0r^r^s6 ;4<7@2 G:r2r^ceZdZdZdZdZy) TestPlanckcBtjjdyr+r,ros r0r-zTestPlanck.setup_methodr.r2cztjjgdd}tgd}t ||y)NrrL)g|dy?g8'\>ggrU!>)r6planckrrrrws r0rzTestPlanck.test_sfs1||y"-23 "$1r2cztjjgdd}tgd}t ||y)N)r@@p@r)gP.gh>gTF)r6rrsrrrws r0 test_logsfzTestPlanck.test_logsf s.||!!"7?:;!$1r2N)rrrr-rrr8r2r0rrs22r2rc$eZdZdZdZdZdZy) TestGennormcgd}tjj|d}tjj|}t ||yNrr)r6gennormr`r%rrjpointspdf1pdf2s r0 test_laplacezTestGennorm.test_laplaces;}}  +}}  (D$'r2cgd}tjj|d}tjj|d}t ||yNrr^g;f?r])r6rr`normrrs r0 test_normzTestGennorm.test_norms=}}  +zz~~fF~3D$'r2ctjjdtjd}|j d}tj ||jjdkDsJtjd}|j d}tjj d}tj||jdkDsJtjd}|j d}tjj dd }tj||jdkDsJy) Nrrsrr1rTrr^g;f?r]r) rarrr6rrrrhpvaluer%ks_2sampr)rjrKr rvs_laplacervs_norms r0rAzTestGennorm.test_rvs s q}}S!hhDh!||C*11C777}}QhhDh!mm''T'2 ~~c;/66<<<}}QhhDh!::>>t><~~c8,33c999r2ctjjdtjddgddgg}|j gd}tj |ddddftjdjdd kDsJtj |ddddftjdjdd kDsJtj |ddddftjdjdd kDsJtj |ddddftjdjdd kDsJy) NrrsrKrwrL)rr^r^r1rrT)rarrr6rrrrh)rjrKrs r0test_rvs_broadcastingz!TestGennorm.test_rvs_broadcasting1s q}}sBi"b23hhLh)||C1aL%--*<*@*@A!DsJJJ||C1aL%--*<*@*@A!DsJJJ||C1aL%--*<*@*@A!DsJJJ||C1aL%--*<*@*@A!DsJJJr2N)rrrrrrArr8r2r0rrs((:"Kr2rcTeZdZejj dddgdZy) TestGibratx, sfx)rgD.?)gJ]bH>r2rceZdZdZej j dgddZej j dgddZy) TestGompertzctjjtjjddd}t |dyN0.++r)r6gompertzrrhrrs r0test_gompertz_accuracyz#TestGompertz.test_gompertz_accuracyRs3 NN  u~~11&! ))!Q/5A**32AEBr2c, ref))rgeUT8?)rgtqq?)rgs{)rgN*6cZttjj||dyr)rr6rr>rjrr|s r0rhzTestGompertz.test_entropyrs ..q13UCr2N) rrrrrrrrrhr8r2r0rrPse#" [[[+MNC NC [[X(EFD FDr2rcTeZdZejj dddgdZy) TestFoldNorm x, c, ref)r:0yE>g:0N<?)rrg:?c\ttjj|||dyrz)rr6foldnormrhrjrVrr|s r0rSzTestFoldNorm.test_cdfs! **1a0#EBr2N)rrrrrrrSr8r2r0rrzs7 [[[+N+M+OPCPCr2rceZdZejj dddgdZejj dgddZejj dd d gejj d gd ejj d ddgejj dddgdZdZ y) TestHalfNormr)r |N?)rW Oul2;cttjj||dttjj ||dyr)rr6halfnormrrrs r0rzTestHalfNorm.test_sf_isfs: ))!,c>**3/?r2x, ref))Ww'&l7g;G<^͛7)C]r2r rvs_scalerurXrrTF fix_scalectjjd}tjj ||d|}|rK|rId}t jt|5tjj|||dddyi}|r||d<|r||d<ttj|fi|d d iy#1swYyxYw Nrrr\r]rrrrrrrrrT) rarrr6rrrr r  halflogisticrr rjrrrrrr error_msgrs r0rz(TestHalfNorm.test_fit_MLE_comp_optimizersii##$78~~!!gYT/2"4 y%I|9= M""&&t')&L M  "DL &DN &ennd )g?gg+c\ttjj|||dyN绽|=r|rr6 truncnormr>rjr.r/r|s r0rhzTestTruncnorm.test_entropyis!$ //15sGr2))r$rghiɮ9?)rrr)g0.+rr)}Ô%IrZ_2?c\ttjj|||dyrrrs r0test_extreme_entropyz"TestTruncnorm.test_extreme_entropy}s! //15sGr2c tjjgddddgdzd}tjtj dd dd d tj g}t ||y) NrrrrsH.?rr^rKrr^r[rfO?l@r)r6rrrarrrrws r0test_ppf_ticket1131z!TestTruncnorm.test_ppf_ticket1131\""#EsB()s1uA#788RVVQ Az1bffMN!$1r2c tjjgddddgdzd}tjtj dd dd d tj g}t ||y) NrrrKrrr^r[rrrr)r6rrrarrrrws r0test_isf_ticket1131z!TestTruncnorm.test_isf_ticket1131rr2cd\}}tjj||ddd}t||j cxkxr|j cxkxr|kncd\}}tjj||ddd}t||j cxkxr |j cxkxr |kycy)N)irrrrWr1)rW r6rrr minrfrjlowhighrVs r0test_gh_2477_small_valuesz'TestTruncnorm.test_gh_2477_small_valuess T OO  T1ab  9aeeg..$./ T OO  T1ab  9aeeg..$././r2cZd\}}tjj||ddd}t||j cxkxr|j cxkxr|knct |||gfd\}}tjj||ddd}t||j cxkxr|j cxkxr|kncd\}}tjj||ddd}t||j cxkxr|j cxkxr|kncd\}}tjj||ddd}t||j cxkxr |j cxkxr |kycy) N)rXrUrrrWr1)r)'i')i)r6rrr r#rfrBr$s r0test_gh_2477_large_valuesz'TestTruncnorm.test_gh_2477_large_valuessF T OO  T1ab  9quuw1!%%'1T12CdA4GG T OO  T1ab  9aeeg..$./ T OO  T1ab  9aeeg..$./" T OO  T1ab  9aeeg..$././r2cddgddgfD]\}}tjtj ||tjg}||zdz }tjj |||}tjj |||}tjj|||}tjgd}tjgd} tjgd} |d krtjgd } t||t|| t|| ttj| d | d z |d ztjgd} tjj| ||} tj|tj|dz|g} t| | |d krWttjj |||dttjj |||dnVttjj |||dttjj |||dtjj|||}ttj|| d z |dzd z y)NrrrrwrrrrrKrKrxrx)rd._MT @BKg?rr)rr2r1rrr^rsrrsrKgĖy @gdv*?g,mj%V?rc) rarrr6rrhrr`rrrr)rjr%r&xvalsxmidcdfssfspdfs expected_cdfs expected_sfs expected_pdfspvalsppfs expected_ppfsr`s r0test_gh_9403_nontail_valuesz)TestTruncnorm.test_gh_9403_nontail_valuess<a&2r(+ MICHHrvvgsD"&&9:EHc>D??&&uc48D//$$UC6C??&&uc48DHH\2M88$89LHH%ABMQw ")E F m 4 \ 2 m 4 }Q'7 a8H'H I #c  +HH]+E??&&uc48DHHc2773< +A4%HIM m 4Qw#EOO$6$6tS$$G$68#EOO$7$7c4$H$68$EOO$7$7c4$H$68#EOO$6$6tS$$G$68//%%dC6C s=+;'; rcr!r) rarrr6rrhrr`rrrrrP)rjr%r&r4r5r6r7r8r9r:r;r<r=r>r`xvals2s r0test_gh_9403_medium_tail_valuesz-TestTruncnorm.test_gh_9403_medium_tail_valuessFr(S#J/, PICHHrvvgsD"&&9:EHc>D??&&uc48D//$$UC6C??&&uc48DHH\2M88$89LHH%KLMQw "*=!> m 4 \ 2 m 4 }Q'7 a8H'H I #c  +HH]+E??&&uc48DHHc2773< +CT%JKM m 4??&&tS$7D e ,Qw#EOO$6$6tS$$G$68#EOO$7$7c4$H$9;$EOO$7$7c4$H$68#EOO$6$6tS$$G$9;//%%dC6C s=+;'; K@casec|\}}}}}}tjj||d\}} } } t|| | | g||||gdy)NrSrTFFgxx{q#c(m+++saeeem+,-quu!u},-.r2cttjdr@tjj dddtjj yy)Nrrr:rr)r-rarr6rrrros r0test_rvs_Generatorz TestTruncnorm.test_rvs_GeneratorXsC 299m , OO  Ra-/YY-B-B-D  F -r2ctjtj tj dtj dg}tjtjtjddtjg}tjgd}gd}tt j ||j ||tt j | | j| |y)NrWr;)rW@re r)g Oul"gځ=!gL!g>EG fg^K[X)rarrrr6rrrs)rjr.r/rVrOs r0test_logcdf_gh17064z!TestTruncnorm.test_logcdf_gh17064^s HHrvvgwRVVGR8 9 HHbffbffaRVV4 5 HH* ++ 1-44Q7BQB/55qb98Dr2cjtjddjd}d}t||y)Nrrrgl).0S?)r6rrr)rjrr|s r0test_moments_gh18634z"TestTruncnorm.test_moments_gh18634is0oob!$++A. S!r2N)rrrr-rrrrhrrrr'r,r?rFrIrar_truncnorm_stats_datarrWrZr\r`rbrgrir8r2r0rresJ [[[BCH CH  [[[DE H E H2 2 00&!MF-P^,  1 = < BFF       &&!            ;"F%BHH%:; [[V%:;D<D + 0 /F E"r2rceZdZejj dgddZejj dgddZejj ddd gd Zejj d d d gdZ ejj d ddgdZ ejj dddgdZ y)TestGenLogistic x, expected))ig4`n)ig4 ncg)rgX =)rXgh@ X)rg hrs r0rhzTestGenLogistic.test_entropys! ))11!4cFr2r)rrWg8.)rgpT oc\ttjj|||dyr)rr6rorrs r0rzTestGenLogistic.test_sfs# )),,Q2CeDr2 q, c, ref)rurg^#@)r[r^gG Ff@c\ttjj|||dyNV瞯s r0rAzTestHypergeom.test_rvss""2r17"; $!)$ $!)$% & D!W,- 9\#::;oo!!"a, 3$%oob!R(,,Q/ 3 ./ )L"99:r2cvd}d}d}|}|}tjjd|||}t|ddy)Ni r3rtr^gkㅒP?r!)r6rrGr)rjMrlNtotgoodhgpmfs r0test_precisionzTestHypergeom.test_precisionsB   ##AsD!4E#8"=r2clttjjddddddttjjddddddttjjddddddttjjddddddy)Nrr^rrKr!rx)rr6rrGros r0 test_argszTestHypergeom.test_argss EOO//1a;S"EEOO//1a;S"EEOO//1a;S"EEOO//1a;S"Er2c tdtjjddddcxkxr dkycy)Nrr0ioi if0rK)r r6rrhros r0test_cdf_above_onez TestHypergeom.test_cdf_above_ones/U__((XtUCJsJKJKr2c vd}d}tjgddz}d}|Dcgc]'}tjj |||z||)}}tjgd}t ||dd gd }tjj |||z|d } gd } t | | dd ycc}w) Ng+@g@)rffffff@333333@rgffffff@@r@@)rgpR(g㘍R2gJޱp9g?Mf= G?rrgƠ>r)g@rg@g@g@)rrg) 9g"1)rarr6rrr) rjorangespears fruits_eatenquantileeatenrrO quantilesres2 expected2s r0test_precision2zTestHypergeom.test_precision2sxx =>D (*!!(GeOWeL**889:XAD90 !!)Wu_guM> iad;*s,B6c>tjddd}|j}tjddg}tj t || }t||tjddd}|j}t|dy)Nrrrrcrx) r6rr>rarrdrrr)rjhgrgrerfs r0rhzTestHypergeom.test_entropysz __Q1 % JJLXXtTl+ ffU:z:;; :& __Q1 % JJLQr2cd}d}d}d}tjj||||}d}t||dd}d }d }d }tjj||||}d }t||d y)NrcA.Aj@gorrNr@Xr g_7 j$r5)r6rrsrrjrSrrlrresultrOs r0rzTestHypergeom.test_logsfs    &&q!Q2FHa8    &&q!Q2 FHb9r2c&d}d}d}d}tjj||||}d}t||dd}d }d }d }tjj||||}d }t||d d}d }d}d}tjj||||}d}t||d t j gd}d }d }d }tjj||||}t j dd }t||d y)Nrrrrg)\UrrNrrr3r g*@Vr5}rtgר)rrr)r6rrrrarfullrs r0rzTestHypergeom.test_logcdfs    ''1a3FHa8    ''1a3&FHb9    ''1a3 FHb9 HH\ "   ''1a377112FHb9r2czd}d}d}tjj|||}||z |z}t||y)NipiPi.)r6rrr)rjrrlrhmrms r0test_mean_gh18511zTestHypergeom.test_mean_gh18511?sB    __ ! !!Q * UQYBr2cd}d}tjdd}d|z}tjj |dz |||}tj |dkDsJtj tj |dksJy)NrWrrr5$@rr)rar r6rrrdiff)rjrlrrpopulation_sizerms r0test_sf_gh18506zTestHypergeom.test_sf_gh18506Jsw   IIa q& OO  q1uoq! <vva!e}}vvbggaj1n%%%r2N)rrrr-rArrrrrhrrrrr8r2r0rrs< ;>FL<& :0,:\   &r2rc8eZdZejj dgddZejj dgddZdZdZ ejj d d d gd Z ejj d gddZ y) TestLoggammaz x, c, cdf))rr^g;Y%?)rgRٲa6_<)gHr[gi|e?)r[g6l ?)i+rTg֬CCf9)irgֺl ctjj||}t||dtjj ||}t||dyr)r6loggammarhrr)rjrVrrhrmys r0rzTestLoggamma.test_cdf_ppf]sH NN  q! $3U+ NN  sA &15)r2zx, c, sf))rrgQOu3;)rXg\Z{0)rr[geɐ?)ig{Gzd?gr0T?ctjj||}t||dtjj ||}t||dyr)r6rrrr)rjrVrrrErs r0rzTestLoggamma.test_sf_isfosH NN  a #2E* NN  r1 %15)r2c`tjjdd}t|ddy)N r^g@rzr|)r6rrr)rjlps r0rqzTestLoggamma.test_logpdfzs& ^^ " "4 +G%0r2ctjgdjdd}|D];\}}}}}tjj|d}t |||||gd=y)N)rsg"~jg46<@goŏ@rKg h"lxg Q?gZd;333333@g(@g{/L@g??gгYҿgh|?5?rrmsvkrTrrN)rarreshaper6rr)rjtablerrvarskewkurtcomputeds r0rXzTestLoggamma.test_statsst wr1~  ). 1 $AtS$~~++Av+>H %hsD$0G./ 1 1r2rrTr[ctjj|d}tj|j sJtjj |}tjtj||kt|}|jd}|jdcxkr|jksJJy)Nrr1r)confidence_levelrs) r6rrraisfinitermedian binomtest count_nonzeror proportion_cir%r&)rjrrVmedbtestcis r0rAzTestLoggamma.test_rvss NN  qv  .{{1~!!###nn##A& 0 0S 93q6B  % 8vv%bgg%%%%%r2r))rg3H໱k3@)rrr)rg8,[H^} )rg90$)rgtum\cZttjj||dyr)rr6rr>rs r0rhzTestLoggamma.test_entropys ..q13UCr2N) rrrrrrrrrqrXrArhr8r2r0rrVs [[[EF*F* [[ZBC * C * 1 1 [[S3,/ &0 & [[X<= D = Dr2rcXeZdZgdZej j dedZy) TestJohnsonsu))rrrg?r)rrrgH';vIh%,=)rrrg?x7rrNc|\}}}}}ttjj||||dttjj |||||yNrr|)rr6 johnsonsurrrjrNrVr.r/rtols r0rzTestJohnsonsu.test_sf_isfP1aS**1a3ReD++B15qsCr2Nrrrcasesrrrrr8r2r0rrs0 ;E [[VU+D,Dr2rcXeZdZgdZej j dedZy) TestJohnsonb))rrrg?Hz>)rrrg0jA:r)g !?rrgQbF5rrNc|\}}}}}ttjj||||dttjj |||||y)Nrr|r)rr6rrrrs r0rzTestJohnsonb.test_sf_isfrr2Nrr8r2r0rrs0 =E [[VU+D,Dr2rceZdZdZdZdZdZdZejjdddgd Z d Z ejjd d d gdZ dZy) TestLogisticctjdd}tjj |}tjj |}t ||yNrr)rarPr6logisticrhrrrjrVrrs r0rzTestLogistic.test_cdf_ppfsD KKR  NN  q ! ^^   "2r2ctjdd}tjj |}tjj |}t ||yr)rarPr6rrrrrs r0rzTestLogistic.test_sf_isfsD KKR  NN  a  ^^   "2r2cd}d}ttjjd|z |ttjj ||y)Ng.funcsDAqD AqA~.RVVTAXN335689A>B$(a&&$(a014&&$(a014678:;$(#&(TAX./ &ennd;r2N)rrrrrrrrrrrrrr rr8r2r0rrs  84)  [[03J3K3MNCNC,F  [[\D%=9 1: 1s r0rAzTestLogser.test_rvs9s||73 $!)$% D!W,- 9\#::;llt$ 3$%ll4 $$Q' 3 ./ )L"99:r2c\tjjdd}t|dy)Nrryg&Y3)r6rrGrrjrUs r0test_pmf_small_pzTestLogser.test_pmf_small_pDs$ LL  Q & 7#r2cZtjjd}t|dy)NrgW?)r6rrrrs r0test_mean_small_pzTestLogser.test_mean_small_pRs" LL  d # ;'r2N)rrrr-rArr r8r2r0rr5s ; $(r2rc eZdZejddZej jdejejgej jdgdej jdgdej jd d d gd d gfd Z ej jd ejdfejdfgdZ y)TestGumbel_r_lfunctionscopec@tjjdSr+rarrros r0rzTestGumbel_r_l.rng^yy$$T**r2rKrrrrrrTrrzfix_loc, fix_scaleTFc|jd|||}t}|r|dz|d<|r|dz|d<t||fi|y)NrXrr\r]rr^rr)rr r) rjrKrrrrrrrs r0rz&TestGumbel_r_l.test_fit_comp_optimizerbs\xxSgY%(*v "Q;DL &]DN &dD9D9r2z dist, sgnrrc|tjgdz}|j|\}}t||dzt|ddy)N)rrrrrrrgW@g@g3qtw>rr|)rarrr)rjrKsgnzr\r]s r0rzTestGumbel_r_l.test_fitwsH :; ;XXa[ U S!3345DAr2N) rrrrfixturerrrr6gumbel_rgumbel_lrrr8r2r0r"r"]sV^^*%+&+ [[Vennenn%EF [[Y 3 [[[*5 [[1#UmeT];=:=64G :  [[[ENNA+>,1NNB+?+ABBBBr2r"c eZdZdZdZej ddZejjdejjddd gejjd d d gejjd dd gdZ ejjddd gejjd d d gejjd dd gejjde ddgdDcgc]}d|vr| c}}e jddZe jddZdZdZycc}}w) TestParetocJ tj5tjdttj j dd\}}}}t |tjt |tjt |tjt |tjtj j dd\}}}}t |tjt |tjt |tjt |tjtj j dd\}}}}t |dt |tjt |tjt |tjtj j dd\}}}}t |dt |tjt |tjt |tjtj j d d\}}}}t|d t|d t |tjt |tjtj j dd\}}}}t|dt|d t |tjt |tjtj j d d\}}}}t|dt|dt|dtjdzt |tjtj j dd\}}}}t|dt|dt|dtjdzt |tjtj j dd\}}}}t|dt|dt|dtjdzt|ddddy#1swYyxYw)NrjrsrSrTrKrrRrwr g?grq@r @gffffff?gK~?g2@g۶m۶m?rUUUUUU?gqq?r@g%I$I?gQ?gUUUUUU@grq?g88Nb@) rnrorprqr6paretorrarrrrrjrUrVrErSs r0rXzTestPareto.test_statssJ $ $ &7 N  ! !'> :++C+@JAq!Q BFF # BFF # BFF # BFF #++C+@JAq!Q BFF # BFF # BFF # BFF #++C+@JAq!Q C BFF # BFF # BFF #++C+@JAq!Q C BFF # BFF # BFF #++C+@JAq!Q Ay ) A2 3 BFF # BFF #++C+@JAq!Q As # At $ BFF # BFF #++C+@JAq!Q Ay ) A2 3 A 2777+;; < BFF #++C+@JAq!Q Ay ) Az * A0277;3GG H BFF #++C+@JAq!Q Ay ) A2 3 A RWWW-== > AL Mo7 N7 N7 Ns Q;RR"c~d}d}d}tjj||d|}||z |z}t||y)NgeAr^rrr[)r6r9rr)rjrVr/r]rmrOs r0rzTestPareto.test_sfsB   LLOOAqauO 5!Ga<8$r2r#r$c@tjjdSr+r'ros r0rzTestPareto.rngr(r2z2ignore:invalid value encountered in double_scalarsrrr^rrrrc tjjd||||}tjj|ddd}tjj|ddd}tjj|ddd}||cxk(r |cxk(rdk(sJJtjjd|||dz|}tjj|d \} } } t | dz|j |dz } | j d} t | | tjtj| | j z z t | dy) NrXrr/r]r\rrp= ף?)rr)rfix_b)rfbr^r) r6r9rrrr#r9rardr)rjrrrrrshape_mle_analytical1shape_mle_analytical2shape_mle_analytical3 shape_mle_a loc_mle_a scale_mle_a data_shiftndatas r0rzTestPareto.test_fitso ||SIY$+# ?!& 0 0A$ 0 G J % 0 0AT 0 J1 M % 0 0A$ 0 G J%)>.%.)-. /. /.||SIY%,q[ E.3ll.>.>t!.>.L+ Y [1_dhhj1AX   #[RVVBFF:jnn6F+F$GHH JY"r2rTfix_shape, fix_loc, fix_scaleTFrrepeatignoreinvalidctjjd||||}i} |r|| d<|r|| d<|r|| d<ttj|fi| y)NrXr>rrr)r6r9rr rjrrrrrrrrrs r0rz&TestPareto.test_fit_MLE_comp_optimizersf||SIY$+# ? "DJ "DL &DN%ellDADAr2c d\}}}tjj|||dtjj d}t tj|y)N)rrrrXið&r)r6r9rrarrr)rjr9locationr]rs r0test_fit_known_bad_seedz"TestPareto.test_fit_known_bad_seedsR ")x||xS-/YY-B-B7-K M%ellD9r2cttjtttjj gddtttjj gdddy)Nrr^r)rr^rrrr)rr6r9rr rros r0test_fit_warningszTestPareto.test_fit_warnings sCELL)lELL$4$4iaHlELL$4$4ia r2ctjjddd|}t|dtjj |}y)Ni~rrX)r\r/rrr)r6r9rr r)rjrrrs r0test_negative_datazTestPareto.test_negative_data s?||DACcJ$" LL  T "r2N)rrrrXrrr0rrfilterwarningsrrr%raerrstaterrTrVrX.0rms00r0r4r4s:Nx%V^^*%+&+ [[!12 [[[1a&1 [[YA/ [[[1a&1#2022 #. [[[2q'2 [[YA/ [[[1a&1 [[<)0$q)I-A!&! -.R[[" B#.203 BR[[":#: #I-s$ Fr4c eZdZdZdZdZdZdZdZdZ dZ d Z e jjd d gd fd dddej dz ej"gfddddej dzdgfdgdfgdZdZy) TestGenparetocbdD]c}tj|}tjj |\}}t |dt tj|etjd}tjj |\}}t||gddgy)NrKrxrxrs) rarr6 genpareto _get_supportrr isposinfr)rjrr.r/s r0test_abzTestGenpareto.test_ab s $A 1 A??//2DAq B  BKKN #  $ JJsO++A.1AS *r2cLtjd}tjddd}t |j |tj j |t |j|tj j|t |j|tj j|tjddd}t |j|tj j|y)Nrxrrrr0rKrW) r6rbrarPrr`rrhrrrjrvrVrvs r0test_c0zTestGenpareto.test_c0' s__r " KK3 #q 5;;??1#56q 5;;??1#56a%++.."34 KKB #q 5;;??1#56r2ctjd}tjddd}t |j |tj j |t |j|tj j|t |j|tj j|tjddd}t |j|tj j|t |jd dy) Nrrgrrr0rxrKrWr) r6rbrarPrr`uniformrhrrrrhs r0test_cm1zTestGenpareto.test_cm13 s __s # KK3 #q 5==#4#4Q#78q 5==#4#4Q#78a%--"2"21"56 KKB #q 5==#4#4Q#78  ! a(r2ctjd}t|jtj |j tj gddgtt j|jtj tjd}t|jtj |j tj gddgtt j|jtj tjd}t|jtj |j tj gddgtt j|jtj y)NrTrgrxrKr) r6rbrr`rarrhr isneginfrrjris r0 test_x_infzTestGenpareto.test_x_infA s __s #82r(C BIIbff-./ __r "82r(C BIIbff-./ __s #82r(C BIIbff-./r2ctjddd}dD]}tjj ||}dD]3}tjj |||z}t ||d5tjj ||}dD]3}tjj |||z}t ||d5y) NrrWr0rrrzg+rr)rzrz)rarPr6rbr`rrh)rjrVrpdf0dcpdfccdf0cdfcs r0test_c_continuityzTestGenpareto.test_c_continuityO s KK2r " 8A??&&q!,D% 8**1a"f5d7 8??&&q!,D$ 8**1a"f5d7 8 8r2c ztjtjdddtjddddd tjdddz f}d D]Z}tj j ||}d D]3}tj j |||z}t||d 5\y NrrurTbaserr0FendpointrK)rxrrtr)rarErrPr6rbrr)rjrvrppf0rvppfcs r0test_c_continuity_ppfz#TestGenpareto.test_c_continuity_ppf] EE"++eT4++dArE:r{{5$S99: ; 8A??&&q!,D% 8**1a"f5d7 8 8r2c ztjtjdddtjddddd tjdddz f}d D]Z}tj j ||}d D]3}tj j |||z}t||d 5\yr|)rarErrPr6rbrr)rjrvrisf0rvisfcs r0test_c_continuity_isfz#TestGenpareto.test_c_continuity_isfg rr2c ^tjtjdddtjddddd tjdddz f}d D]L}t t j jt j j||||d Ny) NrrurTr}rr0FrrK)rgC]r2r{gV瞯Ҽr{r) rarErrPrr6rbrhr)rjrvrs r0test_cdf_ppf_roundtripz$TestGenpareto.test_cdf_ppf_roundtripq s EE"++eT4++dArE:r{{5$S99: ;/ +A EOO//0C0CAq0I1ME + +r2c`tjjdddd}t|dy)NrrurrgpEȜ)r6rbrsrrs r0rzTestGenpareto.test_logsfz s'$$T31512r2zc, expected_statsr)rrr^rrcr7gqq @rWr^gqq?g?g$I$ ?rq?rgll0@r)rsUUUUUU?r333333cdtjj|d}t||ddy)NrSrTrr{r])r6rbr)rjrexpected_statsrs r0rXzTestGenpareto.test_stats s+&&q&&9UGr2c^tjjd}t|ddy)NrgvǼ ?rr|)r6rbrr)rjrVs r0test_varzTestGenpareto.test_var s# OO   %,59r2N)rrrrerjrmrqrzrrrrrrrrarrrXrr8r2r0r^r^ s + 7 ) 0 888+3  [[ \  T2gbggaj="&&1 2 ]T72771:$5v> ? " # %& H & H:r2r^c<eZdZdZdZdZdZdZdZdZ dZ y ) TestPearson3cBtjjdyr+r,ros r0r-zTestPearson3.setup_method r.r2cTtjjdd}tt j |dk(t|j jtdvtjjd}tt|ttjdjd}tt|tjt|j jtdvtt|dk(y)NrTr2r1AllFloatrsr) r6r)rr r8r9rr:rr;rr[rr>s r0rAzTestPearson3.test_rvs s~~!!#G!4 D!W,- 9Z#889nn  % 3&'nnS!%%a( 3 ./ )J"778CA r2ctjjdgd}t|t j gddtjjdd}t|t j dgdtjjgd d}t|t j gd dy) Nr^rxrTr)gtT?g+q?g?rrr.rTND}i?r.rrrr)rgj?gdC?gs?g'M?)r6r)r`rrarris r0rIzTestPearson3.test_pdf s~~!!!_5bhh'KL! #~~!!"c*bhh |44@~~!!"4c:bhh(@AGK Mr2cPtjjdgd}t|t j gddtjjdd}t|dgdtjjgd d}t|gd dy) Nr^r)grE?gTp]0?g~?rrr.rTgE&"J?r)giZ*J?gh+8w?gcK?g|g~׼=gp'+7g;rr|r)rr6r)rr)rjrrVr|s r0rzTestPearson3.test_sf s\% ">))!T2CeD))!Q/q1ANr2N) rrrr-rArIrSrrrrr8r2r0rr s- MK ( -7& Or2rc6eZdZdZdZdZdZdZdZdZ y) TestKappa4cgd}d}dD]P}tjj|||}tjj|| }t ||Ry)N)rxrTrrsrK) gffffffrr皙ɿrrTrrsrKffffff?)r6kappa4rhrbrrjrVrgrSr? vals_comps r0test_cdf_genparetozTestKappa4.test_cdf_genpareto sW   -A<<##Aq!,D++Ar2I D) ,  -r2ctjddd}d}tjddd}tjj |||}tj j ||}t ||y)Nr:rrWrxr.r)rarPr6rrh genextremerrs r0test_cdf_genextremezTestKappa4.test_cdf_genextreme se KKAr "  KKAr "||1a($$((A. i(r2ctjddd}d}d}tjj |||}tj j |}t ||y)NrrWrKrx)rarPr6rrhrrrs r0test_cdf_exponzTestKappa4.test_cdf_expon sR KK2r "  ||1a(KKOOA& i(r2ctjddd}d}d}tjj |||}tj j |}t ||y)Nr:rrWrx)rarPr6rrhr1rrs r0test_cdf_gumbel_rzTestKappa4.test_cdf_gumbel_r sT KKAr "  ||1a(NN&&q) i(r2ctjddd}d}d}tjj |||}tj j |}t ||y)Nr:rrWrrx)rarPr6rrhrrrs r0test_cdf_logisticzTestKappa4.test_cdf_logistic sT KKAr "  ||1a(NN&&q) i(r2ctjddd}d}d}tjj |||}tj j |}t ||y)Nr:rrWrK)rarPr6rrhrlrrs r0test_cdf_uniformzTestKappa4.test_cdf_uniform sT KKAr "  ||1a(MM%%a( i(r2c0tjddyr)r6rros r0test_integers_ctorzTestKappa4.test_integers_ctor! s  Qr2N) rrrrrrrrrrr8r2r0rr s% -)))))r2rc*eZdZdZdZdZdZdZy) TestPoissoncBtjjdyr+r,ros r0r-zTestPoisson.setup_method( r.r2ctjd}tjj gd|}d|dz |dzdz g}t ||y)Nr^rrr^rsr)rarr6r{rGr)rjln2r?rOs r0test_pmf_basiczTestPoisson.test_pmf_basic+ sGffQi}}  C0QQq)h'r2ctjjgdd}gd}t||tjj dd}t |dy)Nrr)rrrffffff?rr)r6r{rGrintervalr)rjr?rOrs r0test_mu0zTestPoisson.test_mu02 sG}}  A.4*==))$2Xv&r2chtjjdd}tt j |dk\tt j |dk(t|jjtdvtjjd}tt|ttjdjd}tt|tjt|jjtdvy)Nrsr2r1rr4r) r6r{rr r8rr9rr:rr;rZr[r>s r0rAzTestPoisson.test_rvs; s}}  7 3 $!)$% D!W,- 9\#::;mm$ 3$%mmC $$Q' 3 ./ )L"99:r2c d}tjj|d}t|||tjd|z d|z gtj gd}tjj|d}||tj ddtjdz gtj ddgf}t||y) Ng0@rSrTrK)rxrKrwrr^rs)r6r{rrarrr)rjrrrOs r0rXzTestPoisson.test_statsF s $$R$8RR#b& AB XXo &$$R$8RVVQ"''!* 537GH)r2N)rrrr-rrrArXr8r2r0rr' s(' ;*r2rcTeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zy ) TestKSTwocBtjjdyr+r,ros r0r-zTestKSTwo.setup_methodR r.r2c dD]}tjdd|z d|z ddd|z z dg}d|z |z}tjj |dz}|dk7rtj |nd}tjdd||zddt jjd|zz tdd|zz ddg}t jj||}t||y)Nrr^rrWrXrrrsrrKr^rx) rarr5rgammalnrr6ksonerrfkstworhr)rjrlrVv1lgelgrOr@s r0rSzTestKSTwo.test_cdfU s) 0A!SUAaCaAgq9:Aa%!B&&qs+B!#q266":aCxxArCx!"Qu{{~~c1'=%=!=!$Q2Xs!3!$!&'H{{q!,H Hh /# 0r2c tjddd}dD]}tjdd|z d|z ddd|z z dg}d|z |z}tjj |dz}|dk7rtj |nd}tjddd||zz dtjjd|ztd|zddg}tjj||}t||y)Nrrr!rrsrKr^) rarPrr5rrrr6rrr#rr)rjrVrlrrrrOrps r0rzTestKSTwo.test_sfi s KK1b !) /A!SUAaCaAgq9:Aa%!B&&qs+B!#q266":aCxxc!"R#X!"5;;>>#q#9!9!$QrT3!45HkknnQ*G GX . /r2ctjddddd}gd}|D][}|tj|z }tjj ||}tj |}t|d]y)Nrr^r!r)r3rXrirrr)rarPrr6rrhrr )rjrVns_xxnprobsdiffss r0test_cdf_sqrtnzTestKSTwo.test_cdf_sqrtnx sn KK1b !!" % , +Bbggbk!BKKOOB+EGGENE eT *  +r2ctjddd}dD]Q}tjj ||}tjj ||}t |d|z SyNrrr!r)rarPr6rrhrr)rjrVrlr@rps r0rqzTestKSTwo.test_cdf_sf sY KK1b !) =A{{q!,HkknnQ*G %hG < =r2ctjddd}dD]i}|tj|z }tjj ||}tjj ||}t|d|z kyr)rarPrr6rrhrr)rjrVrlrr@rps r0test_cdf_sf_sqrtnzTestKSTwo.test_cdf_sf_sqrtn sj KK1b !) =ARWWQZB{{r1-HkknnR+G %hG <  =r2ctjddd}dD]l}||d|z kD}tjj ||}d|k|dkz}tjj ||}t ||||dny) Nrrr!rrsrrr|)rarPr6rrhrrrjrVrlrr@condr?s r0test_ppf_of_cdfzTestKSTwo.test_ppf_of_cdf s KK1b !) =A1s1u9B{{r1-HLX_5D;;??8Q/D DJ4t <  =r2ctjddd}dD]l}||d|z kD}tjj ||}d|k|dkz}tjj ||}t ||||dny) Nrrr!rrsrKrr|)rarPr6rrrr)rjrVrlrvals_isfrr?s r0test_isf_of_sfzTestKSTwo.test_isf_of_sf s KK1b !) =A1s1u9B{{r1-HLX^4D;;>>(A.D DJ4t <  =r2c<tjddd}dD]}|tj|z |d|z kD}tjj ||}d|k|dkz}tjj ||}t||||y)Nrrr!rrsrK)rarPrr6rrhrrrs r0test_ppf_of_cdf_sqrtnzTestKSTwo.test_ppf_of_cdf_sqrtn s KK1b !) 2Abggaj.!c!e),B{{r1-HLX^4D;;??8Q/D DJ4 1  2r2c<tjddd}dD]}|tj|z |d|z kD}tjj ||}d|k|dkz}tjj ||}t||||y)Nrrr!rrsr)rarPrr6rrrr)rjrVrlrrprr?s r0test_isf_of_sf_sqrtnzTestKSTwo.test_isf_of_sf_sqrtn s KK1b !) 2Abggaj.!c!e),BkknnR+GKGdN3D;;??7A.D DJ4 1  2r2ctjddddd}dD]N}tjj ||}tjj ||}t ||Pyr)rarPr6rrrhr)rjrrlrr@s r0r\zTestKSTwo.test_ppf s\ Aq"%ab)) -A*B{{r1-H He , -r2c gd}tjgd}tjgdgdgdgdgdgdg}t|D]x\}}|tjd ztjtj d z |z z}t jj||}t|||d zy) N)rWr3rXrrtr)rcgUUUUUU?rsrr^r)gRT>gr ?gK5 ?gn "5?gU ?gk?)g&6#>gb E>gI5?g\ ?g;?g%1?)g6>gL>g<?g䓀^?gO|6$?g qO?)g}+:>gwQ9>gH{?g]qv (?g)~/v?gmJ?)gV27J=gGk(>gWX?g Y?g{0`?gZ H?)g_R=g4>g̪?gT_@?g<e?g2?r^rr|) rar enumeraterrrbr6rrhr)rjrratiosrOidxrlrVr@s r0test_simard_lecuyer_table1z$TestKSTwo.test_simard_lecuyer_table1 s+8988 - - - - - -    m @FC"RWWRUU1WQY%77A{{q!,H Hhsm$ ? @r2N)rrrr-rSrrrqrrrrrr\rr8r2r0rrQ s?0( / +====22-@r2rceZdZdZdZdZy)TestZipfcBtjjdyr+r,ros r0r-zTestZipf.setup_method r.r2chtjjdd}tt j |dk\tt j |dk(t|jjtdvtjjd}tt|ttjdjd}tt|tjt|jjtdvy)Nrr2r1rr4r) r6zipfrr r8rr9rr:rr;rZr[r>s r0rAzTestZipf.test_rvs szz~~c~0 $!)$% D!W,- 9\#::;jjnnS! 3$%jjo!!!$ 3 ./ )L"99:r2c`tjjd\}}ttj|t |tj tjjdd\}}ttj||gj y)Nffffff@r.rskr.rU)r6rr rarrrrr:s r0rWzTestZipf.test_moments syzz#&1 AQzz#t41BKKA'++--.r2N)rrrr-rArWr8r2r0rr s ;/r2rc$eZdZdZdZdZdZy) TestDLaplacecBtjjdyr+r,ros r0r-zTestDLaplace.setup_method r.r2cztjjdd}tt j |dk(t|j jtdvtjjd}tt|ttjdjd}tt|tjt|j jtdvttjjdduy)Nrr2r1r4rr) r6dlaplacerr r8r9rr:rr;rZr[r>s r0rAzTestDLaplace.test_rvs s~~!!#G!4 D!W,- 9\#::;nn  % 3$%nnS!%%a( 3 ./ )L"99:""3't34r2cxd}tj|}|jd\}}}}d}tj| |dz}|j |} tj | |dzztj | |dzz} } t ||fdt||f| | | dzz dz fd d y) NrKrSrrr^rrrRrzrr)r6rrar rGrdrr) rjr.dlrUrVrErSrrppm2m4s r0rXzTestDLaplace.test_stats s  ^^A XXf% 1a  YYr1Q3  VVBZ2q5!266"RU(#3BaVV$ARAX] 3%dKr2ctjd}tj|}|jd\}}}}t ||fdt ||fdy)NrwrS)rxrx)r @)rarr6rrr)rjr.rrUrVrErSs r0 test_stats2zTestDLaplace.test_stats2 sO FF2J ^^A XXf% 1aaVX&A +r2N)rrrr-rArXrr8r2r0rr s 5 L,r2rceZdZdZej j dddgdZej j dddgfdZdZ d Z d Z ej j d gd d Z xZ S) TestInvgausscBtjjdyr+r,ros r0r-zTestInvgauss.setup_method! r.r2zrvs_mu,rvs_loc,rvs_scale)r^rr)g ףp=@g r@gʡE6@cXtjjd|||}tjj||\}}}||z }t j |}t |t j|dz|dzz z } || z } t| |ddt| |ddt||tjjd|||}tjj||dz |dz\}}}t|dz|t|dz |tjj|d d } tjj|d d } tjj|d d } | | cxk(r | cxk(rd k(sJJy)NrX)rrr\r]rrr{rrrr?)fmur)fix_mur) r6rrrrarrrdrr)rjrvs_murrrrr\r]mu_temp scale_mlemu_mle shape_mle1 shape_mle2 shape_mle3s r0rzTestInvgauss.test_fit$ s~~!!sv&-Y"@++Dw+?Cg~''$-Ir Wr](B!CD " U; 5u5AS'"~~!!sv&-Y"@++Dw{3@g @gGz@c*tjjd}tjj d||||}t ttjtj"}||}tjj|}t||||dd}tjj|dd}t||ttj||tj||dz z dkDsJttj||dz ttj|dttj||tjjdd y) NrrX)rrr\r]rrr^)rrrrr) rar RandomStater6rrrrrrrrrand) rjrrrrr super_fit super_fitted invgauss_fit __class__s r0rz(TestInvgauss.test_fit_MLE_comp_optimizerC s9ii##D)~~!!sv&-YS"R$u~~.C   ~~))$/ \<0!A15 ~~))$QA)> \<0 &enndIvvtw{+q0111%ennd1M &enndC &ennd-/YY^^A->q-A Cr2cttjtjt 5tjj gdddddy#1swYyxYwr)rr6rrr r rros r0test_fit_raise_errorsz"TestInvgauss.test_fit_raise_errorsg sFENN+ ]]< ( 2 NN  yq  1 2 2 2s $A  A)cgd}gd}tjjd|}t||tjjdd}t |dtjj dd}t |d tjjd d }t |d tjjd d }t |dy)N)g4wT;?gjdV&}?g{i\0>gDV_h?gqac X?)rrrrr皙?rr[?gfFngr^:g9̗?rgx_;:g!?gٷ ??)r6rrhrrr)rjrrOrJ cdf_actual sf_actuals r0rqzTestInvgauss.test_cdf_sfm s."##CB#/Xv&^^''$'7  $9:NN%%cd%3  #78 ##GV4 34##Hf5 12r2chtjjdd}t|dtjjdd}t|dtjj dd}t|dtjj dd}t|d y) Nrr)r(giJ.r*gr^ߺr[gpgFgpQ^L)r6rrrrs)rjrrss r0ruzTestInvgauss.test_logcdf_logsf s&&v$&7 12&&sD1 56$$Ut$456$$S$/01r2zmu, ref))g:0yU>g,9)r[g% !)rug40)rgK' @)rg`p @cZttjj||dyr)rr6rr>)rjrr|s r0rhzTestInvgauss.test_entropy s ..r2CeDr2)rrrr-rrrrrr%rqrurh __classcell__r#s@r0rr s [[7')>?A>A>: [[7')>?A CA CD2 !3F2. [[Y)DE E E Er2rceZdZejj dgdejj dgddZejj dgdfdZd Zd Z d Z d Z xZ S) TestLaplacer)r:rrr^r)rr^rrWctjjd}tjj d|||}tj |}tjtj||z t|z }tjj|\}}t||ddt||ddtjj||\}}t||ddtjj||\}}t|||dz}tjtj||z t|z }tjj||\}}t||tjj||\}}t||tttjj||| tttjjtj gtttjjtj"gy) NrrXr,r{rrrr^r)rarrr6r%rrrdrrrrrrr r rr) rjrrrrloc_mlerr\r]s r0rzTestLaplace.test_fit s ii##D)}}  cwi.1!3))D/FF266$.12SY> ]]&&t, UW5u=yu5A]]&&t'&: Uyu5A]]&&tI&> UW%kFF266$*-.T: ]]&&t#&6 UY&]]&&tI&> UWc" lEMM$5$5t'& ( j%--"3"3bffX>j%--"3"3bffX>r2rvs_loc,rvs_scale))r:rWrWr)rsrctjjd}tjj d|||}d}tjj |\}}tttjtj|\}} ||||} ||| |} | | kstj| | ddsJyy)Nrrr,c dt| tjd|zzd|z tjtj||z zz zS)Nrr^r)rrarrdr)r\r]rs r0llz3TestLaplace.test_fit_MLE_comp_optimizer..ll sOCI%8E'266"&&*<#==>? ?r2r{r) rarrr6r%rrrrr) rjrrrrr9r\r]loc_opt scale_optll_mlell_optr#s r0rz'TestLaplace.test_fit_MLE_comp_optimizer sii##D)}}  dy.1!3 ? ]]&&t, U"4 #6#(==66:) C%GY-"++ff38u#F FF#Fr2ctjgd}tjj |d\}}t |dddtjj |d\}}t |dddy)N)rKrKrRrLrrHrrrr{rr)rarr6r%rr)rjrr\r]s r0test_fit_simple_non_random_dataz+TestLaplace.test_fit_simple_non_random_data sgxx78]]&&t!&4 Uqu59]]&&tA&6 UQU7r2c<d}tjj| }|dk(sJtjj|}|dk(sJtjj|}|dk(sJtjj| }|dk(sJy)NrrxrK)r6r%rhr)rjrVp0p1s r0test_sf_cdf_extremesz TestLaplace.test_sf_cdf_extremes s  ]]  r "Syy]]  q !Syy ]]  a Syy]]  qb !Syyr2cd}tjj|}t|t j | dz dy)Nrr^rr|)r6r%rrrar)rjrVrms r0rzTestLaplace.test_sf s5  MM  Q 2661":a66"++e&6&6&<& sii##$78##A3e#14$6} DJ "DNCI  A:MI j9K 3  $$T2T2 3 %e&6&6EE  3 s !CCN) rrrrrrrrrOrTr8r2r0rGrG sDE [[S,/O0O [[S/2 [[\L>: [[WtUm4 [[[4-8F95;3Fr2rGc eZdZejj dddgdZejddZejj dgd ejj d gd ejj d gd ejj de ddgdDcgc]}d|vr| c}}dZ dZ dZ dZ ycc}}w) TestPowerlawzx, a, sf)rcrwg?)g?gp?gSQ>c\ttjj|||dyrz)rr6powerlawr)rjrVr.rs r0rzTestPowerlaw.test_sf\ s! ))!Q/%@r2r#r$c@tjjdSr+r'ros r0rzTestPowerlaw.rngb r(r2r)rTrsrrr^rr)rr*rJTFrrKc*tjjd||||}t} |r|| d<|r6t j |j tj | d<|r|| d<ttj|fi| ddiy)Nr)rr.r\r]rrrrrT) r6rXrr ra nextafterr#rrrQs r0rz(TestPowerlaw.test_fit_MLE_comp_optimizerf s~~!!siW(1"Ev "DJ << RVVG [[Y 3 [[[*5 [[<)0$q)I-A!&! -.<.64? <$ D466{-s> C/rVc,eZdZejj dgddZejj dddgdZejj dgdd Zejj dgd d Z y ) TestPowerLogNormz x, c, s, ref))rXrrga!R()r[rrg;?)r[r}rgE?)MDr}rg=c^ttjj||||dyr)rr6r rrjrVrrEr|s r0rzTestPowerLogNorm.test_sf s% **--aA6%Hr2z q, c, s, ref)g?r}rru)gR4 -rrrc^ttjj||||dy)Ng|=r|)rr6r r)rjrvrrEr|s r0rzTestPowerLogNorm.test_isf s% **..q!Q75Ir2))(,* Er}rg?)rr}rgv6)rrrg+ 94|7)rurrg?c^ttjj||||dy)Ngt =r|)rr6r rhris r0rSzTestPowerLogNorm.test_cdf s% **..q!Q75Ir2))rgr}rgS^Ռe 9)@xDr[rg 0g;)g\)c=Hr[rg7H7c^ttjj||||dy)NgAfc=r|)rr6r r`ris r0rIzTestPowerLogNorm.test_pdf s% **..q!Q75Ir2N) rrrrrrrrrSrIr8r2r0rfrf s" [[^EF I F I  [[^ACEFJFJ [[^AB J B J [[^GHJ HJr2rfceZdZejj dgddZejj dgddZejj dgddZy ) TestPowerNormr))rfrg|<)rr^ge()rXr}g%!@6)rrugT;-c\ttjj|||dyr)rr6 powernormrrs r0rzTestPowerNorm.test_sf s! **1a0#EBr2rv))rrgĿ)gwJ?rXg!X)rr}g缂U)rr}gͫ1@)rr^gD@)Jz5rgU!zYr@c\ttjj|||dyNrr|)rr6rrrrzs r0rzTestPowerNorm.test_isf s! ++Aq13UCr2))irfg.u T9)r^rf?)rrfgsK-)r:r}gk8>)rr}g^u1-c\ttjj|||dyr)rr6rrrhrs r0rSzTestPowerNorm.test_cdf s! ++Aq13UCr2N) rrrrrrrrrSr8r2r0rprp s [[[CD C D C [[[=>D>D [[[BC D C Dr2rpcfeZdZdZdZdZejjdddgdZ y) TestInvGammac tj5tjdttj j dd}gd}t ||gd}tj j |d}gdtjdd gtjd d gtjtjd gf}t||D]\}}t|| dddy#1swYyxYw) Nrjg(\O3@rSr)g~?gCX&?g*7gS?gBqFq@)皙?@gffffff@)rg Ey?gў3oz?g^Yb?g,r?gOD@g2*Z@gFN8@) rnrorprqr6rrrarrr r)rjrSrOr.rVrs r0test_invgamma_inf_gh_1866z&TestInvGamma.test_invgamma_inf_gh_1866 s $ $ & *  ! !'> :>>''%'@D%H D( +A>>''!V'rjr.r|s r0test_large_entropyzTestInvGamma.test_large_entropyG s ..q13UCr2N) rrrr}rrrrrrr8r2r0ryry sC*& ) [[X?:<= D= Dr2ryc$eZdZdZdZdZdZy)TestFc Btjddgg}|D]#\}}}|j|jg|}%|Dcgc]#\}}}|j|jg|%}}}}|Dcgc]\}}}| }}}}t ||ycc}}}wcc}}}w)N)r^rrK)r6fr`r.r) rjr_f_args_correctansr _correct_corrects r0rzTestF.test_endpointsW s&#&'#' ' Bx"&&&&C '9=== E1vrvvbdd#U#==9=>>!5UI9>>!#w/>>s (B5 BcDtjjddd\}}}}ttj|ttj|ttj|ttj| y)Nr!@rSrT)r6rr rarr:s r0test_f_momentszTestF.test_f_momentsa seWW]]2sF]; 1a A A ABKKN"#r2ctj5tjdttj j dgdzgdddddy#1swYyxYw)Nrjr!r)r^rrr;rSdfndfdrU)rnrorprqr6rros r0test_moments_warningszTestF.test_moments_warningsi sS  $ $ & H  ! !'> : GGMMrd1f,M G H H Hs AA!!A*ctjdgdgg}tjddg}tjj||d\}}}}||dz z gdz}t ||d|dzz||zdz z|z |dz dzz |dz z }t ||d|z|zdz tj d|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 || y) Nrr!rMrSrr^rr;rr)rarr6rrr) rjrrrUrVrErSr v2s2k2numk2denk2s r0test_stats_broadcastzTestF.test_stats_broadcasto suhhbT{#hhBx WW]]sV]D 1aS1Wo q 2 aZ39q= )C /37Q, >#' J2us{Q"''!S1W+"66a2773c A #67792cQsURZ(C#IM:Qw37Q,./0sQw37+sSy1}= U]2r2N)rrrrrrrr8r2r0rrV s0$H r2rc eZdZdZdZdZejjdddgdZ ejjdgd ejjd d d gd d gd d ggd gdgd d gd d ggd gd gggdZ ejjd d d gd d gd d ggd gdgd d gd d ggd gd gggdZ dZ y) TestStudentTc^ttjjddgddgy)Nrrg?g?)rr6rrrros r0test_rvgeneric_stdzTestStudentT.test_rvgeneric_std s"!%''++q!f"5 J7OPr2cttjjddtjtj tj tj fttjjdddtjtj tj fttjjdddtjtj tj fttjjddddtj tjfttjjd d tj tjfttjjd d dtjfttjjd d dtjfttjjd d dy)NrrS)rrU)\(?rxr^gGz@g i@rrgGz@rg ףp= @)rxgq@)rr6rrarrros r0test_moments_tzTestStudentT.test_moments_t sXUWW]]a]8VVRVVRVVRVV4 6UWW]]dF];"&&"&&"&&1 3UWW]]a]8"&&"&&"&&1 3UWW]]dF];/266266: <UWW]]a]68HIUWW]]dD]9C=IUWW]]a]6bff FUWW]]dD]9;RSr2cjgd}gd}ttjj||dy)N)rr^r rX)g?@gTM]?ggY?U?rr|rr6rr>)rjrrOs r0test_t_entropyzTestStudentT.test_t_entropy s' ;+XEBr2zv, ref)rXr)rrcZttjj||dyrr)rjrVr|s r0test_t_extreme_entropyz#TestStudentT.test_t_extreme_entropy s *Ce?S*%z!ZK.'ABr2cTtjjdtj|t}tjj dd|j }tj||<tjj|ddd}tjjddd }tjj||ddd}td D]-}t|||||t|||||/tjj|dd }tjjdd }tjj||dd }t|||t|||y) NrrrWr1rrrS)rr\r]rUr\r]rUrrr[)rarrrrrlr9rr6rrrrr>)rjrrr res_ex_inf res_ex_noinfrs r0test_t_inf_df_stats_entropyz(TestStudentT.test_t_inf_df_stats_entropy s` qZZ $7 YY  q":+;+;  <:ggmmrq6mBZZ%%!1f%E ww}}J;Qa,2%4 q ?A Q +Z] ; Q ,l1o > ?ggoo!o4ZZ''AQ'7 ww"j[/qJ S_j1S*%|4r2cgd}gd}gd}gd}ttjj|||dttjj |||dy)N)rrrWr)rd~QJrmr)gZ_2g 9g!ǟuIgdg)g73?rgմFhAW;gm0_?rzr|)rr6rrr`)rjrVr logpdf_refpdf_refs r0test_logpdf_pdfzTestStudentT.test_logpdf_pdf sS  #@ >q"-zF Ar*G%@r2N) rrrrrrrrrrrrrr8r2r0rr s(Q TC [[X68:; =; = [[Z*<= [[\QFQFQF-6 ,B./VaV,<./S1#J,89C 9= C  [[\QFQFQF-6 ,B./VaV,<./S1#J,895 95& Ar2rcTeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zy )TestRvDiscretecBtjjdyr+r,ros r0r-zTestRvDiscrete.setup_method r.r2c gd}gd}d}tjd||f}|j|}tt |t j t||D]7\}}ttt||k(t|z |z dk9|j}tjt|tjsJy)N)rrrr^rr)rxrur'rxrurxrsample)namevaluesr1r)r6r;rr r;r8r[r rrdrrarrinteger)rjstates probabilitysamplesrrVrErms r0rAzTestRvDiscrete.test_rvs s$4    8V[4I J EEwE  1emm,- , @DAq CAF E'N2Q67$> ? @ EEG}}T!Wbjj111r2c:tjgd}tjgd|f}t t || }|j }t||tjgdgdf}|j }t|dy)N)rcrrurr)rKrrrx) rarr6r;rdrr>rr)rjr<rmrfrgs r0rhzTestRvDiscrete.test_entropy sy*+   i%7 8%u-.. IIK:&   i%= > IIKQr2cgd}gd}tj||f}ddgddgg}t|j|dd gd d ggd y)Nr`rsrurrrKrrRr^rsrrxrurzr)r6r;rrG)rjxkpkrirVs r0razTestRvDiscrete.test_pmfs]     r2h /"X!W q sc$*/ 1r2cgd}gd}tj||f}gd}gd}t|j||dt|Dcgc]}|j|c}|dycc}w)Nr`rr)rrKr{rrwrRrr)rrsrsrsrrrrrzr)r6r;rrh)rjrrrix_valuesrOrs r0rSzTestRvDiscrete.test_cdfsf     r2h /55x((? h77 u .7A2cgd}gd}tj||f}gd}gd}t|j||dt|Dcgc]}|j|c}|dycc}w)Nr`rr)rTrsr rrrK)rrr^r^rrrzr)r6r;rr)rjrrriq_valuesrOrvs r0r\zTestRvDiscrete.test_ppfsf     r2h /0%x((? H5q5 u .5rc gdgdf}tj|}t|j|j |j dddz|j ddy)N)rr^rrr;)rTrrururTrrrr)r6r;rrrhr)rjr?ris r0test_cdf_ppf_nextz TestRvDiscrete.test_cdf_ppf_next*sU!:;   d +266"&&s"4t";<559 &r2cDtjdjd}tjgdgdgdg}t j ||f}t |jtj|j|jzdy)NrM)rr)rTrTrr)rTrTrrrrzr) rar rrr6r;rrrdrrrjrrris r0test_multidimensionz"TestRvDiscrete.test_multidimension2ss YYr] " "6 * XX---/0  r2h / RVVBEEBEEM%:Gr2cgd}ddg}tttjfit ||fgd}tttjfit ||fgd}gd}tttjfit ||fgd}gd}tttjfit ||fddg}ddg}tttjfit ||fy)Nrrsr)rs333333?gffffff濩rr^rrr)rururururr)rr r6r;r rjrrs r0test_bad_inputzTestRvDiscrete.test_bad_input;s 3Zj%"3"3MtB87LM j%"3"3MtB87LM  j%"3"3MtB87LM  'j%"3"3MtB87LMV3Zj%"3"3MtB87LMr2cntjdjdtjdd}}t t t jfit||ftjdjdtjdd}}t t t jfit||ftjdjdtjdd}}tt j||fjddy) Nrr^r^r^rgUUUUUU?rrrr^r) rar rrrr r6r;r rrGrs r0test_shape_rv_samplez#TestRvDiscrete.test_shape_rv_sampleOs1%%f-rwwvs/CBj%"3"3MtB87LM1%%f-rwwvs/CBj%"3"3MtB87LM1%%f-rwwvs/CBU&&r2h7;;A>Dr2cgd}gd}tj||f}t|jt j |j |jzdy)N)rr^rrrr!)rTrrrrrTrrzr)r6r;rrrardrrrs r0 test_expect1zTestRvDiscrete.test_expect1^sG  +   r2h / RVVBEEBEEM%:Gr2c tgd}gd}tj||f}t|j|j dt|jt dt ||Ddt|jdt dt ||Ddy) 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:?rxgF%uk?g:vz?rxrxg.nr?g|гY?rxrxrxg@6*?4U0*C?g@ +?gC6z?gnr?g ?gOjM?g n?g1w-!?g:pΈ?gףp= ?g_Le?rxg^)p?g~jtx?gJ4q?gGzt?gJ4q?gMb@?g@Psׂ?g@^)ˀ?rxrxgN@s?g1w-!_?rgൄ|г?rxgH}}?rxg F%u?rxrxg^)ˀ?gv?rxrrzrc3,K|] \}}||zywrmr8r\rVws r0 z.TestRvDiscrete.test_expect2..s9daAE9sc |dzSNr^r8rs r0rFz-TestRvDiscrete.test_expect2.. AqDr2c32K|]\}}|dz|zyw)r^Nr8rs r0rz.TestRvDiscrete.test_expect2..s<AAqD1H"',,"2"21"5 7!%"2"2"6"6qA"6">"',,"2"21"5 7!%"2"2"6"6qA"6">"',,"2"21"5 7r2ctjjdtjjddzdz }tjjddzdz }gd}gd}t t j j|||t t j j|||t t j j|||y)NrrWr^rr) 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?) rarrrrr6rr`rhr)rjr.rVr`rhs r0test_skewcauchy_Rz TestSkewCauchy.test_skewcauchy_Rs& q IINN2  "Q & IINN2  #a '%$ ((,,Q2C8((,,Q2C8((,,S!4a8r2N)rrrrrr8r2r0rrs 7 9r2rc~eZdZdZej dZejjdgddZ y) TestJFSkewTcdx}}|dz}gd}gd}tj||}tj|}t|j ||j |t|j ||j |t|j ||j |t|jd|jdy)Nrr^)rrxrKrw)rxrTrcrrrKrS)r6 jf_skew_trrr`rhr)rjr.r/rrVrvjfrs r0test_compare_tzTestJFSkewT.test_compare_ts A U ! - __Q " GGBKq 1558,q 1558,q 1558,(!''&/:r2ctjttjdz }tj j |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)raloadr__file__parentrec fromarraysrs r0gamlss_pdf_datazTestJFSkewT.gamlss_pdf_datasAww N ! !$H H vv  [ 99r2za,b)r)r;r)rM c||d|k(|d|k(z}|d|d}}t|tj||j|dy)zCompare the pdf with a table of reference values. The table of reference values was produced using R, where the Jones and Faddy skew t distribution is available in the GAMLSS package as `ST5`. r.r/rVr`rr|N)rr6rr`)rjrr.r/rrVr`s r0test_compare_with_gamlss_rz&TestJFSkewT.test_compare_with_gamlss_rs_  S !Q &?3+?1+D E cDK3U__Q266q9Fr2N) rrrrrr0rrrrr8r2r0rrsH;  ^^ : : [[U$>? G@ Gr2rr^rg@rgףp= 1@r5gRZ@igS㥛Ԋ@rTrUg&@iQi'i0ybilHO1Zi3r.irWirXikri1rii4i Ni(lEI.@ iceZdZdZdZdZdZdZdZdZ e jjde d Zd Zd Zy ) TestSkewNormc$td|_yr+)rrros r0r-zTestSkewNorm.setup_methods%d+r2ctjddd}ttjj |dtj j |yr)rarPrr6skewnormr`rrs r0 test_normalzTestSkewNorm.test_normalsB KKAs #!%.."4"4Q!"4"<"'**.."3 5r2cd}tjjd||j}t ||j tjjd||j}t ||j y)N)rrrr)r.rrr.)r6rrrrr9)rjr9rVs r0rAzTestSkewNorm.test_rvssa NN  E  IUAGG$ NN  %dhh  GUAGG$r2ctjjdtddd|j}t j |t j|tj|tj|g}tjjdddd}t||dtjjd tddd|j}t j |t j|tj|tj|g}tjjd ddd}t||dy) Nrrrr^)r.rr\r]rrS)r.r\r]rUrNr) r6rrrZrrarrrkurtosisr)rjXrOrs r0rWzTestSkewNorm.test_moments"s  NN  Sq,0HH  6GGAJq 5::a=%..:KL>>''!!V'L!(Ha@ NN  #c(,0HH  6GGAJq 5::a=%..:KL>>''"!1f'M!(Ha@r2cgdgdgdgdgdgdgdg}|D]4\}}}tjj||}t||d 6y) N)rrgEAV)rrgV|@$a)rrg0rY)rrsZk)rBrr")rrļ)r^gcr#rr|)r6rrr)rj logpdfvalsrVr. logpdfvalrps r0test_pdf_large_xzTestSkewNorm.test_pdf_large_x/sY 2 3 0 2 4 5 5  * 8OAq)>>((A.D D)$ 7 8r2ctjjgdd}t|t j ddtjjdd}t|ddy) N)rWrr0rrrzr|r r rK)r6rrhrraonesrs r0test_cdf_large_xzTestSkewNorm.test_cdf_large_x?sP NN  |R 02771:E2 NN  r3 '3U+r2cgdgdgdgdgdg}|D]d\}}}tjj||}t||dtjj | | }t||dfy)N)rdrgzbLe9)rr^gn'/2;)rrg::)rMrg|<)rrrrr|)r6rrhrr)rjcdfvalsrVr.cdfvalrms r0test_cdf_sf_small_valuesz%TestSkewNorm.test_cdf_sf_small_valuesHsy . + , . /  $ 2LAq&""1a(A AvD 1!!1"qb)A AvD 1  2r2z a, momentsct|dD]3\}}tjj||}t ||d5y)Nr)startrzr|)rr6rrr)rjr.rUorderrOrNs r0test_noncentral_momentsz$TestSkewNorm.test_noncentral_momentsYs>(: 7OE8..''q1C C 6 7r2c Xtjjd}d\}}}tj|||}|j d|}tjj |dd\}}} tjj |dd\} } } || cxk(rdk(sJJ|| k7sJtjj |ddd \} }}|dk(sJtj| ||}|jd }tj|tj|f}t||tjj d d|}tjj |}tjtj|sJtjj |d \}}}tj|sJtj|tj|}}t|||tjdtj z zzt||dzd dtj z z ztjj |d\}}}tjj | d\}}}t|||g| | |gtjj |d \}} }!tjj | d \}"}#}$t|"|#|$g| | |!gy)Nl# ke)rr6rsrXrrrrgmmrmethodmsrTrr5r^mle)rarrr6rrrrrrr9rrisinfrrrb)%rjrr.r\r]rKra2loc2scale2a3loc3scale3a4loc4scale4dist4rr|ra5loc5scale5rUrVa6ploc6pscale6pa6mloc6mscale6ma7ploc7pscale7pa7mloc7mscale7ms% r0rzTestSkewNorm.test_fit_sii##$78$ 3~~ae,hhCch2!>>--c4a-@D& >>--c4a-@D&t q     Rxx!>>--c1Qt-LD&{{r40kk$k'ggclEJJsO+S!||#>nn  &vvbkk#&'''!>>--d4-@D&xx||wwt}bffTl14&2771RUU7+;";;<619AI 67$nn00U0CUG#nn00#e0DUGeW-ufg/FG#nn00T0BUG#nn00#d0CUGeW-ufg/FGr2cX tjgdddgzzdgz}tjj |}tjj ||}tjj |d}tjj ||}||dz ksJtj jd d d d d } fd }tjtj|||}tjj||jdy)N)r:rrrMrrT)superfitrsly ND)r:r)rrW)rzrWr.r\r]c t||S)N)r)r$)funrrs r0 optimizerz0TestSkewNorm.test_fit_gh19332..optimizers)#vC@ @r2)rXrr|) rarr6rrrrrtestingrparams) rjrVrZr params_superr|rrX fit_resultrs @r0test_fit_gh19332zTestSkewNorm.test_fit_gh19332s HH*R1#X5; <##A&nn!!&!, ~~))!d); nn!!,2S3Yii##$78y;G AYYu~~q&IN  ""6:+<+<4"Hr2N)rrrr-rrArWr&r)r-rrr_skewnorm_noncentral_momentsr1rr]r8r2r0rrsZ,5 % A8 ,2" [[\+GH7I7 .H`Ir2rc$eZdZdZdZdZdZy) TestExponcVttjjddyr)rr6rr`ros r0 test_zerozTestExpon.test_zerosU[[__Q'+r2cttjjddttjj tjj ddy)Nrr)rr6rrhrrros r0 test_tailzTestExpon.test_tails=U[[__U+U3U[[__U[[^^B%78"=r2ctjdddddtjg}ttt j j|yNo_?46@yX5ͻ@j+?UX @)rarrrr r6rrrs r0test_nan_raises_errorzTestExpon.test_nan_raises_error5 HHfffffbffE Fj%++//15r2ctjdddddtjg}ttt j j|yrf)rarrrr r6rrrs r0test_inf_raises_errorzTestExpon.test_inf_raises_errorrmr2N)rrrrbrdrlror8r2r0r`r`s,>6 6r2r`cfeZdZdZdZdZejjdddgdZ y) TestNormctjdddddtjg}ttt j j|yrf)rarrrr r6rrrs r0rlzTestNorm.test_nan_raises_error5 HHfffffbffE Fj%**..!4r2ctjdddddtjg}ttt j j|yrf)rarrrr r6rrrs r0rozTestNorm.test_inf_raises_errorrsr2cbgd}tttjj|dy)Nrshrimp)plate)rrr6rrrs r0test_bad_keyword_argzTestNorm.test_bad_keyword_args i(Cr2r\rrcd}tjjd|zd|z|}t||dtjjd|z d|z | }t||dy)Ngg {F.:r!rMr\rr|)r6r _delta_cdfr)rjr\rOrs r0test_delta_cdfzTestNorm.test_delta_cdfsm) %%bfbf#%>xe4 %%3i2c6%Exe4r2N) rrrrlrorxrrrr|r8r2r0rqrqs;5 5 D [[UQF+ 5, 5r2rqceZdZdZdZdZy) TestUniformgh-10300ctjdddddtjg}ttt j j|yrf)rarrrr r6rlrrs r0rlz!TestUniform.test_nan_raises_error7 HHfffffbffE Fj%--"3"3Q7r2ctjdddddtjg}ttt j j|yrf)rarrrr r6rlrrs r0roz!TestUniform.test_inf_raises_errorrr2N)rrr__doc__rlror8r2r0r~r~s8 8r2r~c 6eZdZdZdZdZdZejjdgddZ ejjdgd gd gd gd gd gdZ ejjdgdgdgdgdgdgdgdZ y) TestExponNormc2d}d\}}}d||zz }tjj|||d}t|||||d\}}}d||zz }tjj|||d}t|||||d\}}}d||zz }tjj|||d}t|||||d\}}}d||zz }tjj|||d}t|||||y) Ncdd||zdzz z}d||zdzz |dzz}dd||zdzzdzz}|d|z z||zd||zz z||gS)NrKrr^rr@rr8)lamsigropK2exp_skewexp_kurts r0get_momsz,TestExponNorm.test_moments..get_momsszc#g\))DC#I>)D4L8Ha39q.0B77H3JC#s3w- 78L Lr2)rrrrKrSr)r.r^rT)rrr)r:r!r6)r6 exponnormr)rjrrrrKstss r0rWzTestExponNorm.test_momentss. M C 39 oo##A2S&#IC#sB!78! C 39 oo##A2S&#IC#sB!78 C 39 oo##A2S&#IC#sB!78" C 39 oo##A2S&#IC#sB!78r2ctjdddddtjg}ttt j j|ddy Nrgrhrirjrkrrr)rarrrr r6rrrs r0rlz#TestExponNorm.test_nan_raises_error; HHfffffbffE Fj%//"5"5qqKr2ctjdddddtjg}ttt j j|ddyr)rarrrr r6rrrs r0roz#TestExponNorm.test_inf_raises_errorrr2cTttjjdddttjjdddttjjdddttjjdddy)Ni|rrxru)rr6rr`ros r0test_extremes_xzTestExponNorm.test_extremes_x snEOO//a8#>EOO//a8#>EOO//d;SAEOO//d;SAr2zx, K, expected))rrug6 N-)rrug՜n+H?)rrugi?)rrugbJI-)rWrgI8?)rWr*gQ3|-0?c\ttjj|||dyru)rr6rr`)rjrVrrOs r0 test_std_pdfzTestExponNorm.test_std_pdfs! ++Aq18%Hr2zx, K, scale, expected)rrurgVAҤ?)r:{Gzt?rg'^ >)r rurXrx)r rurgbr ;)rr[rgVMe?c~tjj|||}|dk(r|dk(sJyt||dy)Nrrxrr|)r6rrhrrjrVrr]rOrms r0test_cdf_small_KzTestExponNorm.test_cdf_small_K5s= OO  1E  2 s?8O8 Axe 4r2)rWrurgh G}$;)r^rrg ]fJ?)rrrsg31"g#;)rWrrsgf +-)rrrsrx)r.r[rga9S?c~tjj|||}|dk(r|dk(sJyt||dy)Nrrx-a=r|)r6rrrrs r0test_sf_small_KzTestExponNorm.test_sf_small_KNs= OO  q!5  1 s?8O8 Axe 4r2N) rrrrWrlrorrrrrrrr8r2r0rrs96L L B$ [[-BCICI [[4>D4G? AB 5 B 5& [[4B@DF3@ BC5C5r2rceZdZdZdZej jdgddZej jdgddZ y) TestGenExponcddlm}tjj t j dddddd}t||dddy) Nr)simpsonrWrursrw)dxr)scipy.integraterr6genexponr`r8r r)rjrrms r0test_pdf_unity_areaz TestGenExpon.test_pdf_unity_area^s?+ NN  u||Ar48#sC HGA$/A6r2ctjjtjdddddd}t tj d|k|dkzy)NrrWrursrwr)r6rrhr8r r r)rjrhs r0test_cdf_boundszTestGenExpon.test_cdf_boundsdsGnn  aT!:CcJ 18q123r2z x, p, a, b, c))r5gM((++Aq13WE((,,S!4aeDr2N)rrrrr8r2r0rrsEr2rceZdZdZy) TestExponpowcttjjdddttjj tjj ddddy)Nr rwryrr)rr6exponpowrhrrros r0rdzTestExponpow.test_tailsLENN..ub95AENN..u~~/@/@B/GL r2N)rrrrdr8r2r0rrsr2rceZdZdZdZdZy) TestSkellamctjdd}d\}}tjgd}ttj j ||||dy)Nrr5r6)gYjP'?g$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~?rN)r8r rrr6skellamrG)rjrSmu1mu2skpmfRs r0razTestSkellam.test_pmfsO LLb !S - . EMM--ac:FBOr2ctjdd}d\}}tjgd}ttj j ||||dy)Nrr5r6)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?rrN)r8r rrr6rrh)rjrSrrskcdfRs r0rSzTestSkellam.test_cdfsO LLb !S - . EMM--ac:FANr2cd\}}}ttjj|||ddttjj |||ddy)N)rrgs1Crrzrr)rr6rrGrh)rjrVrrs r0test_extreme_mu2zTestSkellam.test_extreme_mu2sK. 3 ))!S#6F ))!S#6Fr2N)rrrrarSrr8r2r0rrsP*O*Gr2rc eZdZdZdZej ddZejjdddgejjd gd ejjd gd ejjd e ddDcgc]}d|vr| c}}e jddZ dZycc}}w) TestLognormctj5tjdttj j gdd}t|gddddy#1swYyxYw)Nrjrrsrr)rxg~r?ge3E?)rnrorprqr6rr`rrjr`s r0rIzTestLognorm.test_pdfsZ $ $ & J  ! !'> :--##K3C %c+H I J J Js A A))A2c d\}}}ttjj||z |tjjt j ||z |z ttjj||z |tjjt j ||z |z y)N)g(\5i@gOn?rD)rr6rrrrarrs)rjrrsigmas r0rzTestLognorm.test_logcdfs* B ((B%(8 bffRUmE&9: < ++BrEU+; ((2u)<= ?r2r#r$c@tjjdSr+r'ros r0rzTestLognorm.rngr(r2rrTr^r)rrr^r)rrrrJ)FTrrKFrMrNctjjd||||}i} |r|| d<|r|| d<|r|| d<ttj|fi| ddiy)NrX)rrEr]r\rrrrrT)r6rrrrQs r0rz'TestLognorm.test_fit_MLE_comp_optimizersu}}  cYi%,3!@ "DJ "DL &DN &emmT a"&&!"56r2cfgd}tttjj|dddy)NrTrsr rrrv)rrrw)rrr6rrrs r0test_fit_bad_keyword_argsz"TestBeta.test_fit_bad_keyword_argss$ i1$ &r2cdgd}tttjj|ddy)Nrrs)fafix_a)rr r6rrrs r0#test_fit_duplicated_fixed_parameterz,TestBeta.test_fit_duplicated_fixed_parameter"s! j%**..!3Gr2zOverflow, see gh-14901reasoncfd\}}}ttjj|||dy)N)g?gR@g0xAgx)>)rr6rr)rjrmr.r/s r0test_issue_12635zTestBeta.test_issue_12635(s+71a q!Q/1FGr2c0tjgd}tjgd}d}tjj ||dzd|z }t ||tjj ||dzd|z }t ||y)N)g@3@?g^?gNC?)rWrXrr$rr)rarr6rrrr)rjinv_R count_listrminvrs r0test_issue_12794zTestBeta.test_issue_127944s~12XXo. jjnnQ Q0CDU#jjmmCa*1DEQr2cd}tjdd}d}d|z |dz||z }}}tjj |||}tjj |||}t |d|z y)Nh㈵>rrr)rar r6rrrhr) rjalpha_2count_nobsrvr.r/rrs r0test_issue_12796zTestBeta.test_issue_12796Fsq1b!g+vz4&=a1jjnnQ1%jjnnS!Q'Q[)r2chd\}}ttjjd||tj d\}}ttjjd||tj d\}}ttjjd||dttjjd||dd\}}ttjjd||dttjjd ||dy) NrQr)rrr)rrr+ph)rrrK)rr6rr`rar)rjr.r/s r0rzTestBeta.test_endpointsRs1UZZ^^Aq!,bff51UZZ^^Aq!,bff51UZZ^^Aq!,a0UZZ^^FAq1151UZZ^^Aq!,a0UZZ^^Ha3Q7r2z!Does not warn on special codepathcd\}}}tjt5tjj |||dddy#1swYyxYw)N)gףp= ?gvH7B@0B)rwarnsrqr6rr)rjrvr.r/s r0test_boost_eval_issue_14606z$TestBeta.test_boost_eval_issue_14606isB'1a \\. ) $ JJNN1a # $ $ $s "A  Ar5a, b)r)@)rrc<d} ||||y#t$rYywxYw)Nr) OverflowError)rjr5r.r/rms r0 test_beta_ppf_with_subnormal_a_bz)TestBeta.test_beta_ppf_with_subnormal_a_bos-   1aO   s  r))rsrsgο)r[rg)rr*g&׾k )rrg*)Mc`ttj||j|yrmrr6rr>rs r0rhzTestBeta.test_entropys"  1a(002C8r2za, b, ref, tol))rrWgCprz)rWrg8EOr)gNAgNAg(4Fr=)gSAgSAg8TAUr)rg _Bg[VVuD&r$)rrgR#Lr{)r^rg?r5r$)r^rm\rz)rWrgnQc}4r=)rWrmg{CErz)rWr%\rz)rmr^rrz)rmrrrz)rrWrrzcdttj||j||yrHr)rjr.r/r|rs r0rzTestBeta.test_extreme_entropys%H  1a(002CcBr2N)rrrrqrrrrrskipif MACOS_INTELrrrrxfailrrr6rrrrrhrr8r2r0rrsy,7& H  [[ ,DE HF H [[ ,DE F " [[ ,DE *F *8. [[AB$C$  [[X  'GH [[Vnn%EFGI@ [[[DE 9 E 9 [[ . C/. Cr2rcTeZdZgdZdZdZejjdgddZ ejjdedZ ejjd egd zd Z ejjd d d gdZ dZ dZdZy) TestBetaPrime) )rgY@rD>?)rrrm嗽?)rrrTgPK?)rrrg%p?)r rrTg#|/?)r rrgsM <)r rr$5Є*?)^ 9^;rrTgompP?)rrrg7j"!9)rrrz ^J?)rrrTgܷ"+>)rrrgrNs: )rrrgK>cXd\}}tjgd}tj||}t tj |j |jt|j|tj|j |y)Nrr) rarr6rr rrrrr`rrs r0rqzTestBetaPrime.test_logpdfsn t HH_ % OOE4 ( AHHQK(,,./a"&&!"56r2c tjjddd}t|dd\}}t j gd}tjj|||}t t j|jtjj}|Dcgc]}|tj|||}}t||ddycc}w) Nrrrurxrr-=r) r6rrhrrarr rrr< _cdf_singler)rjrVrrr6gen_cdfr@cdfs_gs r0rSzTestBetaPrime.test_cdfs OO  3 ,Q t HH_ %""1eT2 D!%%'(%%11HIJ'%//3t<JJf159Ks5 C'zp, a, b, expected))ru?r gV)?)rrr gWJB9*=)rrr gOGJ<)rPrc@gΣ01)?rcrg8ǘ`?)>q?rrTgMDcbtjj|||}t||dyr)r6rrr)rjrmr.r/rOrVs r0r\zTestBetaPrime.test_ppfs( OO  1a (8%0r2z x, a, b, pc^ttjj||||dyr)rr6rr)rjrVr.r/rms r0test_ppf_gh_17631zTestBetaPrime.test_ppf_gh_17631s!++Aq!4aeDr2zx, a, b, expected))rrrrv)rrrTgV[?)rgrrTrc^ttjj||||dyr)rr6rrh)rjrVr.r/rOs r0test_cdf_gh_17631zTestBetaPrime.test_cdf_gh_17631s# ++Aq!4hUKr2)rrrTg%?)rrrgoXr?cptjj|||}|dksJt||dy)NrKgh㈵>r|)r6rrhr)rjrVr.r/rOrs r0test_cdf_extreme_tailsz$TestBetaPrime.test_cdf_extreme_tailss3 OO  1a (3ww8$/r2cgd}gd}gd}gd}tjj|||}t||dy)N)rrr^rrrrrrrrrrr)rr^rrTrTrTrTrrrrrrr)rrmꌠ9Y>)Frgr rrrgrr rrrr )g/:g U/7gKH9g<![a?gw 4?g)J?g5?rrrrg%?gsM s7 6QqI !q!''/r2ctjdg}tjdddgj d}t ||y)NgooB?r^rgffffff@r)rarr6rrr)rjr|rs r0test_moment_gh18634z!TestBetaPrime.test_moment_gh18634Es<vv()ooa#s,33A6S!r2N)rrrcdf_valsrqrSrrrr\rrrrrr!r8r2r0rrsH 7:> [[ B11 [[\84E5E [[   L L [[ . / 120 204*0 "r2rc FeZdZdZdZdZdZejjdddgdZ ejjd gd d Z ejjd gd ejjdgdejjdgd ejjdddgejjdddgejjdddgdZ y) TestGammactjjddd}t|dtjjddd}t|dy) NZirrg CTb?rrWgBΖ?)r6rVr`rrs r0rIzTestGamma.test_pdfRsFkkoob#To2C-kkooa4o0C+r2c\tjjdd}t|dyr)r6rVrrrs r0rqzTestGamma.test_logpdfZs$##Aq)FA&r2cdgd}tttjj|ddy)Nrrrv)rrw)rrr6rVrrs r0rz#TestGamma.test_fit_bad_keyword_args`s i!!8Lr2ctjtjj ddddsJtjtjj dddd sJy) NrPrgplC@rzrrsrXg1}t@r)raiscloser6rVrros r0rzTestGamma.test_isfds\"zz%++//%3+%9 99zz%++//%5+%9 99r2r]rKrLcrtjj|dz|dzd|}t|ddy)Nrrrg>S*rr|)r6rVr{rrjr]rs r0r|zTestGamma.test_delta_cdfzs6 &&uSy%)Qe&L6UCr2z a, ref, rtol))rgt.r{)r^rrr{)rXgX>k-־ @r)rgwM7@r{)gNgmCg%og$6@r{)roܘ#]@r{cZttjj|||yrH)rr6rVr>)rjr.r|r}s r0rhzTestGamma.test_entropys  ++A.$?r2r.)rurrr\)rurrrTFrrc.tjjd}tjj |||d|}i} |r|| d<|r|| d<|r|| d<dt | z } | dk(rId } tjt| 5tjj|fd d i| dddytjj|fd d i| } tj| } | d k\r-t| jtj|| dk\r1t| jdtj|dz| dk\r2t| jdtj|dzyy#1swYyxYw)NrrXrrrrrrrrr5r3rr^)rarrr6rVrrrr r rrrr)rjr.r\r]rrrrrrrSrthetarKs r0 test_fit_mmzTestGamma.test_fit_mmsWii##$78{{qcS,/1 DJ DL "DNCI  A:MIz; ; :T:T: ;  :T:T:{{E" A: DIIK 7 A: DKKNBGGD!G,< = A: DKKNBGGD!G,< =  ; s #F  FN) rrrrIrqrrrrrr|rhr3r8r2r0r$r$Qs,' M9, [[WsCj1 D2 D [[^BC@C@ [[S.1 [[UN3 [[Wn5 [[WtUm4 [[Yu 6 [[[4-8>975642 >r2r$cd}tjd|dzz d|dzz dd}t|jddy) Nr[g;f?r^rrr[rKgV{q@)r6r*rr`)jitterZs r0test_pdf_overflow_gh19616r7sCF 6FAI-q619}!1MAAEE#J 12r2ceZdZdZej j dgddZej j dgddZej j dgdd Z d Z y ) TestDgammactjjd}d}|jd|}|j d|}t j j||}t jjtj||dz }t||t j |}t|j||dy)NlOP($rWr)r&rr^ryr|) rarrnormalrlr6dgammar`rVrr)rjrrrVr.rr|rKs r0rIzTestDgamma.test_pdfsii##$78 JJRdJ + KKRdK +llq!$kkoobffQi+a/S!||A Su5r2zx, a, expected))rrggrU>)rBrg$IC<)irg2Wj<)rg~)A.=)rrgf?cxtjj||}t||dtjj ||}t||dtjj | |}t||dtjj ||}t|| dyr/)r6r<rhrrrr)rjrVr.rOrhrrrs r0test_cdf_ppf_sf_isf_tailz#TestDgamma.test_cdf_ppf_sf_isf_tailsllq!$XE2llx+QU+ \\__aR #H51llx+aRe,r2r))rgmqn@)?g?)r{gx?cZttjj||dyrrr6r<r>rs r0rhzTestDgamma.test_entropys  ,,Q/5Ar2))rr)r g>_)rg5i)rgo@)rIg4Fa3@)rgrO]@cZttjj||dyr rBrs r0test_entropy_entreme_valuesz&TestDgamma.test_entropy_entreme_valuess"  ,,Q/5Ar2ctjgd}tjj |}t t |D],}||tjj ||k(r,Jy)N)rrrmr)rarr6r<r>rr)rjrVrrs r0test_entropy_array_inputz#TestDgamma.test_entropy_array_inputsa HH' ( LL  #s1v 6AQ45<<//!55 55 6r2N) rrrrIrrrr?rhrDrFr8r2r0r9r9s 6, [[-:; - ; - [[X89 B 9 B [[X:; B; B6r2r9c`eZdZdZdZej jdgddZy)TestChi2cttjjddddttjjddddy)Nrgޞw1D?rrNrXg6:֜?rr6chi2r`ros r0rzTestChi2.test_precisions@EJJNN468N$& (EJJNN346J$& (r2c|d}tjjd|}t|ddtjjd|}t|ddd}tjjd |}t|d dtjjd |}t|d dy) Nrgλm:=6g'bd5)rgƯʉ?)rXgn>@)g͔v0@)rIg9:3@cbttj|j|dyr)rr6rKr>rs r0rhzTestChi2.test_entropy;s!  2..0#EBr2N) rrrrr\rrrrhr8r2r0rHrHs9( F0 [[Y:; C ; Cr2rHcfeZdZdZdZdZejjdddgdZ y) TestGumbelLctjdd}tjj |}tjj |}t ||yNr)r)rarPr6r2rhrrrs r0rzTestGumbelL.test_cdf_ppfGsD KKb ! NN  q ! ^^   "2r2ctjdd}tjj |}tjj |}tj |}tj| }t||yrR) rarPr6r2rrsrrexpm1r)rjrVrr/urVs r0ruzTestGumbelL.test_logcdf_logsfMsb KKb ! NN ! !! $ NN  # FF1I ]]1  1r2ctjdd}tjj |}tjj |}t ||y)Nrr)rarPr6r2rrrrs r0rzTestGumbelL.test_sf_isfUsD KKQ  NN  a  ^^   "2r2r\rrctjjd|}tjj||\}}t ||y)NrX)rr\r)r6r2rrr)rjr\r fitted_locrs r0test_fit_fixed_paramz TestGumbelL.test_fit_fixed_param[sD~~!!s!4**4c*: AZ%r2N) rrrrrurrrrrYr8r2r0rPrPEs:   [[URG,&-&r2rPceZdZdZdZy) TestGumbelRcZttjjdddy)Nr3?~T}%m;rzr|)rr6r1rros r0rzTestGumbelR.test_sffs# ))"-/E" $r2cZttjjdddy)NrPr*rzr|)rr6r1rros r0rzTestGumbelR.test_isfos# **513D" $r2N)rrrrrr8r2r0r[r[ds $$r2r[cp eZdZejddZejdZejdZejdZejjdejdejd ejj gejjd d d gejjdgdejjdddgdZ ejjejjdddgdZdZejj!dejjdddgejjdd d gdZd Zd!Zd"Zejjd#ejgd$gd%gd&ejgd'gd(gd)ejj ejgd*ej,d+d,d-ej,d.dd/ejj. gd0Zejjd#ejgd$gd%gd&ejgd'gd(gd)ejj ejgd*ej,d+d,d-ej,d.dd/ejj. gd1Zejjd2d3dgejjd4d5d6gd7Zejjd8d9d:gd;d:ggd<Zejjd=d>d3ej8ej:ej:fgd?d@ggdAZejjdBgdCejjdDej@jBdEej,dFd3dGdHfej@jDdEej,dFd3dGdHfej@jBdIej,d3dJdGdEfej@jDdIej,d3dJdGdHfgdKZ#ejjdLgdMdNZ$ejj ejjdLgdOdPZ%yQ)RTestLevyStableT)autousecdtj_dtj_dtj_tj j tj_y)z2Setup default parameters for levy_stable generatorS1 piecewiseN)r6 levy_stableparameterizationcdf_default_methodpdf_default_method _levy_stable _QUAD_EPSquad_epsros r0reset_levy_stable_paramsz'TestLevyStable.reset_levy_stable_paramszsH.2*/:,/:,%*%7%7%A%A"r2ctjttjdz }tj j |jd}|S)a Sample data points for pdf computed with Nolan's stablec See - http://fs2.american.edu/jpnolan/www/stable/stable.html There's a known limitation of Nolan's executable for alpha < 0.2. The data table loaded below is generated from Nolan's stablec with the following parameter space: alpha = 0.1, 0.2, ..., 2.0 beta = -1.0, -0.9, ..., 1.0 p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5, and the equivalent for the right tail Typically inputs for stablec: stablec.exe << 1 # pdf 1 # Nolan S equivalent to S0 in scipy .25,2,.25 # alpha -1,-1,0 # beta -10,10,1 # x 1,0 # gamma, delta 2 # output file z.data/levy_stable/stable-Z1-pdf-sample-data.npyx,p,alpha,beta,pctr rar rr rrrTrs r0nolan_pdf_sample_dataz$TestLevyStable.nolan_pdf_sample_datasL6ww N ! ! < = vv  /C D r2ctjttjdz }tj j |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.npyrnr rors r0nolan_cdf_sample_dataz$TestLevyStable.nolan_cdf_sample_datasMJww N ! ! < = vv  /C D r2cdtjttjdz }|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)rar rr rrs r0nolan_loc_scale_sample_dataz*TestLevyStable.nolan_loc_scale_sample_datas/ww N ! ! ? @  r2 sample_sizer3rmarksrfS0rcz alpha,beta))rKr)rKr)rr)rrsz gamma,deltarrrc|tj_tj||||}tj|j |d|j \}} | dkDsJy)N)rrr]r\rrr)r6rerfrrrh) rjrfrrrVrrvlsrrms r0rAzTestLevyStable.test_rvssb&.>*   d%U || FF $F 7 14xxr2rrsrctjjdd}d}d}tjj ||||d}tj |d||||f\}}|d kDsJy ) z3Additional test cases for rvs for alpha equal to 1.h:rKrsrrr\r]rrerruN)rarrr6rerr)rjrrr\r]rVstatrms r0test_rvs_alpha1zTestLevyStable.test_rvs_alpha1sv y!    ! !%3e'+ " -,,q-%*D#u$=?a4xxr2czgd}tjj|\}}}}t|dddt |ddt |dd t |d d|gd z}tjj|\}}} } t |dt |d t | d d t | dd y)N)wgrrxrxrxrx羼u?rrrr67',?rrrrtA}˜.?rrrrGz?rrur])\(̿r^gۧ1?rg9]c?)rrrrrrgv?r)r6rerrrr rjrValpha1beta1loc1scale1ralpha2beta2r;r<s r0rzTestLevyStable.test_fit s  ',&7&7&A&A!&D#tV148E4+FGQ/ '1 9 9&+&7&7&A&A"&E#tVVQUBFFA.D&!,r2zUnknown problem with fitstart.rzalpha,beta,delta,gamma)rr'r^r)rKr'r^rparametrizationc|tj_tjj||||dd}tjj |}|\}} } } t ||||g|| | | gdy)z7Test that fit agrees with rvs for each parametrization.r*rrrur|N)r6rerrrr) rjrrrrVrrr alpha_obsbeta_obs delta_obs gamma_obss r0 test_fit_rvszTestLevyStable.test_fit_rvs!s-<)  $$ 4U%e$% ))$/471 8Y  D% ' )Y 7 r2cNtjgd}tjj |\}}}}tjj | \}}}} t |d|dk7sJt ||t || t || t | |y)N rrrrrWrWrWr0r0rXrXrr)rarr6rerrr) rjrVrrrrrrr;r<s r0test_fit_beta_flipz!TestLevyStable.test_fit_beta_flip:s HH? @&+&7&7&A&A!&D#tV&+&7&7&A&A1"&E#tVUAqyyFF+EE6*D4%(FF+r2c6d}tjgd}tjj | \}}}}tjj | |z\}}} } t ||t ||t | ||zt | |y)Nrr)rarr6rerr) rjSHIFTrVrrrrrrr;r<s r0test_fit_delta_shiftz#TestLevyStable.test_fit_delta_shiftFs HH? @&+&7&7&A&A1"&E#tV&+&7&7&A&A1"u*&M#tVFF+E5)D$,/FF+r2cpgd}tjj|\}}}}|dks Jd||t|ksJdt|d|gd}tjj|\}}} } |dkDs Jd|| t |kDsJdt |d| y) N) rrrrrWrWrWr0r0rrzExpected alpha < 1, got zExpected loc < z, got ) rrrrrWrWrWr0r0rzExpected alpha > 1, got zExpected loc > )r6rerr#rfrs r0test_fit_loc_extrapz"TestLevyStable.test_fit_loc_extrapQs 6&+&7&7&A&A!&D#tVz>5fX>>zc!f}DAxvdVDD} 7&+&7&7&A&A"&E#tVz>5fX>>zc"g~FR vFF~r2z pct_range,alpha_range,beta_range)rursr)rTrr^)rrr)rurrsrr)rTrsrrr^)grrrur r) rurrTrcffffff?rs?rrrrrTr^rrcP|}tj}|jdk(xr|jdk(dj |j|j|j g}ddfdgddfd gddfd gdd fd gd dfdgd dfdgg}t |D]Y\} \} } } | tj_ | || |n|} t5}|jtdtjj| d| d| ddd}tjd5t!| gd|tj"|| dz tj"|| dz tj"| dz g}ddd|d| k\tj$|z}d| d | d!|d"|j&j(d#| }t+|| d| |d$%ddd\y#1swYnxYw#1swYtxYw)&z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnirc vtj|dtj|dztj|dz|ddk(|ddk(z|ddk\|ddk\z|ddk(zz|ddktj|dd d gzz|dd ktj|dd d gzz|ddktj|dddgzz|ddk(tj|dddgztjtj|dgdzz|ddk(tj|ddgztjtj|ddgzz|ddk(tj|dddgztjtj|dgdzz|ddk(|ddk(z|ddk(zz|ddk(|ddk(z|ddk(zz|ddk(|dd k(z|ddk(zz|ddk(tj|ddgztjtj|dgdzz|ddk(tj|dddgztjtj|dgdzz|ddk(tj|dd d gztjtj|dddgzz|ddk\zzS)Npctrrrrsrrr'rurrurrrrTrcr)rsr r rr)gٿ333333ӿrur'rsrrKrTrrur')rrrKrr{)raisinrr alpha_range beta_range pct_ranges r0rFz7TestLevyStable.test_pdf_nolan_samples..sGGAeHi0GGAgJ 45GGAfIz23 vY!^uX_.vY#-wZ3.0uX_. wZ3.GGAeHsCj9: wZ3.GGAeHsCj9:$wZ3.GGAeHr2h78%,wZ3.GGAeHsCj9:GGBFF1V9$5|DE-6wZ3.GGAeHrd34GGBFF1V9$5t<=7@wZ3.GGAeHsCj9:GGBFF1V9$57MNOA#JwZ3.vY#-/uX-/K(TwZ3.vY$.0uX-/U-^wZ3.vY#-/uX-/_2hwZ2-GGAeHrd34GGBFF1V9$57GHIi7rwZ2-GGAeHsCj9:GGBFF1V9$5|DEs<|wZ2-GGAeHsCj9:GGBFF1V9$5RyAB}AF7s*GC,EHr2rdr$ctj|dtj|dztj|dz|ddkDz|ddk7zS)NrrrrrKrarrs r0rFz7TestLevyStable.test_pdf_nolan_samples..snGGAeHi0GGAgJ 45GGAfIz23wZ#%'wZ2% 'r2c|ddk( ztj|dzdvztj|dzS)NrrKrrr)rrr is_linux_32rs r0rFz7TestLevyStable.test_pdf_nolan_samples..s]wZ2%$_&GGAeHi01;&(GGAfIz2 3r2g& .=ctj|dtj|dztj|dz|ddkzS)Nrrrrrrs r0rFz7TestLevyStable.test_pdf_nolan_samples..s[GGAeHi0GGAgJ 45GGAfIz23wZ3&(r2 fft-simpsonrc|ddk\tj|dztj|dztj|dzS)Nrrrrrrs r0rFz7TestLevyStable.test_pdf_nolan_samples..s[wZ3&GGAeHi01GGAgJ 45GGAfIz23r2rctj|dtj|dztj|dz|ddkDz|ddkzS)Nrrrrrrrs r0rFz7TestLevyStable.test_pdf_nolan_samples..smGGAeHi0GGAgJ 45GGAfIz23wZ!^%wZ#% 'r2Nz2Density calculations experimental for FFT method.*rVrrrrr]r\rMrbcalcabserrrelerrrmrz pdf test  failed with method 'z ' [platform: z]  Ferr_msgverbose)platformunamesystemmachinejoin processorrr6rerhr recordrqr`rarZrrisnanrr r)rjrqrrrrr platform_desctestsixdefault_methodr} filter_funcsubdatasuprmsubdata2failuresmessagers ``` @r0test_pdf_nolan_samplesz%TestLevyStable.test_pdf_nolan_samples]s2% llg-I%--62I  \\5==%// :< tJL ^U% U% W' t& t& kC L"+5!1*  B3AE   0 + 7;t,=A "$%  "H%%))CLG$FO *[[h/ 04FF1ws|#34FF1ws|#34rvvgcl7KK H $H%-((1+  t#88HI""/HNN4H4H3IH:W CL#! ?% %  * $  % % s'*AHAH"A!HH HH% cz|}ddfdgddfdgddfdgdd fd gdd fd gdd fdgg}t|D]V\}\}} } |tj_| || |n|} t 5} | j t dtjj| d| d| ddd} tjd5t| gd| tj| | dz tj| | dz tj| dz g}ddd|d| k\tj| z}d|d|d|jjd|}t| | d| |d !dddYy#1swYkxYw#1swYqxYw)"z4 Test cdf values against Nolan's stablec.exe output.rdr cXtj|dtj|dztj|dz|ddk(tj|dgdz|ddk(z|ddk(tj|dgdz|ddk(zzzS NrrrrK)rrrrurTrrurrrs r0rFz7TestLevyStable.test_cdf_nolan_samples..QsGGAeHi0GGAgJ 45GGAfIz23 wZ2-GGAfI/ABCuX-/ wZ2-GGAfI?@uX-/  r2rcVtj|dtj|dztj|dz|ddk(tj|dgdz|ddk(zz|ddk(tj|dgdz|ddk(zzSrrrs r0rFz7TestLevyStable.test_cdf_nolan_samples..fsGGAeHi0GGAgJ 45GGAfIz237r)& +=>?5T)+ 7r)& ?;<5T)+ r2rrctj|dtj|dztj|dz|ddkDzS)Nrrr333333?rrs r0rFz7TestLevyStable.test_cdf_nolan_samples..xs[GGAeHi0GGAgJ 45GGAfIz23wZ#%'r2rctj|dtj|dztj|dz|ddkDz|ddkzS)Nrrrrrrrs r0rFz7TestLevyStable.test_cdf_nolan_samples..nGGAeHi0GGAgJ 45GGAfIz23wZ#%'wZ3& (r2r[ctj|dtj|dztj|dz|ddkDz|ddkzS)Nrrrr@rrrs r0rFz7TestLevyStable.test_cdf_nolan_samples..rr2ructj|dtj|dztj|dz|ddkDz|ddkzS)NrrrrKr@rrs r0rFz7TestLevyStable.test_cdf_nolan_samples..rr2Nz[Cumulative density calculations experimental for FFT method. Use piecewise method instead.*rVrrrrrrMrbrrmrz cdf test rz' rFr)rr6rergr rrqrhrarZrrrrr r)rjrsrrrrrrrr}rrrrmrrrs ``` r0test_cdf_nolan_samplesz%TestLevyStable.test_cdf_nolan_samples4s*2%U% ,T$ &t& t& t& t& GL \"+5!1(  B3AE   0 + 7;t,=A "$#  "@ %%))CLG$FO *[[h/ 04FF1ws|#34FF1ws|#34rvvgcl7KK H $H%-((1+'rd*??Os&nn2232hZACL#! ;# #  ( $  # # s'AF0AF$:AF0$F- )F00F: rrrNr`rhc tj}|jdk(xrdtjdv}|r|dk(rt j d|}dt j_dt j_ ||d|k(}d|t j_ |d vsJ|dk(rt jjnt jj}||d |d |d d d} t| ||dy)zGTests for pdf and cdf where loc, scale are different from 0, 1 r32bitrr`z4Test unstable on some platforms; see gh-17839, 17859rdrS)r`rhrVrrr^rrrN)rrr architecturerrr6rergrhrfr`rhr) rjrurrNrrrrr#rs r0test_location_scalez"TestLevyStable.test_location_scales llg-W'X=R=R=TUV=W2W  45= KKN O*0;,/:,tG}-./0[*~%%%%)U]E   ! !8I8I8M8M  CL''*GFO1!  GDM40r2zmethod,decimal_placesrrrdc tjgd}tjgd}tjgd}tjd5t5}|j t d|t j_t jj|d|dd }t||||d d d d d d y #1swYxYw#1swYy xYw) z sample points extracted from Tables and Graphs of Stable Probability Density Functions - Donald R Holt - 1973 - p 187. )rrrrrrrrr^r^r^r^rrrrrrrr)gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g ?gDioɴ?g r?gH?g+?gHPs?gX?g&?g 0*?gv/?ga2U0*?)rrcrsrrrcrsrrrcrsrrrcrsrrrcrsrrMrzDensity calculation unstable.*)categoryrrrrN) rarrZr rIrqr6rerhr`r)rjr5decimal_placesxsdensitybetasrr`s r0'test_pdf_alpha_equals_one_beta_non_zeroz6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerosXX H ((     [[X & (9(; s JJ'8  4:E   0##''AuA1'EC Wnf       s% C#'ACC#C C##C,zparams,expected)rrrr)r^rrWr)rWr8rrc|tjj|d|d|d|dd}t||y)Nrrr^rrSr)r6rer)rjrZrOobserveds r0rXzTestLevyStable.test_statssG$$** 1IvayfQivay+  Hh/r2r)rcrsrzfunction,beta,points,expectedrKr=rWrxrr cd|cxkrdksJJt||||tjt||y)a\Ensure the pdf/cdf routines do not return nan outside support. This distribution's support becomes truncated in a few special cases: support is [mu, infty) if alpha < 1 and beta = 1 support is (-infty, mu] if alpha < 1 and beta = -1 Otherwise, the support is all reals. Here, mu is zero by default. rrrrN)rrarr)rjrr#rrrOs r0!test_distribution_outside_supportz0TestLevyStable.test_distribution_outside_supports@P5}1}}} V5t 4 GGCK * r2zx,alpha,beta,expected))r/iZ?s0?gz5F?)r~H?|/mg>m?)r.d5 ?L ,ٿg깃\?)r>?ЀjoؿgA]4?)rpa2?Յ пgqQ?cdtj_ttjj ||||y)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=rNr6rerkrr`rjrVrrrOs r0test_x_equal_zetaz TestLevyStable.test_x_equal_zetaJs9Z&-"    ! !!5t ! <  r2) )rrrgz¶?)rrrgV?)rrrgRE)3\?)rrrgB?)rrrg/^?)-C6rrgH?)rrrgn?)rrrgx\?)rrrgVM%?)rrrgm?cdtj_ttjj ||||y)aTest pdf for x near zeta. With S1 parametrization: x0 = x + zeta if alpha != 1 So, for x = 0, x0 will be close to zeta. When case "x near zeta" is not handled properly and quad_eps is not low enough: - pdf may be less than 0 - logpdf is nan The points from the parametrize block are found randomly so that PDF is less than 0. Reference values taken from MATLAB https://www.mathworks.com/help/stats/stable-distribution.html rrNrrs r0test_x_near_zetazTestLevyStable.test_x_near_zeta~s9D&-"    ! !!5t ! <  r2N)&rrrrr0rlrqrsrurrrrrArrrrrrrrarPrrrrrrrrXr6rerhr`rrrr8r2r0r`r`ysnV^^D!B"B ^^B ^^))V ^^   [[ FLL lfll4v{{7G7GH   [[/$> [[C [[]VV,<=>? $ [[ [[Vc1X. / -0 [[>? [[    [[D$<  @   , , G [[* FLL  FLL(#(kk&&   FLLD CB' B2&kk''  - *@+*@D [[* FLL  FLL(#(kk&&   FLLD CB' B2&kk''  - *z+*zx [[Wq!f- [[VeU^415.1@ [[ AJ !  @ [[ !RVVRVVRVV!< =  / 00 [[W&78 [['!!%% CB'  !!%% CB'  !!%% Ar2&  !!%% Ar2&  ' : ;9<  [[& )8 98 0 [[ [[   !" r2r`ceZdZdZdZy)TestArrayArgumentcBtjjdyr+r,ros r0r-zTestArrayArgument.setup_methodr.r2ctjjtjdtj dd}t |jdy)Nrr6r)r6rrrar r(rr9rjrs r0test_noexceptionz"TestArrayArgument.test_noexceptions>jjnn"))A,rwwqz")+SYY(r2N)rrrr-r r8r2r0rrs )r2rceZdZdZdZy) TestDocstringc:tjj3tdtjjj vtj j4tdtj jj vyy)Nr!r)r6r!rr lowerrros r0test_docstringszTestDocstring.test_docstringssg >> ! ! - J%.."8"8">">"@@ A ?? " " . K5??#:#:#@#@#BB C /r2cTtjtjyrm)r6r<r;ros r0test_no_name_argzTestDocstring.test_no_name_args  r2N)rrrrrr8r2r0rrs Dr2rctgd}t|dkD|d\}}t|gdt|dgtddkD|d\}}t||t|dgtj|zt|dkD|d\}}t||t|dgtj|zy)N)rrr^rr^rrrr^)rr^r^rrr)rrrrarr.r/rs r0test_args_reducers #$A a!eQ "DAqq/*q1# a!eQ "DAqq!q1# *+ a!eQ "DAqq!q1# *+r2cReZdZgdZdZgdZejjde dZ dZ dZ dZ d Zd Zd Zd Zejj$ejjd ddgdZejjd ddgdZy) TestFitMethod)ncfrrcBtjjdyr+r,ros r0r-zTestFitMethod.setup_methodr.r2)rrrlz dist,argsc||jvrtjd|ztjdddddtj g}tjdddddtj g}tt|}tt|j|dtt|j|dy ) rz"%s fit known to fail or deprecatedrgrhrirjrkrrN) fitSkipNonFiniterrrarrrr$r6rr r)rjrKr&rVrdistfuncs r0!test_fit_w_non_finite_data_valuesz/TestFitMethod.test_fit_w_non_finite_data_valuess 4(( ( KK.mlefunc%sAAB!"BKKA&Eufw{{1~566ufw{{1~5668DKr2)rrcrsrrrrrr^)rrrr)rrrrsr)rrr)rrrr)rrrr) rarr6rrrrrrr )rjr0rVr.r/r\r]dadbrr:b2r;r<rs r0test_fix_fit_betazTestFitMethod.test_fix_fit_beta"s  HH' ( ::>>!!A>>1c5S!UA1a(1a&t< HH' ( ::>>!!>D1c5QS!UAAq!BAD)U$zz~~bQQq~IBfRT1VQR$BAD)B" j%**..!#aH HHZ j%**..!!AFj%**..!!A!Lj%**..!!A!L j%**..!aQ (r2ctjgd}tjj |\}}t |dt |dtjj |d\}}t |dt |dtjj |d\}}t |dt |dy)N)r^r^rrrrrr;r^rrrrr)rarr6rrrr$s r0test_expon_fitzTestFitMethod.test_expon_fitYs HH- .[[__Q' US!UA[[__Qq_1 US!UA[[__QQ_/ US!UAr2c @tjgd}tj|dz }tjj |d\}}}t ||jdt|dt |tj|jdtjj |dd\}}}t |tj|tjdz dzjdt|dt|dtjj |dd \}}}t|d t|dt |tj|jdy) N)rrrWr5rrrrr|rrr^r)rfix_s) rarrr6rrrrrrrrr)rjrVlnxm1r9r\r]s r0test_lognorm_fitzTestFitMethod.test_lognorm_fiths3 HH- .q1u !MM--aa-8sEuyy{7S!rvvejjl3%@!MM--aa-BsErww):Q(>'D'D'FG" $S!UA!MM--aat-DsEUD!S!rvvejjl3%@r2ctjgd}tjj |\}}t ||j t |tj|tjj |d\}}t |dt ||jtjj |d\}}t |dt |dtttjj|dtttjj|dy)N)rKr{r"@rrrWrrwrL) rarr6rlrrr#r]rfrr r$s r0test_uniform_fitzTestFitMethod.test_uniform_fit|s HH) *]]&&q) US!%%'"UBFF1I&]]&&qq&1 US!UAEEG$]]&&q&4 US!UBj%--"3"3QSAj%--"3"3QsCr2r5MLEMMc >d\}}tjj||dd}tjj|d|}tjj|d|}t ||dd tjj|d| }t ||dd tjj|d | }tjj|d | }t ||dd tjj|d |}t ||dd t t tjj|dd|t t tjj|dddd|tjj|ddd|} | \} } } } t| | | ggdd}tjj|d}tjj|||\} } } t| |y)N)rRrrXrrrR)rr5)rr5rr)rr5r)rr5)rAr5)r@r5rr^)rrr5rr)rrrrr5)rrrr5)rRrrr1) r6rrrrrr rrV)rjr5r.r/rVres_1res_2res_3res_4res_5aabbr9ssrs r0 test_fshapeszTestFitMethod.test_fshapess 1 JJNN1acN = qR7 qR7u5u= q6:u5u= qR7 qR7u5u= q6:u5u= j%**..!aO j%**..!aQv 7  qRa&IBBb"b\:. {{qs+[[__Ta_? BRr2ctj}|jdd}td}t t |j |fi|d|iy)Nr^rX)rri) enikibenikir5)r6rrr rrr)rjr5rKrr%s r0test_extra_paramszTestFitMethod.test_extra_paramssCxx!#x&t$i4F3FvFr2N)rrrrr-rrrrrrr"r%r*r4r6r;r>rrJrMr8r2r0rrs $D4 [[[(3=4=@ $3L5(n A(D$ [[ [[Xt}5$6$L [[Xt}5G6Gr2rcBeZdZdZdZdZdZdZdZdZ dZ d Z y ) TestFrozencBtjjdyr+r,ros r0r-zTestFrozen.setup_methodr.r2ctj}tjdd}|jd}|jddd}t|||j d}|j ddd}t|||j d}|j ddd}t|||j d}|j ddd}t|||jd}|jddd}t|||j}|jdd}t|||j}|jdd}t|||j}|jdd}t|||j}|jdd}t|||j}|jdd}t|||jd}|jddd}t||t|j|jt|j|jy)NrrRr[r rcr^)r6rr`rrhrrrrrrrrr>rr.r/)rjrKfrozenresult_frs r0rzTestFrozen.test_norms zzC0::d#$D4Xv&::d#$D4Xv&::d#$D4Xv&::d#$D4Xv&99T?4s3Xv&==?S1Xv&;;=t3/Xv&::<d#.Xv&::<d#.Xv&>>#$c2Xv&==#QD4Xv&VXXtvv&VXXtvv&r2cd}tj}tj|}|jd}|jd|}t|||j d}|j d|}t|||j d}|j d|}t|||j d}|j d|}t|||jd}|jd|}t|||j}|j|}t|||j}|j|}t|||j}|j|}t|||j}|j|}t|||j}|j|}t|||jd}|jd|}t||t|j|jjt|j |jj y)Nrwr rcrr^)r6rVr`rrhrrrrrrrrr>rr.rKr/)rjr.rKrRrSrs r0 test_gammazTestFrozen.test_gammas {{Q::d#$"Xv&::d#$"Xv&::d#$"Xv&::d#$"Xv&99T?q!Xv&==?QXv&;;=1Xv&::<!Xv&::<!Xv&>>#aXv&==#Q"Xv&VXXv{{}}-VXXv{{}}-r2ctjd}|jd}|jd|jd}t||y)Nrr^rSrT)r6rrr)rjrRm1r s r0test_regression_ticket_1293z&TestFrozen.test_regression_ticket_1293/sHq! ]]1  V $]]1  Rr2cd}tj|}|jj|\}}t ||gddgd}tjj d|t |jj|dt jgd}tj|}|jj|\}}t ||gddgd}tjj d|t |jj|jjftjj|tjd}t|j|judD]}t j|}tj|}|j|j}}t |dtt j|t jd}tjj|\}}t||gdd gy) NrrgrxrrTrr`rars)r6rbrKrcrr`rarr.r/r rrdr)rjrrir.r/rv1s r0rezTestFrozen.test_ab>s  __q !ww##A&1aVb#Y'  A#RWW))!,q"&&k:  __q !ww##A&1aVb#Y'  Aq!bggii+U__-I-I!-LMoo$'( /A 1 A1%B44qA B  BKKN # 3A??//2DAq QFRI . /r2cJtttjdy)N rv_frozen)r r-r6r7ros r0test_rv_frozen_in_namespacez&TestFrozen.test_rv_frozen_in_namespacejs++[9:r2cftj}tt|dd|_t |jj tjjdj tjjd}|jd|y)Nr*rr;r) r6rr r-rr get_staterarrr)rjrRrndms r0test_random_statezTestFrozen.test_random_statens/0!V((224YY**2.88: <yy$$T*  -r2cTtjdd}tjd}tjgdgdf}|||fD]}d|_|j d t j|}|j d }t j|}|j d }t|||jd |jd g} t| d | d t|j| d |j| d y) Ngdsz@g@e?rR)rrr^rrrrr;r1rsrr) r6rr{r;rrpickledumpsloadsrrrh) rjrpoissrdistfnrEr0 unpickledr1medianss r0 test_picklingzTestFrozen.test_pickling|s zz,.AB b!""<+?+ABUF+ 4F"&F  JJAJ  V$A#B QIA&B R zz# c(:;G WQZ 0 GAJ/"wqz2 4 4r2c d}tjddd}tjdd5|j |ddd }tjj |d ddddd }dddt tj dd }|j |}tj j |dd}t ||y#1swYlxYw)Nc|Srmr8rs r0rz$TestFrozen.test_expect..funcsHr2r^rrrUrM)rOdividerT)rub conditionalr^r&r\r]rrqrrrz)rr&r\)r6rVrarZrrr{)rjrgmgm_val gamma_valrmp_val poisson_vals r0 test_expectzTestFrozen.test_expects [[1!1 - [[( ; IYYtaTYBF **4d./A4+II I  * MM! #mm**4d*B {+ I Is .s1qs r2rr^r[rrrNc|Srmr8rs r0rFz&TestExpect.test_norm..sr2rrcyrr8rs r0rFz&TestExpect.test_norm..rr2r\r]rrqrcyrr8rs r0rFz&TestExpect.test_norm..rr2Tr\r]rrqrrrK)r6rrrr)rjrVrUrrqprob90prob90cs r0rzTestExpect.test_norms JJ  3!  DAq"- JJ  m!  <Aq"- ZZ^^Daq^ 1 ZZ^^Daq^ 1"";AQ2""MFC4**##KQaB204$6GR4r2c 0tjjdddd}t|ddtjjd dd d }t|d dtjj d dddd}tjj ddddd}tjjddd d ||d}t|ddtjjdddd||d}t|ddy)Nc|dz |dz zS)NUUUUUU@r8rs r0rFz&TestExpect.test_beta..s51U7(;r2r6rr^)r&r\r]qq?rrNc|Srmr8rs r0rFz&TestExpect.test_beta..sr2rLrwrrrWr[rcy)NrKr8rs r0rFz&TestExpect.test_beta..rr2)rWrWFrtrcyrr8rs r0rFz&TestExpect.test_beta..rr2TrK)r6rrrr)rjrVrUrqrrrs r0 test_betazTestExpect.test_betas JJ  ;'"#1  .Avr2 JJ  kRr  JAub1 ZZ^^D"baq^ 9 ZZ^^D"baq^ 9"".Qr2)rrWr;rurrNc|dz dzSNr=r^r8rs r0rFz+TestExpect.test_hypergeom..sadQYr2rc|dz dzSrr8rs r0rFz+TestExpect.test_hypergeom..sQrTAIr2r)r&r\rrqrcyrr8rs r0rFz+TestExpect.test_hypergeom..rr2rrMcyrr8rs r0rFz+TestExpect.test_hypergeom..rr2T)r&r\rrqrrcyrr8rs r0rFz+TestExpect.test_hypergeom..rr2r)r&rrq)r6rrrrGrd) rjm_truev_truerUrVv_bounds prob_true prob_boundsprob_bcprob_bs r0test_hypergeomzTestExpect.test_hypergeomsx..r2qb.A OO " ";[b " IAvr2 OO " "#6[') # +Avr2??))*=/:.0Q2*? Hfb9eoo))1b'2r1!)DHHJJ oo,,[{13b-B KB?//((;B,-"$)HGQ3'' ++,(4FAr2r2ctjjdddd}dtjjddz }t ||d tjjd ddd }t |dd y) Ncyrr8rs r0rFz)TestExpect.test_poisson..rr2rsrF)r&rrrrr^rrNcyrr8rs r0rFz)TestExpect.test_poisson..rr2T)r6r{rrhr)rjr prob_b_trueprob_lbs r0 test_poissonzTestExpect.test_poissonsymm**;Ta7<+>  ))!Q// KbA--&&{!37'9GQ3r2ctj}|jd}|jd|jd}t||dy)N)rr)rsrrN)r6genhalflogisticrr)rjhalflogres1rs r0test_genhalflogisticzTestExpect.test_genhalflogisticsI''~~6~*F#~~6~*D$3r2cttjtjj ddttjtjj ddttjtjj ddttjtjj ddy)NrGz?cyrr8rs r0rFz/TestExpect.test_rice_overflow.. rr2)rrcyrr8rs r0rFz/TestExpect.test_rice_overflow.. rr2cyNrr8rs r0rFz/TestExpect.test_rice_overflow.. rr2)r rarr6ricer`rros r0test_rice_overflowzTestExpect.test_rice_overflows  EJJNN3567 EJJ--k-HIJ EJJ--k-HIJ EJJ--k-HIJr2cd\}}tjjd|f}t|||dz z t j d|z z dtjjd|f|}t|||zdy) N)rurc|Srmr8rSs r0rFz(TestExpect.test_logser..ar2rrKr{rc|Srmr8rs r0rFz(TestExpect.test_logser..rr2ru)r6rrrrar)rjrmr\res_0res_ls r0 test_logserzTestExpect.test_logsers~3 ##Kqd#;QV rvvb1f~5E C ##Kqd#Dus{7r2cd\}}tjjd||f}tjjd||f}t|||z dt||dzz ||zdy)N)rrc|Srmr8rs r0rFz)TestExpect.test_skellam..sAr2rc |dzSrr8rs r0rFz)TestExpect.test_skellam.. rr2rrr^)r6rrr)rjrBp2rWr s r0 test_skellamzTestExpect.test_skellamsoB ]] ! !+RH ! = ]] ! !.Bx ! @BG%0RU BG%8r2c d\}}tjjd||f}t|t dt ||D||z z dy)N)rqc|Srmr8rs r0rFz)TestExpect.test_randint..(rr2c3 K|]}|ywrmr8r\rs r0rz*TestExpect.test_randint..*s5!A5s r{r)r6r7rrrdr)rjlohirs r0 test_randintzTestExpect.test_randint$sQBmm"";R95uR}55bA Or2cZtttjjddy)Nc |dzSrr8rs r0rFz&TestExpect.test_zipf../s q!tr2rs)r rqr6rrros r0 test_zipfzTestExpect.test_zipf,s^UZZ%6%6#T +r2ctjjdd}tjjddddd}t||d y) Ncyrr8rs r0rFz/TestExpect.test_discrete_kwds..3rr2rsrcyrr8rs r0rFz/TestExpect.test_discrete_kwds..4rr2r) r)r&maxcount chunksize tolerancerrN)r6r{rr)rjn0n1s r0test_discrete_kwdszTestExpect.test_discrete_kwds1sL ]] ! !+D ! 9 ]] ! !+D+/2"OBB/r2cd}dD]6}tjjd|}t|||d8y)NcH|dzd|dzzzd|dzzzd|dzzz|zS)NrrWrr rr5r^r8r(s r0 poiss_moment5z-TestExpect.test_moment..poiss_moment5;s8q52b!e8#bQh.BE9B> >r2)rrrr r|)r6r{rr)rjrrm5s r0 test_momentzTestExpect.test_moment8s? ? ?B%%a,B B b 1 > ?r2cttjjdddttjjdddttjjdddttjjdd ttj jd d y) NrCrKr[rrWrT)rrUrz)rr6rrrVrros r0test_challenging_cases_gh8928z(TestExpect.test_challenging_cases_gh8928Bs  ))b)>$2!IIOOD!4 #56H!I(*@*C" $)+A" $99>>&!,IIOOFA. ,.@A."3%@ >=r2c lttjjddt ddy)Nr^ir)rr6rrhrros r0test_cdf_large_nczTestNct.test_cdf_large_ncs! aE%L91=r2N) rrrrrrrrrr8r2r0rras!C2$  >,>r2rc$eZdZdZdZdZdZy)TestRecipInvGausscRtjjdd}|dk(sJy)Nrr rx)r6 recipinvgaussr`rs r0test_pdf_endpointz#TestRecipInvGauss.test_pdf_endpoints%    # #As +Cxxr2cptjjdd}|tj k(sJy)Nrr )r6rrrarrs r0test_logpdf_endpointz&TestRecipInvGauss.test_logpdf_endpoints,""))!S1wr2cdtjjdd}d}t||dy)Nrrsg9V9s;rzr|)r6rrhrrjrmrOs r0test_cdf_small_xz"TestRecipInvGauss.test_cdf_small_xs-    # #D# .(8%0r2cbtjjdd}d}t||dy)NPrsglH EJJNN1N3488:; EJJ--a2-67;;=>  EJJNN1N3488:;zz62 D!%%'(  q!,ejjnnQ.BQ (r2ctjj}t|djdt|ddj dy)NrRr r)rr)r/r)r6rrrrr9r s r0 test_rice_rvszTestRice.test_rice_rvss8jjnnS2Y^^Q'S2F+116:r2ctjjtjdddtjddd}gd}t ||tjddd}tjj |dd}gd }t ||tjjj d tjdd d}gd }t ||y) NrW)g/ Ƹ?g[jNJ\?g ?g9LJ?g#O?gXx?glO?g٥a%?gVzӯ?gTQ+xQ?g?`J?go?gbu=?gIo|?g"Z6?rTrg@_@rr) g<~@gwd @gC?@gb 0@g` A@@g'NxP@g33-a@g4pv@g$F@rs)gJ-$@g+f4@gce*D>@g$D@gnHGI@grN@g< uQ@giffT@g9r[V@g3bXQY@gq xJ[@g`*DD^@g@`@gdAa@)r6rrhrar rrr5)rjrhcdf_exp probabilitiesrppf_exps r0test_rice_gh9836zTestRice.test_rice_gh9836sjjnnRYYr33RYYr35KL O W% #q#. jjnn]En; L W%kk""3 "c2(>? ; W%r2N)rrrr r r r8r2r0r r s(*; '&r2r ceZdZdZdZdZy) TestErlangcBtjjdyr+r,ros r0r-zTestErlang.setup_method r.r2c tj5tjdtt tt j jddddgd}t j j|d}t jj|d}t||d dddy#1swYyxYw) Nrjr@rrrr)rsrKrwrrr[r|) rnrorprqrr6erlangrrrVr)rjr result_erlang result_gammas r0test_erlang_runtimewarningz%TestErlang.test_erlang_runtimewarnings $ $ & D  ! !'> : .,,**CQaa I (D!LL,,Ta,8M ;;??4A?6L M.scale_mle:s,FFD4KA-.!c$i-@RG Gr2rr r)r6r!rrr)rjrrrr scale_expectr\r]s r0rzTestRayleigh.test_fit5s~~!!sy!I H!w/ ^^''7'; US'"UL)^^''R'8 UUB ^^''- UUIdC01r2rrug̡=E?g@1d?c|tjjd||}ttj|y)Nrr)r6r!rr)rjrrrs r0 test_fit_comparison_super_methodz-TestRayleigh.test_fit_comparison_super_methodNs- ~~!!sy!I%ennd;r2c6ttjyrm)rr6r!ros r0rVzTestRayleigh.test_fit_warningsVsENN+r2ctjjd}d\}}}tjj ||||}tjj |\}}|tj|ksJtjj ||\}}|tj|ksJ||k(sJy)Ni)r3rrtrr)rarrr6r!rrr#) rjrr\r]rrrrrs r0test_fit_gh17088zTestRayleigh.test_fit_gh17088Ysii##C('UDnn  e$S I^^'', $$$"^^//E/B$$$E!!!r2N) rrrr-rqrrrrrr$ rVr' r8r2r0r r (s"0" [[03K3K3MN2N2. [[0D$<4> 3K3MN<N< , "r2r ceZdZdZdZdZejjdgddZ ejjdgdd Z y ) TestExponWeibcd}d}d}tjj|||}tjj|||}t ||gddgy)NrTrKrg:23W+g~`9k)r6 exponweibr`rr)rjrVr.rrmrps r0test_pdf_logpdfzTestExponWeib.test_pdf_logpdfhsY    OO  1a (%%aA.D /1DE Gr2cntjddd}d}d}tjj |||}tj j ||}t ||tjj|||}tj j||}t ||y)NrrrrrX)rarr6r+ r` weibull_minrrrjrVr.rrmrOrps r0 test_a_is_1zTestExponWeib.test_a_is_1ss KKB "   OO  1a ($$((A.8$%%aA.$$++Aq1h'r2cjtjddd}d}d}tjj |||}tj j |}t ||tjj|||}tj j|}t ||y)NrdrrW)rarr6r+ r`rrrr/ s r0test_a_is_1_c_is_1z TestExponWeib.test_a_is_1_c_is_1s KKAr "   OO  1a (;;??1%8$%%aA.;;%%a(h'r2z x, a, c, ref))rr rg=J ?)r3r rg$+PR>)rr rg ><)rr rggX.X:)r?rgRy9)rr3 rRg'vR0=)g_QPrr}gQ: [[ 5 - -* [[ 4..r2r) ceZdZdZdZy)TestFatigueLifec`tjjdd}t|ddy)Nrr X9rr|)r6rrrrs r0 test_sf_tailzTestFatigueLife.test_sf_tails)     ,0u=r2cdd}tjj|d}t|ddy)Nr9 r rrr|)r6rrr)rjrmrvs r0 test_isf_tailzTestFatigueLife.test_isf_tails+ !    ! !!S )5u-r2N)rrrr: r< r8r2r0r7 r7 s  >.r2r7 ceZdZdZdZej jdddgdZdZ ej jdd d gd Z y ) TestWeibullc\tjjdd}t|dyr)r6r. rrr s r0rqzTestWeibull.test_logpdfs$    $ $Q *Qr2cXd}d}d}tjj|||}t|t j ddz tjj |||}t|dt jdz tjj|||}t|tjd tjj|||}t|t jtjd tjj|||}t|t j dtjj|||} t| dtjjddd}t|t j d tjjddd} t| d d }tjj|||}t|t j ddz tjj |||}t|dt jdz tjj|||}t|t j dtjj|||}t|dtjj|||}t|tjd tjj|||} t| t jtjd tjjd dd}t|tjd  tjjd dd} t| t jtjd  y) NrrwrRrrrr0r^r)rg& .gCe)r6r. r`rrarrrrhrrTrrrs weibull_max) rjrVr.r/rmrrlcrEr|s r0test_with_maxima_distribz$TestWeibull.test_with_maxima_distribs?.       ! !!Qa ! 0266%=?+    % %a! % 4EBFF1I-.    ! !!Qa ! 0GMM%001    % %a! % 4BFFGMM%$8#89:    AQ /266%=)    $ $Q $ 3E"    Qa 0266$<(    $ $R! $ 4D!     ! !!Qa ! 0266%=?+    % %a! % 4EBFF1I-.    ! !!Qa ! 0266%=)    % %a! % 4E"    AQ /GMM%001    $ $Q $ 3BFFGMM%$8#89:     3GMM*@AAB    $ $UAQ $ 7BFFGMM2H$I#IJKr2r]rKrTcntjj|dz|dzd|}t|dy)Nrer;rrg>)r6r. r{rr.s r0r|zTestWeibull.test_delta_cdf@s;"!!,,U3Ya38-:56r2ctjjd}d\}}}tj|||}|j d|}tjj |dd\}}} tjj |dd\} } } || cxk(rdk(sJJ|| k7sJtjj |ddd \} }}|dk(sJtj| ||}|jd }tj|tj|f}t||y) Nl>)r^r6rsrXrrrrrr3r4r6rT) rarrr6r. rrrrr)rjrrr\r]rKrc2r;r<c3r>r?c4rArBrCrr|s r0 test_fit_minzTestWeibull.test_fit_minUs2ii##$78# 3  C/hhCch2!,,00c0BD& ,,00c0BD&t q     Rxx!,,00a$0OD&{{!!"dF3kk$k'ggclEJJsO+S!r2r)r3rr])rrgq뮕qH)cttjj|||dttjj |||dyr)rr6r. rrrs r0rzTestWeibull.test_sf_isfssB )),,Q2CeD))--c15quEr2N) rrrrqrC rrrr|rI rr8r2r0r> r> su RLh [[WsCj1727("< [[[+J,D+EFFFFr2r> ceZdZdZdZy) TestDweibullc2tjjd}d|jddz}tj j |}tjj |tjdz }t||dy)Nq>~).rWrXrrsr{r|) rarrr;r6dweibullr>r. rr)rjrrrr|s r0rhzTestDweibull.test_entropy|ssii##$78  2 . .nn$$Q'''*RVVC[8Su-r2c6tjjd}d|jddz}d|j z}t j j||}dt jj||z}t||dy)NrN rWrrrsr{r|) rarrr;rlr6rO rr. r)rjrrrVrr|s r0rzTestDweibull.test_sfsii##$78   , ,  nn1%E%%((A..Su-r2N)rrrrhrr8r2r0rL rL {s  ..r2rL cBeZdZdZdZdZdZdZdZdZ dZ d Z y ) TestTruncWeibullchtjjddgddd}t|ddgy)NrTrwg)\(?gףp= ?rx)r6truncweibull_minr`rr s r0test_pdf_boundsz TestTruncWeibull.test_pdf_boundss0  " " & &Sz3d CQc #r2ctjjdddtj}t |dtjjdddd}t |dy)NrwrKrxrg~?)r6rT rrarrrr s r0rqzTestTruncWeibull.test_logpdfsU  " " ) )#sC @Q  " " ) )#sC =./r2chtjjddgddd}t|ddgy)NrxrKrwrT)r6rT rrr s r0test_ppf_boundsz TestTruncWeibull.test_ppf_boundss0  " " & &Sz3S AQc #r2cgd}tjj|ddd}tjj|ddd}t ||yN)rxrTrcrsrrrKrwrxrR)r6rT rrhrrjrvrVq_outs r0test_cdf_to_ppfz TestTruncWeibull.test_cdf_to_ppfsI 0  " " & &q"b" 5&&**1b"b95!r2cgd}tjj|ddd}tjj|ddd}t ||yrZ )r6rT rrrr[ s r0test_sf_to_isfzTestTruncWeibull.test_sf_to_isfsI 0  " " & &q"b" 5&&))!RR85!r2c d d d fdtjjd }t|dtjjd }t fd \}}t ||tjjd }t fd  \}}t ||tjjd }t fd  \}}t ||tjjd } t fd  \} }t | | y)NrwrKrRcT||ztjj|zSrm)r6rT r`)rVrlr.r/rs r0xnpdfz)TestTruncWeibull.test_munp..xnpdfs)a4..221aA>> >r2rrc|dSrr8rVrb s r0rFz,TestTruncWeibull.test_munp.. a r2r^c|dSrr8rd s r0rFz,TestTruncWeibull.test_munp..re r2rc|dSrr8rd s r0rFz,TestTruncWeibull.test_munp..re r2rc|dS)Nrr8rd s r0rFz,TestTruncWeibull.test_munp..re r2)r6rT rrrr)rjrQrW m1_expectedrr  m2_expectedm3 m3_expectedr  m4_expectedr.r/rrb s @@@@r0 test_munpzTestTruncWeibull.test_munps#    ? # # * *1aA 6R  # # * *1aA 63Q: QK(  # # * *1aA 63Q: QK(  # # * *1aA 63Q: QK(  # # * *1aA 63Q: QK(r2c 8d}d}d}tjdtjdtjdtjdz zz }tj j ||||}t|dtj j||||}t|tjd tj jd|||}t||tj j||||}t|dtj j||||} t| tjd tj jd|||} t| |y)NrKrRrwrrsr) rarrrr6rT rhrrrrrsr) rjr.r/rx_medrhrB rrr|rs r0test_reference_valuesz&TestTruncWeibull.test_reference_valuessB   BFF3"rvvbz/0B)C#CDDE$$((1a8S!  # # * *5!Q :RVVBZK($$((aA6U#  # # & &uaA 6C  # # ) )%Aq 9RVVBZK($$((aA6U#r2cd}d}d}tj}d}tjj |||}tj j |||||}t ||tjj|||}tj j|||||} t || tjj|||} tj j|||||} t | | tjj|||} tj j|||||} t | | tjj|||}tj j|||||}t ||tjj|||}tj j|||||}t ||tj jdd||d}t |tjd tj jdd||d}t |d y) NrrwrxrRrr0r^rr)) rarr6r. r`rT rrrhrrrsr)rjrVrr.r/r]rmp_truncrlp_truncrh cdf_truncrB lc_truncrEs_truncr|ls_truncs r0test_compare_weibull_minz)TestTruncWeibull.test_compare_weibull_mins1    FF    ! !!Qe ! 4((,,Q1au,E7#    % %a% % 8))00Aq!50IH%##Aq#6**..q!Q.G Y'    % %a% % 8))00Aq!50IH%    AU 3((++Aq!Qe+D7#    $ $Q $ 7))//1a%/HH%  " " % %b!Q % ;266$<(  # # ) )"aAQ ) ?D!r2cd\}}}tj||d}tjj ||||}tjj ||||}tj j ||tj j ||z }tj j |||z }tj j ||tj j ||z |z } tjj||tjj|| y)N)r rcrrX) rarPr6rT r`rhr. rYr) rjrr.r/rVrrrrrs r0test_compare_weibull_min2z*TestTruncWeibull.test_compare_weibull_min2s"1a KK1c "%%))!Q15%%))!Q15  $$Q*U->->-B-B1a-HH  $$Q*T1!!%%a+e.?.?.C.CAq.II4O ""4. ""4.r2N) rrrrU rqrX r] r_ rn rq ry r{ r8r2r0rR rR s0$ 0$ " " )6$0'"R/r2rR c`eZdZdZdZej jdgddZy) TestRdistctj}gd}t|j|j |dd|dy)NrZg@rrN)r6rdistrrhr)rjrhrs r0test_rdist_cdf_gh1285zTestRdist.test_rdist_cdf_gh1285"s5$FJJvzz&%'@%H"A /r2ctjddd}d}tdtj|dz |dz j |dzdz ztj |j |y)NgGzrrWg@rsr^r)rarPrr6rr`r )rjrVrs r0test_rdist_betazTestRdist.test_rdist_beta)sd KKtR ( C 1Q3! 4 8 8!a% CC!KKN..q1 3r2r))rig?)rTg;|bZ?)rsig79)riUg޻S/c\ttjj|||dyr)rr6r rrs r0 test_rdist_sfzTestRdist.test_rdist_sf7s  q!,c>r2N) rrrr r rrrr r8r2r0r} r} !s7/3 [[ ??r2r} c0eZdZdZdZdZdZdZdZy) TestTrapezoidcHgd}|D]}d|dg}ttjj|||tjj||ttjj |||tjj ||y)N)rrursrrr)rr6rr`triangrh)rjmodesmoderVs r0test_reduces_to_triangz$TestTrapezoid.test_reduces_to_triangEs  ;DD! A  3 3AtT B % 0 0D 9 ;  3 3AtT B % 0 0D 9 ;  ;r2cRtjddd}ttjj |ddtj j |ttjj|ddtj j|yNrrrW)rarPrr6rr`rlrhrs r0test_reduces_to_uniformz%TestTrapezoid.test_reduces_to_uniformNsl KK1b !EOO//1a8%--:K:KA:NOEOO//1a8%--:K:KA:NOr2c ttjjddddttjjddddttjjddddttjjddddttjjd ddd ttjjdddd ttjjd ddd ttjj d ddd ttjj ddddttjj ddddttjj d dddttjj ddddy)Nrr^rrsrrrrKrTg?rrr3 rg?)rr6rr`rhros r0 test_caseszTestTrapezoid.test_casesSsfEOO//1a8!<EOO//1a8!<EOO//Q</ 1EOO//S#>/ 1 EOO//S#>FEOO//S#>EEOO//S#>FEOO//S#>HEOO//S#>FEOO//S#>DEOO//S#>HEOO//S#>Dr2cV d\ z z z z z z z f\}}}}d z z z z fd}|d}|d|dzz }d z z z z z z z z tjd z z z zz}ttjj |||||dttjj |||||dttjj|||||dttjj ddd d d dttjj ddd d ddttjj ddd d d dy) N)r.rr^rr^c|dzz|dzzz z z |dzz|dzzz z z z z|dzz |dzz S)Nr^rr8)rlr.r/rdrgs r0rz6TestTrapezoid.test_moments_and_entropy..momentnsn!ac(Q1X-!A#6!Hq1Q3x/AaC89:qSqS" #r2rrsrrNrr.rrr)rarrr6rrrr>)rjrBrr\r]rrrr>r.r/rr rgs @@@@@r0test_moments_and_entropyz&TestTrapezoid.test_moments_and_entropygs" 1acac]QqSQqSM1acABU 1QqM # # ayQi$'!1Qq/QqSU1W-sac!eAg0GGEOO00ReD " .EOO//BUC -EOO33BCG#R 1 EOO00Ar1=r2NEOO00Ar1=q"MEOO//1b!r2ctjddd}ttjj |ddtj j |yr )rarPrr6r?r`rlrs r0 test_trapzzTestTrapezoid.test_trapzs> KK1b !EKKOOAq!4emm6G6G6JKr2N) rrrr r r r r r r8r2r0r r Ds$;P E(M6?4Lr2r ceZdZdZy) TestTriangcJtjd5ttjj dddttjj dddttjj dddttjj dddttjj dddttjj ddd ttjj dddttjj ddd ttjj dddttjj dddttjj ddd ttjj ddddddy#1swYyxYw) NraiserrrwrsrKrrxr^rrc)rarZrr6r r`rhros r0test_edge_caseszTestTriang.test_edge_casessg [[W % 6 ))!Q/ 4 ))#q12 6 ))!Q/ 4 ))!Q/ 3 ))#q12 6 ))!Q/ 3 ))"b12 6 ))#r2D 9 ))#r2C 8 ))"b12 6 ))#r2D 9 ))"b11 5 6 6 6s G9HH"N)rrrr r8r2r0r r s6r2r ceZdZejj dddgdZejj dgddZy) TestMaxwellr)rgCR5&.)rug7q?cZttjj||dyr)rr6maxwellrrs r0rzTestMaxwell.test_sfs  ((+Su=r2r))r[g1!@)g?g?)gr2Nr4r8r2r0r r s\  [[X::<=>=>  [[X:;? ;?r2r ceZdZdZdZy) TestMielkecd\}}ttj||jdtj ttj|djdtj t t jtj|djdy)N)g rh@gv?rrKr)rr6mielkerrarr r)rjrSrEs r0rWzTestMielke.test_momentssz1U\\!Q'..q1266:U\\!S)003RVV< ELLD188;<=r2ctjddd}d\}}ttjj ||||z tj j |||y)NrurXr3)g@gHzG@)rarPrr6burrr`r )rjrVrSrEs r0test_burr_equivalencez TestMielke.test_burr_equivalencesO KKc2 &1 q!QqS15<<3C3CAq!3LMr2N)rrrrWr r8r2r0r r s >Nr2r c$eZdZdZdZdZdZy)TestBurrc tjddgtjddgtjddgtjddgtjddgtjddgtjd d gg}|Dcgc]#\}}}|j|j g|%}}}}|Dcgc]\}}}| }}}}t |||Dcgc]#\}}}|j|j g|%}}}}|Dcgc]\}}}tj|}}}}t ||ycc}}}wcc}}}wcc}}}wcc}}}w) N)rr)rsr^)rr)r^rsrQrsrK)rr^rw) r6fiskr burr12r`r.rrrar)rjrrrrrrrs r0test_endpoints_7491zTestBurr.test_endpoints_7491s7ZZq ! ZZ1 % ZZ # ZZ1 % \\8S ) \\63 ' \\63 ')9=== E1vrvvbdd#U#==9=>>!5UI9>>!#w/;?@@<2uayryy&&@@AEFF)=UI266)$FF!#w/ >>AFs(D?9 E(E  Ecd\}}tj||j\}}d\}}t||t||y)N)rLr)g4U?g&MI?)r6r r)rjrr rvariancemean_hc variance_hcs r0test_burr_stats_9544zTestBurr.test_burr_stats_9544sI1Aq)//1h Gg&+.r2c<d\}}tj||j\}}ttj|ttj|d\}}tj||j\}}ttj |ttj|d\}}tjj tjgd||\}}}}ttj|ttj|ttj|ttj|d\}}tjj gd||\}}}}ttj |ttj|ttj|ttj|d\}}tjj gd||\}}}}ttj |ttj |ttj|ttj|d\}}tjj gd||\}}}}ttj |ttj |ttj |ttj|d\}}tjj gd||\}}}}ttj |ttj |ttj |ttj |y)N)rsr)rrrL)r r)r6r)r8r)r6r r rarr_munpr) rjrr rr e1e2e3e4s r0test_burr_nan_mean_var_9544z$TestBurr.test_burr_nan_mean_var_9544s1Aq)//1h"#1Aq)//1h D!""#1))"((<*@!QGBB    1)),1=BB B    1)),1=BB B  B   1)),1=BB B  B  B  1)),1=BB B  B  B  B r2cxd\}}gd}gd}ttjj||||dy)N)rLrR)rTr ryr)g+&?gI$_@gKT@gؗVArzr|)rr6r r)rjrr rvr|s r0 test_burr_isfzTestBurr.test_burr_isf$s61 &# q!Q/5Ar2N)rrrr r r r r8r2r0r r s0( /(!TBr2r cZeZdZejj dddgdZdZy) TestBurr12zscale, expected)rKgd~)r6gR톇T chtjjdddd|}t||dy)NgjAgjArr;rrr|)r6r r{r)rjr]rOrs r0r|zTestBurr12.test_delta_cdf1s/( ''S!Qe'Dxe4r2c0d\}}tjdz }dtjdzdz z }tjdzd|dzzz }tj}||||g}tj||jd }t ||d y) Nrrrr^rrrrrSrzr|)rarbrr6r r) rjrr rrrrr|rs r0test_moments_edgezTestBurr12.test_moments_edgeHs 1uuQw"%%(2+ouuaxCH%66S$)ll1a &&v.Su-r2N)rrrrrrr|r r8r2r0r r /s6 [[.<;=>5>5( .r2r c eZdZgdZgdZgdZejeeefZgdZ ddddd ejgZ gd Z e eee e e eZd d ddejd fddejdfddejdfgZdZej(j*dZej0j3eZdZeej0j=ee5Ze jBeZ"dddej(jGde"ddZ$ej(jGde"ddZ%ej(j*ej(jMdej(jGde"ddZ'dZ(ej(jRdZ*ej(jGded Z+ej(j*ej(jMdd!Z,ej(jRd"Z-d#Z.d$Z/d%Z0y#1swYQxYw)&TestStudentizedRange)gQ1@g33333F@g ףp=*K@gHzM@g/$@g~j!@g33333$@g{Gz&@gh|?5 @gQ8@g&1@g|?5@g@gOn@g!rhm@gB`"@rgʡEs@g|?5^@g/$@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@)rrrrrrWrx)r^r;rr)rTri)#gupm1f?)rrWrg?<-=A?gv"?rgd暕?ga-A?c|jD]:\}}|\}}}tjj|||}t ||d<y)Nrr|)rr6studentized_rangerhr)rjpvkrv p_expectedrVrSres_ps r0test_cdf_against_tablesz,TestStudentizedRange.test_cdf_against_tablessKii :FC" J1++//1a8E E:D 9 :r2c|jD]:\}}|\}}}tjj|||}t ||d<y)NMb@?r|)rr6r rr)rjr q_expectedrmrVrSres_qs r0test_ppf_against_tablesz,TestStudentizedRange.test_ppf_against_tablessJ#yy :OCGAq!++//1a8E E:D 9 :r2z&data/studentized_range_mpmath_ref.jsonN case_resultcdf_datac|d}|d}|d|d|df}tjj|}t|||d|dy Nsrc_case mp_resultrvrSrV expected_atol expected_rtolr)r6r rhrrjr r r qkvrs r0test_cdf_against_mpz(TestStudentizedRange.test_cdf_against_mp`z* , smXc]HSM9%%))3/Y%o6%o6 8r2pdf_datac|d}|d}|d|d|df}tjj|}t|||d|dyr )r6r r`rr s r0test_pdf_against_mpz(TestStudentizedRange.test_pdf_against_mpr r2z+intermittent RuntimeWarning: invalid value. moment_datac|d}|d}|d|d|df}tjd5tjj|}dddt ||d|d  y#1swYxYw) Nr r rUrSrVrMrNr r r)rarZr6r rr)rjr r r mkvrs r0test_moment_against_mpz+TestStudentizedRange.test_moment_against_mpsz* , smXc]HSM9[[ * 7))00#6C 7 Y%o6%o6 8 7 7s A**A3cd\}}ttjjdtj ||f}t |ddy)NrrWrrr)rr6r r`rarr)rjrSrVrs r0test_pdf_integrationz)TestStudentizedRange.test_pdf_integrations=15**..266AGA"r2cd\}}tjddd}tjj |||dd}tjj |||}t ||}t||dy) Nr rrWru)steprrr|)rar r6r rhr`rr)rjrSrVrVy_cdf y_pdf_rawy_pdf_cumulatives r0test_pdf_against_cdfz)TestStudentizedRange.test_pdf_against_cdfsv1 IIa$ '''++Aq!4QR8++//1a8 / 1= (%d;r2 r_case_resultc|\}}}}tjd5tjj |||}dddt |y#1swYxYw)NrMrN)rarZr6r rhr)rjr rvrSrVr_resrs r0test_cdf_against_rz'TestStudentizedRange.test_cdf_against_rsV'1a [[ * 7))--aA6C 7U# 7 7s "AAc~tjd5tjj ddgddgddg}dddt j d tjtd 5tjj dddggd dddy#1swYixYw#1swYyxYw) NrMrNrr^rrrWr!rsz...could not be broadcast...r)rWr!rM) rarZr6r r rr9rr r rs r0test_moment_vectorizationz.TestStudentizedRange.test_moment_vectorizations[[ * H''--q!fq!fr2hGA H & ]]:-K L C  # # ) )!aV\ B C C  H H  C Cs(B'8&B3'B03B<c`t5}tjd5|jtt j jgd\}}}}ddddddtt j jy#1swY;xYw#1swY?xYw)NrMrNr) r rarZrIrr6r rr _argcheck)rjrrSrrs r0test_fitstart_validz(TestStudentizedRange.test_fitstart_valids   GCX)F G JJ) *11;;IFKAr1a G G ''11!R89  G G G Gs"B$ Zd>%%))!R8,,00B> Zd>r2c0tjjddd}tjjddd}tjjddd}ttt ||ddt ||ddtjj ddd}tjj ddd}tjj ddd}ttt ||ddt ||ddy)NrrWrr irr)r6r r`rAssertionErrorrrh)rjrr res_sanitys r0test_df_cutoffz#TestStudentizedRange.test_df_cutoffs%%))!R8,,00B> ,,00B> nosJd , JTE%%))!R8,,00B> ,,00B> nosJd , JTEr2c|d\}}}tjj|||}t|dd|dk\sJy)N)gaRA@riSrr r)r6r rr)rjrvrSrVrms r0 test_clippingz"TestStudentizedRange.test_clippings@.1a  # # & &q!Q /15)Av vr2)1rrrq05q01q001rarqspsrvskslistr r%rr_datar rrrr ospathdirnamer  path_prefix relative_pathopenrfilejsonr pregenerated_datarr r xfail_on_32bitr r rr r r r r r r r8r2r0r r Ws 'C  'C  (D c4( )B B QBRVV $B B GBB', -D *( Arvv() Arvv() B)* F:  [[:: ''//(+K,,RVVS9:;..rvvs;<=++BFFC89:,,RVVS9:;//<=>,,RVVS9:;,,RVVS9:;#<<A H %9%--++AB+789a0 XXemm''#1'= >Fa0 XXemm''d': ;Fa0 XXemm''d'; H!4)99s 95IIctjjdtjj d}tjj |}d}t||dy)Ni rXr1)g ףp= ?gʡE?rrN)rarrr6r!rrr)rrZrOs r0test_regression_ticket_1530r, xsNIINN6 ,,    $C \\  c "FH!4r2ctjjdtjjd}dD]C}tj j ||z\}}t||dt|ddEy)Nrr_)rg6ArKrr )rarrrr6r!rr)rVoffsetr\r]s r0test_gh_pr_4806r/ sgIINN4 A'.\\%%a&j1 UV#.s-.r2cbtjjdd}dtjdzdz ddg}t ||dtjjd d}gd }t ||dtjjd d}gd }t ||dy) NrrSrTr^rrrWrNg ףp= @)rgz5v?rgRTgQ?)rgNg@rgJFٻ)r6r(rarbr)rYrOs r0"test_tukeylambda_stats_ticket_1545r1 s    F 3B255!8A:q#&HHb1    v 6BCHHb1    v 6BCHHb1r2c|ttjtjj ddy)Nrr)r rarr6r{rr8r2r0test_poisson_logpmf_ticket_1436r3 s$ BKK ,,T37 89r2czddg}|D]2\}}tjj|d}t||4y)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)) )rK)rsrrxr)rw)gUUUUUU?rg^cQg333333rSrTN)r6rXr)rr. exact_mvskrSs r0test_powerlaw_statsr6 sG>, = ?E4 :~~##Av#6!$ 34r2c\tjjdd}t|dy)Nrrrx)r6rXrrrms r0test_powerlaw_edger9 s" a#ACr2cvtjjdd}t|dtjj dgd}t|t j ddgtjjdgd}t|t j dt j gy)Nrrrx)rcrKrrK)r6rrrr`rarr8 s r0test_exponpow_edger; s a#AC 1./ARVVS#&' a!12ARVVS266'*+r2c^tjjddd}t|dy)NrrrK)r6gengammar`rr8 s r0test_gengamma_edger> s$ 1a#ACr2za, c, ref, tol))g`6Arg2j!@r{)rrggA@r{)rrr/r{)rrg#@r)g`FArgI~mr{)gl$W}Lrg.I#Ur{c\ttjj||||yrH)rr6r= r>)r.rr|rs r0test_gengamma_extreme_entropyr@ s!"ENN**1a0#C@r2ctjjddd}|dk(sJtjjddd}|tj k(sJy)Nrrrrx)r6r= r`rrar)rmrps r0!test_gengamma_endpoint_with_neg_crB sO 1a$A 8O8 >> Ar *D BFF7??r2ctjjddd}t|dtjjddd}t|dy)NrrrKg>rWgqq?)r6r= r rr8 s r0test_gengamma_munprD sF Rb)A:& RR(A6"r2c\tjgd}tjd5t5}|j t d|j t dtjj|ddddddy#1swYxYw#1swYyxYw)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*˿rMrNz:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integer) rarrZr rIrrqr6rr)r rs r0test_ksone_fit_freezerF s  / 0A X &   C JJ)# $ JJ~F H KKOOA     s# B"A BB"B B""B+c Ttjttddd }gd}t t j j||dt t j j|dzj|dt j j|dzd z j}tjt j j|t j j|z }t ||d y) 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/Mrry+=y|=r ) rarr rrr6rrrealimagrr)rVrOderivderiv_expecteds r0test_norm_logcdfrL s Dq#q)* ++A0HEJJL''*H4@EJJL''F 388(NZZ  q6z *5 0 6 6EVVEJJ--a05::3D3DQ3GGHNE>6r2ctjgd}tjgd}tjj |}t ||dtjj |}t ||dy)N)rrKrsrTrur[)g~V1?rgba"?g܄4ťY?rg$%+Ir r|r)rarr6rrhrr)rVrOrrs r0test_levy_cdf_ppfrN 6sf 34Axx12H  qAAxe,  !BB&r2ctjgd}tjgd}tjj |}t ||dy)N)rIrkgMraB3Gr)gep[>g}XEQ=gѭEGrrarGrr+ rrs r0test_distribution_too_many_argsr` sIINN4 C!$A)U[[__aA3?)U[[__aAqcB)U[[__aAq!<)U[[__aA3cJ)U[[__b!CH)U[[__aQCsK)U[[__aQCsK)U[[..A3cJ)U[[00"aSL)U[[__aQCsK KKOOAq! KKOOAq!Q KKb! KKb!Q KKb!Q% KKOOB1a  KKOOEKKOOBQO/4 JJNN1aQN)UZZ^^Q1a8)UZZ^^Q1!<)U[[__a<)U__00!Q1#F)U__00!Q1c3G)UYY]]Aq!QsC)UYY]]Aq!Q3cJ IIMM!Q1a%r2ctjjtjddddd}tjj tjddddd}t ||ddy) Nrr rr^gYZ@r[rr])r6ncx2rhrar _cdfvecrr<s r0test_ncx2_tails_ticket_955rd sZ  ryyR-q.AA 299RS11nEAAqt!,r2c tj5tjdtt t j jdtjddddt j jdtjddd}dddttjjtj5tjdtt t j jddd dtt j jddd d dddy#1swYxYw#1swYyxYw) NrjriTi^r^rr*rrMgsq6)rnrorprqrr6rb r`rar rr rorr)logvals r0test_ncx2_tails_pdfrg s  ">g~6UZZ^^Aryyc':A>B""1biiS&91=>  BKK  # # %&  "Mg~6UZZ^^E1b115 ))%B79KLMM>>MMsBE&,A1E2&E/2E;zmethod, expectedrhg u%>g ;Q=r`ggRz\R>rgʎK$/gԆX1rgfHu@ge:@cjttj|dddgd}t||dy)NrTrrrW)rrr{r)r$r6rb r)r5rOrs r0test_ncx2_zero_ncri s/ )WUZZ (!QB ?FFH51r2ctjjddd}tjjdd}t ||dy)NrWrr)rrr)rrr{r)r6rb rrKr)rrOs r0test_ncx2_zero_nc_rvsrk s>ZZ^^raa^ 8Fzz~~!~4HFH51r2cdtjddz}ttjj dd|dy)NrWrrrrrr)rar rr6rb rh)rs r0test_ncx2_gh12731rn s4 RYYq"  Bb115r2ctjgd}d\}}tjj |||}gd}t ||dy)N) gю] @gj%@gb y/7@gH@gIZ@g Xl@g'/2?8@gݰmА@gU @gy]`'@g@g*\@g48c@)rgh?8@rm ) rKrKrKrKrKg?gy[qD?rxrxrxrxrxrxrr)rarr6rb rr)rVnurr sf_expecteds r0test_ncx2_gh8665rr sM " #A %GB qRC (B'K B %0r2c d}d}tjtjj d||tjj d||d}tjj |||}tj j |||ztjd|zd|zz}t||d y) Ni,ir[rr*r^ r^rrr) rarPr6rb rr`rrr)rrrVncx2_pdf gauss_approxs r0test_ncx2_gh11777rv  s B B EJJNN5"b1JJNN5"b1u >Azz~~aR(H::>>!R"Wbgga"fq2vo.FGLHl6r2zx, c, expected))r^rg|1q?)r^r^g~?)rrV<3T1=)7yQCru lY<)rgvHGBg^b!*1=)rrgS?c^tjj||}t||dyNr )r6 foldcauchyrrrVrrOrs r0test_foldcauchy_sfr~ / s(     Q "BB%(r2rm))r^g?)rrw )rx ry )g6ްPg8R#/c\tjj|}t||dyr{ )r6rrr)rVrOrs r0test_halfcauchy_sfr = s&     Q BB%(r2z p, expected))g?g*wӄZ>)333333?gN9?)rsrK)rug8<,O@)rzg:B)gl ׶w/gMb}[PcZtjj|}t||yrm)r6rrr)rmrOrVs r0test_halfcauchy_isfr I s$ QAAx r2chtjdd}t|jddy)Nrrr)r6rrrh)ris r0test_foldnorm_zeror U s$  #BAr2))r^rgwo {?)rrgGd-P/)rWr5gof?)r r5g Oul";c^tjj||}t||dy)Nrz)r6rrrr} s r0test_foldnorm_sfr i s&   1a BB%(r2ctjjgddd}tjjddgdd}td|D}t||tjjgd}tjjddg}td |D}t||y) N)rxrsrKrrsrKc3bK|]'}tjtj|f)ywrmrarErrs r0rz-test_stats_shapes_argcheck..x s!8q"%% *8-/)r^rrr^rc3bK|]'}tj|tjf)ywrmr rs r0rz-test_stats_shapes_argcheck..~ s!8q"%%266 *8r )r6rtuplerr)mv3mv2 mv2_augmenteds r0test_stats_shapes_argcheckr s s ..  3 7C ..  Sz1c 2C8C88M$ --  l +C --  q#h 'C8C88M$r2ceZdZdZy) _distr_gencyNr_r8rjrVr.s r0_pdfz_distr_gen._pdf sr2Nrrrr r8r2r0r r sr2r ceZdZdZy) _distr2_gencd|z|zSr r8r s r0_cdfz_distr2_gen._cdf Avzr2N)rrrr r8r2r0r r sr2r ceZdZdZdZy) _distr3_genc ||zSrmr8rjrVr.r/s r0r z_distr3_gen._pdf s 1u r2cd|z|zSr r8r s r0r z_distr3_gen._cdf sAvzr2Nrrrr r r8r2r0r r s r2r ceZdZdZdZy) _distr6_genc||z|zSrmr8r s r0r z_distr6_gen._pdf ssQwr2cd|z|zSr r8r s r0r z_distr6_gen._cdf r r2Nr r8r2r0r r s r2r creZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdZy)TestSubclassingExplicitShapescXtdd}t|jdddy)Ndummyr.rrrrr_r rr`rj dummy_distrs r0test_correct_shapesz1TestSubclassingExplicitShapes.test_correct_shapes s% gc: [__Q!_,b1r2cjtdd}tt|jdfit dy)Nr Ar rr)r rrr`r r s r0test_wrong_shapes_1z1TestSubclassingExplicitShapes.test_wrong_shapes_1 s' gc: i!AtayAr2crtdd}tddd}tt|jdfi|y)Nr za, b, cr rr^rr)r r rrr`)rjr r%s r0test_wrong_shapes_2z1TestSubclassingExplicitShapes.test_wrong_shapes_2 s1 gi@ Q!q!i!;s;r2cHtdd}tttfi|y)Nr r_r )r rrr rjr%s r0test_shapes_stringz0TestSubclassingExplicitShapes.test_shapes_string s+i3s3r2cHtdd}tttfi|y)Nr z(!)r r r SyntaxErrorr r s r0test_shapes_identifiers_1z7TestSubclassingExplicitShapes.test_shapes_identifiers_1 s.k:55r2cHtdd}tttfi|y)Nr 4chanr r r s r0test_shapes_identifiers_2z7TestSubclassingExplicitShapes.test_shapes_identifiers_2 0k:55r2cHtdd}tttfi|y)Nr zm(fti)r r r s r0test_shapes_identifiers_3z7TestSubclassingExplicitShapes.test_shapes_identifiers_3 s1k:55r2cHtdd}tttfi|y)Nr za=2r r r s r0"test_shapes_identifiers_nodefaultsz@TestSubclassingExplicitShapes.test_shapes_identifiers_nodefaults s.k:55r2cHtdd}tttfi|y)Nr z*argsr r r s r0test_shapes_argsz.TestSubclassingExplicitShapes.test_shapes_args r r2cHtdd}tttfi|y)Nr z**kwargsr r r s r0test_shapes_kwargsz0TestSubclassingExplicitShapes.test_shapes_kwargs s 3k:55r2cHtdd}tttfi|y)Nr za, b, c, lambdar r r s r0test_shapes_keywordsz2TestSubclassingExplicitShapes.test_shapes_keywords s(9:k:55r2cGddtj}|d}t|jddtjjddzy)NceZdZdZy)FTestSubclassingExplicitShapes.test_shapes_signature.._dist_gencFtjj||zSrmr6rr r s r0r zKTestSubclassingExplicitShapes.test_shapes_signature.._dist_gen._pdf zzq)A--r2Nr r8r2r0 _dist_genr  .r2r r.rrsr^rr6r<rr`rrjr rKs r0test_shapes_signaturez3TestSubclassingExplicitShapes.test_shapes_signature sI .++ .$TXXcQX')?r2cGddtj}|d}tt|jdfit ddy) NceZdZdZy)STestSubclassingExplicitShapes.test_shapes_signature_inconsistent.._dist_gencFtjj||zSrmr r s r0r zXTestSubclassingExplicitShapes.test_shapes_signature_inconsistent.._dist_gen._pdf r r2Nr r8r2r0r r r r2r rr rsrr^r<)r6r<rrr`r r s r0"test_shapes_signature_inconsistentz@TestSubclassingExplicitShapes.test_shapes_signature_inconsistent s; .++ .'i3A$a.Ar2cGddtj}|d}t|jddtjjddzt|jddtjjddzt t |jdfitdy) NceZdZdZy)?TestSubclassingExplicitShapes.test_star_args.._dist_gencP|d}tjj||zSNrr )rjrVr& extra_kwargs r0r zDTestSubclassingExplicitShapes.test_star_args.._dist_gen._pdf s#"1g zzq)K77r2Nr r8r2r0r r s 8r2r r r rs!r )xxx)r6r<rr`rrrr r s r0test_star_argsz,TestSubclassingExplicitShapes.test_star_args s 8++ 8  .TXXcrX2EJJNN34G4JKTXXc2& s(;B(>?i3?$2,?r2cJGddtj}|d}t|jdddtjjddzdzt|jdddtjjddzdzy) NceZdZdZy)ATestSubclassingExplicitShapes.test_star_args_2.._dist_gencV|d}tjj||z|zSr r )rjrVr. r&r s r0r zFTestSubclassingExplicitShapes.test_star_args_2.._dist_gen._pdf s("1g zzq)K7&@@r2Nr r8r2r0r r s Ar2r zoffset, extra_kwargr rsor )r. r r r s r0test_star_args_2z.TestSubclassingExplicitShapes.test_star_args_2 s A++ A  56TXXc#2X>ZZ^^C(+c1 3TXXc3+ZZ^^C(+c1 3r2cGddtj}|d}t|jddtjjdy)NceZdZdZy)BTestSubclassingExplicitShapes.test_extra_kwarg.._distr_gencj|jdd}tjj||zS)Nr r)popr6rr )rjrVr&kwargsr s r0r zGTestSubclassingExplicitShapes.test_extra_kwarg.._distr_gen._pdf !s,%jj: zzq)K77r2Nr r8r2r0r r !s 8r2r r r rrr r )rjr rKs r0test_extra_kwargz.TestSubclassingExplicitShapes.test_extra_kwarg!sD 8,, 8/TXXaQX/1BCr2cGddtj}|d}t|jdtjjdy)NceZdZdZy)ITestSubclassingExplicitShapes.test_shapes_empty_string.._dist_genc@tjj|Srm)r6rr`rs r0r zNTestSubclassingExplicitShapes.test_shapes_empty_string.._dist_gen._pdf!szz~~a((r2Nr r8r2r0r r !s )r2r r rsr r s r0test_shapes_empty_stringz6TestSubclassingExplicitShapes.test_shapes_empty_string!s? )++ )#TXXc]EJJNN3$78r2N)rrrr r r r r r r r r r r r r r r r r r8r2r0r r s\2B< 4 6 666666 @B @ 3 D9r2r ceZdZdZdZej jeddZ ej jeddZ dZ dZ d Z d Zy ) TestSubclassingNoShapescVtd}t|jdddy)Nr rrrr_r r s r0test_only__pdfz&TestSubclassingNoShapes.test_only__pdf !s# g. [__Q!_,b1r2cVtd}t|jdddy)Nr r rr)r rr`r s r0test_only__cdfz&TestSubclassingNoShapes.test_only__cdf$!s#!w/ KOOAO3Q7r2docstring strippedrctd}t|jdt|jdt j d|j }tt|dk(y)Nr r rr.zlogpdf\(x, a, loc=0, scale=1\)) r rnumargsrrefindallrr rrjr rs r0test_signature_inspectionz1TestSubclassingNoShapes.test_signature_inspection)!sX!g. [((!,[''-jj:$,,.CA r2ctd}t|jdt|jdt j d|j }tt|dk(y)Nr r r^rz!logpdf\(x, a, b, loc=0, scale=1\)r) r rr rr r rr rr s r0test_signature_inspection_2argsz7TestSubclassingNoShapes.test_signature_inspection_2args4!sX"w/ [((!,[''0jj=$,,.CA r2c0tttdy)Nr r )rrr ros r00test_signature_inspection_2args_incorrect_shapeszHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapes>!si7;r2clGddtj}tt|fit dy)NceZdZddZy)>TestSubclassingNoShapes.test_defaults_raise.._dist_gencyr r8r s r0r zCTestSubclassingNoShapes.test_defaults_raise.._dist_gen._pdfE!r2N)r_r r8r2r0r r D!s r2r r r r6r<rrr rjr s r0test_defaults_raisez+TestSubclassingNoShapes.test_defaults_raiseB!* ++  iAd.@Ar2clGddtj}tt|fit dy)NceZdZdZy)>TestSubclassingNoShapes.test_starargs_raise.._dist_gencyr r8)rjrVr.r&s r0r zCTestSubclassingNoShapes.test_starargs_raise.._dist_gen._pdfL!r r2Nr r8r2r0r r K! r2r r r r r s r0test_starargs_raisez+TestSubclassingNoShapes.test_starargs_raiseI!r r2clGddtj}tt|fit dy)NceZdZdZy)._dist_gencyr r8)rjrVr.r s r0r zATestSubclassingNoShapes.test_kwargs_raise.._dist_gen._pdfS!r r2Nr r8r2r0r r R!r r2r r r r r s r0test_kwargs_raisez)TestSubclassingNoShapes.test_kwargs_raiseP!r r2N)rrrr r rrrDOCSTRINGS_STRIPPEDr r r r r r r8r2r0r r !sy28  [[+4HIJ [[+4HIJ<BBBr2r r cgd}tjD]o}tt|}t|tjtj fs>|D]-}t tj||jdu/qy)N)z,\s*,z\(\s*,z^\s*:) r6rHr$r;r;r<r r searchr)badonesdistnamerKregexs r0rrX!sp-GMM@uh' dU..0C0CD E  @ %6$>? @@r2cttjjtj dddttj jtj dddy)NrWr!rr;rTr)rr6rrrarrb r r8r2r0test_infinite_inputr& b!sB ((R8!< 37;r2ctjjtjjddd}t |dyr)r6lomaxrrhrr8 s r0test_lomax_accuracyr) g!s/  2A6AAvr2ctjjtjjddd}t |dyr)r6rrrhrr8 s r0test_truncexpon_accuracyr+ m!s7 U--11&!>,,Q2A6A3+r2ctjd5}tjdtjj ddtjj ddtjjddtjjtj dt|}t|ddddy#1swYyxYw)zregression test for gh-6219T)ralwaysrsrrxN) rnrorpr6rrhr`rrrarrr)rnumber_of_warnings_throwns r0 test_genextreme_give_no_warningsr1 y!s   -3h' R# R# R# -$'F!.2333s Brrrar) euler_gammargs r0test_genextreme_entropyr4 !s $K   &AAq}q(u5   #AA{QU3   %AA   R 0AA{1}rvvbz1A5EB   $AAr+~)6   %AAr+~)6r2c d}tjj|d}t|dtjj |d}t||d}tjj|d}t|dtjj |d}t||d}tjj|d}t|dtjj |d}t||y) Nrrg'b%4gQ@rgؗҜ;rg.l6?)r6rrrr)rVrErs r0test_genextreme_sf_isfr6 !s2 A Av&AA-.     a (BB A Au%AA()     a 'BB A Aq!AA-.     a #BBr2cbd}tjj|dd}t|dy)Nrzr^rgH&8>)r6r rr)probrs r0test_burr12_ppf_small_argr9 !s, D||a+HH45r2ctjddddd}tjj |dd}tj gd }t ||d tjj |dd }tj gd }t ||d tjj |dd dd}tj gd}t ||d tjj|dd}tj gd}t ||d tjj|dd }tj gd}t ||d tjj|dd dd}tj gd}t ||d y)z All values are calculated using the independent implementation of the ROOT framework (see https://root.cern.ch/). Corresponding ROOT code is given in the comments. r! rLrNrrKrw)rrU)gC,d Ɣ?gH㸘?g5?gM" M#w?gɫs ^?g @?gƴ?g@w?ɫs ^?|?q?gC?r< r; gJó?g,BV\ۤ?g;?g#ek?g%ǓE?g(Ȍx?g>J>r[r|rR)g#{`?gdf?gJq?gSS){?g' w?uL? T)? c AJ?GTn?R1#?gA]P?rA r@ r? r> gvӢ?gKq?gL?g Nrs)rrUr\r])g=aO}?gI8?g#T?aW)?ǓI? J?E?d۳?GTn?8?R1#?kP?g(*T?rI rH rG rF rE rD rC rB )g D )?g:3P?g9?g?S[?r; gOqx?g D )?g9?gɫs ^?gK?gX?g3<֌?g M+?gyS c?gI`s?g辜?g{i?g^0?g?#c?)g%r?gc@v?ghtj}?g(˔^?gHK4U?r= ğ@_?y}D?焂Rr/?N?YjhG?a0L?4f?<@?@CH?g ސF?g5+-#?g?g?q?rJ )g}'v?r= g*V ?rK gr/0+?rL g[8 ?rM gΥ?rN gY?rO g#)a?rP g?̔?rQ g]ؚ?rR g|c?rS )rarPr6 crystalballr`rrrh)r  calculatedrOs r0test_crystalball_functionrV !s D#r"3B'A""&&qsc&:Jxx&'H Hju5""&&qsc&:Jxx34H Hju5 ""&&qscs#&NJxx$%H Hju5""&&qsc&:JxxKLHHju5""&&qsc&:Jxx#$H Hju5 ""&&qscs#&NJxxKLHHju5r2ctjgd}tjgd}tjgd}tjj d||}t ||dtjgd}tjdd tj d d g}||z }tjj d ||}t ||dtjtj tj tj d dg}||z }tjj d||} t || dtjtj tj tj tj dg}||z } tjj d||} t | | dtjtj tj tj tj dg}||z } tjj d||} t | | dtjtj tj tj tj dg}||z }tjj d||}t ||dy)zg All values are calculated using the pdf formula and the integrate function of Mathematica )rwrKrRrwrR)rRrRrwrr=)rKrKrKrKrKrr[r|)gԚh@g [&@gͪ@g2dQ@gn6-@g?ޫV&̿gBgQCRgQF\jrg @gn(@r^g?Җ)rgMg'#@rg('UHrN)rarr6rT r rr)rrUexpected_0th_momentcalculated_0th_momentrr.expected_1th_momentcalculated_1th_momentexpected_2th_momentcalculated_2th_momentexpected_3th_momentcalculated_3th_momentexpected_4th_momentcalculated_4th_momentexpected_5th_momentcalculated_5th_moments r0!test_crystalball_function_momentsrd "s* 88- .D *+A((#<=!--33AtQ?')>UK 88D ED (HbffiCDAd(!--33AtQ?')>UK "&&"&&"&&&(;UK "&&"&&"&&"&&*=>Ad(!--33AtQ?')>UK "&&"&&"&&"&&':;Ad(!--33AtQ?')>UK "&&"&&"&&"&&(;UKr2ctjdd}|j}d\}}}tj|||}t t |j||}t||dy)Nr^r)ir0rrr|) r6rT r>rarPrrr`r)cbrrrrrVrs r0test_crystalball_entropyrg M"s`   1a B :: library(evd) > library(fitdistrplus) > x = c(1, 1.25, 2, 2.5, 2.8, 3, 3.8, 4, 5, 8, 10, 12, 64, 99) > result = fitdist(x, 'frechet', control=list(reltol=1e-13), + fix.arg=list(loc=0), start=list(shape=2, scale=3)) > result Fitting of the distribution ' frechet ' by maximum likelihood Parameters: estimate Std. Error shape 1.048482 0.2261815 scale 3.099456 0.8292887 Fixed parameters: value loc 0 rc$t||||ddS)Nr)r&dispxtolftol)r#)rx0r&rj s r0rXz&test_invweibull_fit..optimizero"sD"4dUKKr2)rrr^r rrrrrr;rWrM@c)rrXg`?rr|g [@N)r8r)rarr6rrr)rXrVrr\r]s r0test_invweibull_fitrp X"s_.L HIA$$((i(HMAsEAxd+ !8O8E8$/r2))rrg7Ըh?)rrgz]r>)rg"@goBڱ9)rIrg$=cC;c`tjj||}t||dyrz)r6rrr)rVrrOrs r0test_invweibull_sfrr z"s( ""1a(HHhU3r2zp, c, expected)rsr g9?)geK@g&4I,)?)decimals)r6rrhrraround) scipy_val check_vals r0test_ncf_cdf_spotcheckr "s6  b!R.IIIrxx A>?r2rz(On some 32-bit the warning is not raisedcXtjddd}d|d<d}tjt5t j j|g|}|Dcgc]"}t j j|g|$}}dddtycc}w#1swYxYw)Nrrrrz)rTr^rrr) rarPrrrqr6rrr)rVparrvxiq0s r0test_ncf_ppf_issue_17026r "s Aq#A AaD C n %3 IIMM! "c "01 2"eiimmB%% 2 23Ar333s%B 'BB B  B)c0eZdZdZdZdZdZdZdZy) TestHistogramcPtjjdtjgdd}t j ||_tjjdddd }tj|d }t j ||_ y) Nr)rr^r^rrrrrrrrrrrrrrrrrrrr;r;rfr;binsrKr r*{rr3) rarr histogramr6r=templaterr norm_template)rjr rnorm_histograms r0r-zTestHistogram.setup_method"s{ tLL"@FGI **95 zz~~#Su3~Od4"//?r2ctjgd}tjgd}t|jj ||t |jj ddt |jj ddt |jj ddt |jj ddtjd d d }t|jj |tjj |d d dy)NrxrsrKrrwr rRr6rr8rL@rrrrer!@r=r)rxrxrDrD{Gz?r Q?r {Gz?r rrr r r r r r rxrxrr r r=rxrrr^rWrKr r[rTr|) rarrrr r`rrPr r6r)rjr pdf_valuesrVs r0rIzTestHistogram.test_pdf"sMNZZ!IJ  ))&1:> DMM--c2H=DMM--c2H= DMM--c2H=DMM--d3X> KKAr "**..q1 qc=C Ir2ctjgd}tjgd}t|jj ||t|jj |dd|ddtjddd}t|jj |jj ||tjddd}t|jj |jj ||tjd dd }t|jj |tjj |dd d y)Nr )rxrxrxr}rDr r ףp= ?Q?{Gz?r'rsr (\?RQ?= ףp=?)\(?r[ rKrKr^rrKr=rXrxrrWr r[rTr|) rarrrr rhrrPr r6r)rjr cdf_valuesrVs r0rzTestHistogram.test_cdf_ppf"s)MNZZ!MN  ))&1:> ))*Qr*:;VAb\J KKS# & ))$--*;*;A*>?C KKS# & ))$--*;*;A*>?C KKAr "**..q1 qc=C Ir2cd}|jj|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&kDdy)'Nr*r rrKrxrwrDrr|r r rRr rTr6r rr r8r rLr'rr rsrr rr rr rer rr r r[ r=)r rrrardr)rjrrs r0rAzTestHistogram.test_rvs#s """<RVVFSL)3/v}-x!|#Fv}-x!|#Fv}-x!|#Fv}-x!|#Fv}-x!|#Fv}-x!|#Fv}-y1}4Hv}-y1}4Hv}-y1}4Hv}-y1}4Hv}-y1}4Hv}-y1}4Hv}-y1}4Hv}-y1}4Hv}-y1}4Hv}-y1}4HRVVFSL)3/r2ctdD]L}t|jj|t j ddj |dNy)NrrKr rr|)rrr r r6rrrws r0rn zTestHistogram.test_munp#sNq GA D..44Q7!JJsC077: G Gr2ct|jjtjjdddy)NrKr r[rr|)rr r>r6rros r0rhzTestHistogram.test_entropy!#s5**224 **s#*>T Kr2N) rrrr-rIrrArn rhr8r2r0r r "s%@ I4I,0,G Kr2r cddggd}}tj||fd}tjj |j ddgddg|j dk(sJtj||fd}tjj |j ddgd |j d k(sJd }tjt| 5tj||f}|j d k(sJ dddtj|gd f}|j dk(sJy#1swY8xYw)Nr)rrr)F)rrsrr Tg'^P?gH@z(Bin widths are not constant. Assuming...rr) r6r=rarYrr`rrrrq)countsr rKrs r0test_histogram_non_uniformr &#s&FLDF   vtne #sii##K0   h 0ff%cf2ii##K0x1wwEw4c",,rxx}26adhhj6DHHJ6$66666vvbiio,-333r2r5r8r3c>tjjd}tjj ddd|}tjj ||\}}}}|dk(sJtjj |d|\}}}}|dk(sJy) Nr rTrrrr7r^r4)rarrr6r rr)rjr5rrr.r/r\r]s r0test_fit_overridez TestLogUniform.test_fit_overrideO#sii##K0""33"G ++//F/C1c5zz ++//Af/M1c5zzr2ctjjd}d\}}tj||}|j ddd}t |j|j|||jd}t |j|j||dtjdd z}|j|}t |dd |ddz d ||z tj|tj|z z } t |j| y) NleVi P)gN~hgZbtirrrr1ri8rrrW)rarrr6r rlrrhrrr r`rr) rjrr.r/rKrhrrVr`rs r0 test_overflowzTestLogUniform.test_overflow\#sii##$7811%kk!QTk*#/5hhDh!#/5 4% %hhqkCRQR("-Aq BFF1I-. T*r2N) rrrr rrrr r r8r2r0r r =#s54" [[Xt}5 6 +r2r ceZdZdZej j dddgddgddggd Zej j d d d gd Zej j dgddZ ej j dgddZ ej j dgddZ ej j dgddZ ej j dgddZ ej j dgddZej j dgddZy )! TestArgusctjjddd}ttjdj |j dy)Nr3rtErrrN)r6argusrrrrs r0test_argus_rvs_large_chiz"TestArgus.test_argus_rvs_large_chit#s= KKOOBSsO ;EKKO002AFFHaHr2zchi, random_staterTr r@r6ctjj|d|}tj|d|f\}}t |dkDy)Nrtrr rr6r rrr )rjrrrVrrms r0rAzTestArgus.test_rvsy#s@ KKOOCc O E||Aw01Dr2rr=rctjj|dd}tj|d\}}t |dkDy)Nrtie rcdd|dzz dzz S)Nrr^rr8rs r0rFz.TestArgus.test_rvs_small_chi..#sa!Q$h#->)>r2rr )rjrrrrms r0test_rvs_small_chizTestArgus.test_rvs_small_chi#s= KKOOCcO ?||A>?1Dr2zchi, expected_mean))rgщi?)rWg.憃?)rg\paP?)rg ?)ro g,6?cbtjj|d}t||dy)Nrrrr|)r6r rr)rjr expected_meanrUs r0rzTestArgus.test_mean#s) KK  S  *=u5r2zchi, expected_var, rtol))rgLH'B?r)rWgo$?r$)rg =>r)rg2W>r)ro gb~P>rcbtjj|d}t|||y)Nrrr|)r6r rr)rjr expected_varr}rVs r0rzTestArgus.test_var#s& KKOOCqO )r{)r[gF=rz)rg߹Q#B=rz)rg0ޟ$?g;Lf?gaW?)ru)gx?g43n?gwY?)r[)go7🤎?g +-oGn?gIQ9‹Y?)r)g T?gGn?g@̋Y?)r)gU?g{Gn?giG͋Y?)r=)gDU?g{Gn?gH͋Y?ctjgd}ttjj |||dy)Nr rr|)rarrr6r rhr s r0test_cdf_small_chizTestArgus.test_cdf_small_chi#r r2))rs)g Q)?g6{?r)gB`"۹?)g?g8%?r$)rT)g388?gV%?r)ru)g*j?gRS%?r)r[)g! |?gZ%?r)r)gy[|?gG%?r)r)g"3|?gW%?r)r=)g!3|?gW%?rcbtjj|d}t|||y)NrYrTr|)r6r r)rjrrOr}r@s r0test_stats_small_chizTestArgus.test_stats_small_chi#s)kkT2XD1r2N)rrrr rrrrAr rrr r r r r r8r2r0r r s#sI  [[0 #J #J #J3      [[UT4L12 [[189 6 9 6  [[6BC 4 C 4  [[2DE>E> [[ M NG NG  [[ N OF OF  [[ P QG QG  [[ C D2 D2r2r ceZdZdZdZej jdgddZej jdgddZ dZ ej jd gd d Z ej jd ej jdgdej jdgdej jdgddZ ej jdgdej jdgddZy) TestNakagamicdd}d}tjj||}t|dy)Nr r gM+)r6nakagamirr)rjrp rVrps r0rqzTestNakagami.test_logpdf#s/ ~~$$Q+12r2cd}d}tjj||}t|ddtjj ||}t||dy)Nr rLg"S+:rr|)r6r rrr)rjrp rm rrs r0rzTestNakagami.test_sf_isf#sS  ^^  r2 &1> ^^  B 'BU+r2zm, ref))rg|Bd븿)rsr)rWg/ۿcZttjj||dy)Ng^~z=r|rr6r r>rjrUr|s r0rhzTestNakagami.test_entropy$s ..q13WEr2))rg}Ô%I)r gq_)gScAgB4U)gcAgu1U)rgb >%)rgWҙ\cVttjj||yrmr r s r0test_extreme_nuzTestNakagami.test_extreme_nu$$s ..q137r2ctjtjj dsJtjtjj dsJy)Nrr)rarr6r _entropyros r0test_entropy_overflowz"TestNakagami.test_entropy_overflow+$sD{{5>>2259:::{{5>>226:;;;r2znu, ref))rg2H?)rg:U?)r g>cZttjj||dyr)rr6r r)rjrp r|s r0rzTestNakagami.test_mean/$s ++B/5Ar2z+Fit of nakagami not reliable, see gh-10908.rrp )rr rr\)rvrW#r])rrrc d tjj |||d tjj \}}}t ||dt ||dt ||d fd} fd} fd} t ||||d d t ||||d d t | |||d d y) NrX9rrp r\r]rrr|cd|zdztjd|z z zd|z|dzz tj|z zzS)Nrrr^rard)rp r\r]rs r0 dlogl_dnuz(TestNakagami.test_fit..dlogl_dnuJ$sPUQY"&&GcM):";;d5!8mbffWs]&;;< =r2cdtj|ztd|z zdtjtj|z |z zztj|z |z dzz S)Nrrr^)rarrrdrp r\r]rrs r0 dlogl_dlocz)TestNakagami.test_fit..dlogl_dlocN$spRVVBZ)Ar*::;rvvw}&=>??@ffw}59:; .dlogl_dscaleS$sF!GbL5("fuz)BFFGcMa3G,HHI Jr2rr[r)r6r rrr) rjrp r\r]nu_estloc_est scale_estr r r rrs @@r0rzTestNakagami.test_fit;$s ..$$!+0t%E%*^^%7%7%@"-3/ 5s3 = <  J  &'9=qtL 67I>M VWi@!$Or2cxd}d}tjj||||d}tjj||\}}}t j |} t j t j||z dz} t||dt|| dt|| dy) NrsrXr r rr^rr|) r6r rrrar#rrr) rjr\r]rp rlrr r r loc_theo scale_theos r0 test_fit_nuzTestNakagami.test_fit_nu[$s  ..$$!+0t%E%*^^%7%7B%7%G"66'?WWRWWg&7A%=>? .5 :D9r2N)rrrrqrrrrrhr r rrrr r8r2r0r r #sI3",& [[X $% F % F [[X DE8 E8< [[Y>?B ?B [[KL [[T?3 [[UN3 [[Wk2P344MP8 [[UN3 [[Wk2:34:r2r ceZdZdZdZdZy)TestWrapCauchyctjddgddgg}tjdgdgg}tjj ||}|j dk(sJtj ||fDcgc]%\}}tjj ||'}}}t|j|d ycc}}w) NQ?rcrsrrKrrrr|) rarr6 wrapcauchyrhr9nditerrr )rjrrVrmrr scalar_valuess r0test_cdf_shape_broadcastingz*TestWrapCauchy.test_cdf_shape_broadcastingq$s HHtTlS$K0 1 HHsecU^ $    A &ww&   )+Aq6):<%b"))--b"5< < =u=?!a"))Brvvbeebdl/C,C"DRUU"JJKr2N)rrrr r rSr8r2r0r r o$s >,Lr2r cGddtj}|d}ttd5|j dddy#1swYyxYw)NceZdZdZy)/test_rvs_no_size_error..rvs_no_size_gencyrr8ros r0_rvsz4test_rvs_no_size_error..rvs_no_size_gen._rvs$sr2N)rrrr r8r2r0rvs_no_size_genr $s r2r rvs_no_sizer z_rvs\(\) got (an|\d) unexpectedr)r6r<rrr)r r s r0test_rvs_no_size_errorr $sJ%--"}5K y(J Ks AAzdistname, argsct|tvrtjd|dtt|}t |tj rt|dk7rF|j|\}}t|tjt|tjd\}}|jg|||\}}t|tjt|tjy|j|\} } t| tjt| tjy)Nz6skipping test for the support method for distribution .rrs) $skip_test_support_gh13294_regressionrrr$r6r;r<rsupportrrar) r# r&rKa0b0rra1b1r.r/s r0test_support_gh13294_regressionr $s77 $$,:Q0 1 5( #D$++, t9>!T\\4(FB RVV $ RVV $  f2t2T262BR R t||T"1QQr2ctjjgdgd\}}tjtj tj tj tj g}tjtj tj tj tj g}t||t|||j|jk(sJ|j|jk(sJtjjgg\}}tjgtjg}}t||t|||j|jk(sJ|j|jk(sJtjjgddg\}} tjdtj gz} tjdtj gz} t|| t| | |j| jk(sJ| j| jk(sJy)N)rrrr)rrrrrr) r6rr rarrrrr9) r r ex_a0ex_b0r r ex_a1ex_b1r:r3ex_a2ex_b2s r0,test_support_broadcasting_gh13294_regressionr $s ZZ   m >#u % + +v 55 5r2)gn! g:I"<)gQ @gE?cttjj||ttjj | |yrm)rr6cosinerhr)rVrOs r0test_cosine_cdf_sfr! $s6ELL$$Q'2ELLOOQB'2r2))rgkM6O)rPg0ӭ! )r g;'u(@cttjj||ttjj || yrm)rr6r rr)rmrOs r0test_cosine_ppf_isfr# $s8 ELL$$Q'2ELL$$Q'(3r2ctjjtj tjg}t |dy)NgrB)r6r rrarbr )rps r0test_cosine_logpdf_endpointsr% $s1 <<   /Dd./r2c0tDchc]\}}t|tr|}}}tDchc]\}}| }}}||k(sJtDchc]\}}| }}}t Dchc]\}}| }}}||k(sJycc}}wcc}}wcc}}wcc}}wrm)rr;rBrrr)rrdiscrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamess r0test_distr_params_listsr+ $s/;474'c2441@AgdATAA !6 66 6*23wtQd3N3-89'$99 . .. .4A49sB B B ) Bctjjddtjjdddk(sJtjj dddk(sJy)NrrSrr)r0r.rR)r6r_statsrr r8r2r0test_moment_order_4r. $s` NNAs+ >> qA .# 55 5 >>  1 % ,, ,r2c eZdZejdZej jdgddZej jdgddZ ej jdejd d ej j ejd d ej j ejddej j gdZ y)TestRelativisticBWctjttjdz }tj j |jd}|S)a&Sample data points for pdf computed with CERN's ROOT See - https://root.cern/ Uses ROOT.TMath.BreitWignerRelativistic, available in ROOT versions 6.27+ pdf calculated for Z0 Boson, W Boson, and Higgs Boson for x in `np.linspace(0, 200, 401)`. z-data/rel_breitwigner_pdf_sample_data_ROOT.npyzx,pdf,rho,gammar rors r0ROOT_pdf_sample_dataz'TestRelativisticBW.ROOT_pdf_sample_data%sLww N ! ! ; < vv  /@ A r2zrho,gamma,rtol))qVEB@gj+@r)‰FC@Gz@rz)ND@_LU?rc||d|k(|d|k(z}|d|d}}t|tjj||||y)NrhorVrVr`rr|)rr6rel_breitwignerr`)rjr2 r: rVr}rrVr`s r0test_pdf_against_ROOTz(TestRelativisticBW.test_pdf_against_ROOT'%sg$ !% (C /#G,5 7 cDK3 &&**1c*?d r2zrho, Gamma, rtol))r3 r4 r)r5 r6 r)r7 r8 g& .>cd}tjddd}tjj |||}tjj |||}||||z|}t |||y)Nc tj|dz|dz|dzzz}dtjdz|z|z|ztjtj|dz|zzz }||dz|dzz dz|dz|dzzzz Sr)rarrb)ErGammarVrSs r0r`zFTestRelativisticBW.test_pdf_against_simple_implementation..pdf@%sGGAqDAqD5!8O45ERWWQZ!#e+e3EEBGGAqD5L113AA1q(1a4q=89 9r2rrrWrr|)rarPr6r; rr`r) rjr: r@ r}r`rmrVrr|s r0&test_pdf_against_simple_implementationz9TestRelativisticBW.test_pdf_against_simple_implementation8%ss : KKdB '  ! ! % %aE % :##''3e'<!SY&St,r2z rho,gammar3 r4 rwr5 r6 r7 r8 cd}tjj|}tjj ||d|}tjj |d}t|d|df||fd|d dk(sJtjj |d| }t|d|d |d |dfd|fk(sJy ) zpTests fit for cases where floc is set. `rel_breitwigner` has special handling for these cases. ls ; rl#r)r]rrrrr^rr|rrruN)rarrr6r; rrr)rjr: rVrrrrs r0 test_fit_flocz TestRelativisticBW.test_fit_flocL%s$#ii##D)$$(( u4c) ##''1'5QQ(3,TB1v{{##''1U'CA$/AAAu:---r2N)rrrrr0r2 rrr< rA rrrrC r8r2r0r0 r0 %s ^^$ [[    [[/2  -  - [[ FLL"F&++2B2B  FLL!5 0A0A  FLL & 0A0A    . .r2r0 cTeZdZejj dddgdZy) TestJohnsonSUrN)rV r{r}rg={?g?5mV>gn?g\}\1@)g`fo@g$ں _@rrgvUg Nv>T!"XE2r2N)rrrrrrrG r8r2r0rE rE l%s9 [[V O J&KL 3 L 3r2rE c eZdZdZej j dddgej j dddgej j dddgej j dddgdZy ) TestTruncParetoc.d\}}tjdd}tj||j |}tj |j |tj |j |z }t||y)N)?333333@rK rL )rarPr6 truncparetor`r9rhr)rjr/rrVrr|s r0rIzTestTruncPareto.test_pdf}%sr1 KKS !1%))!,ll1o!!!$u||A':':1'==S!r2rTFrr@rPctjjd}d\}}}} tj|||| } | j d|} i} |r|| d<|r| | d<|r|| d<|r|| d <|rM|rK|rI|rGd } t jt| 5tjj| fi| dddyttj| fi| y#1swYyxYw) NlZ #Lm)rK rL rr r[rtrrrrrrr) rarrr6rM rrr r rr)rjrrr@rPrr/rr\r]rKrrrs r0rzTestTruncPareto.test_fit%s ii##$78+1c5  A3e<xxSsx3 DL "DN DJ DJ yUuKG|7; 4!!%%d3d3 4 4 *%*;*;T JT J 4 4s !CC%N)rrrrIrrrrr8r2r0rI rI |%s" [[Yu 6 [[[4-8 [[WtUm4 [[WtUm4K5597Kr2rI ceZdZdZy) TestKappa3cdtjjddz }tjjdd}t ||y)Nrrsgj@)r6kappa3rhrr)rjsf0rs r0rzTestKappa3.test_sf%s=%,,""3,,llooc3'S!r2N)rrrrr8r2r0rP rP %s"r2rP rN))rR NNNN)rJNNNN)rNNNN)r( NNNN)r9NNNNc|\}}}}}tjd}|xsd}|xsd}|xsd}|xsd}tt|}t t |}||} tj ||} | j| j| } t| | ||dtj ||dz } | j| j| } t| | ||y) Nrsiirrrrr) rar r$r6r rrrrr) rNr# lp1lp2rr}lpmrKrZ dist_frozenr|rs r0test_sf_isf_overridesrY %s&*"Hc3d ((3-C +C *C 91D =5D 5( #D (^H %F-K ++c3 C ..- .CC4d3 bkk#sB' 'C ..- .CC4d3r2rm)NF(rrnr rrdpathlibrr r r numpy.testingrrrrrr r r r rr rr8rarrnumpy.lib.recfunctionsrr5rscipy._lib._utilrrrrrr scipy.statsr6!scipy.stats._distn_infrastructurerscipy.stats.distributions scipy.specialrrrscipy.stats._distr_paramsrrtest_discrete_basicrrscipy.stats._continuous_distnsr r!scipy.optimizer"r#r$ itertoolsr%flagsoptimizer rrr r1r9rPrRrrrrr'r)rUrrrrrrrr-r6r^rrrrrrrrrrrrlrrrrrrr"r4r^rrrrrrrr2rGrVrfrpryrrrrrrrbr^rr`rqr~rrrrrrrrr$r7r9rHrPr[r`rrrrrOr}rrr r r r) r7 r> rL rR r} r r r r r r r r r r# rr% r' r* r, r/ r1 r3 r6 r9 r; r> r@ rB rD rF rL rN rQ rT rW rY r\ r` rd rg ri rk rn rr rv r~ r r r r r r<r r r r r r rr& r) r+ r- r1 r4 r6 r9 rV rd rg rp rr rt r{ r} r rr r r r r r r r r r r r! r# r% r+ r. r0 rE rI rP rY r8r2r0ri s[   AAA* "4/338 00;>C==ii((1,||x'M.>h.>.>.@H.L )6z'B$$ 8 F@F@R4D..>? 6 ? 699>G,G,T**>/B/Bd##>*'D'DT C CA2A2H44D;6;6|**. G GFK"K"\=I=I@`&`&FXDXDvDD,DD,U<Ui>V 3P6P6f'C'CT&&>$$*l  l  ^))   , lGlG^e,e,Pw;w;t>>>>B",",JB&B&J668;";"|e.e.P...SFSFl..2J/J/Z ? ?F[L[L|66(??, N NRBRBj%.%.PAAH <9 !*'0EF/G/ <*585.2(:#4L , )JK AK A#072'0 -.*FG1G1 -& 9%&P-M"+ HBHHo7 89 HBHHo7 89 xrxx|456 HBHHk;/ 01 . 2  226 16 7:);<)<):; ) ; );<!<! ();< ) < ) %*$$ %%% %%%%%%u9u9p8B8Bv'0DE@F@<   , 37.)X 6D6N+L\+0D)FG 4 G 4 )<<>?4?4  !" "#_ =  = *@CKK5(EGG^K^KB.3+3+lv2v2r@:@:FLL8 )?[+HI J 4#26;467373 784 84 0 /-(V.V.r 3 3 #K#KL"""GH 4 H 4r2