+ 0ieRt^RIt^RIt^RIt^RIt^RIt^RIHt^RIt^RI t ^RI t ^RI H t H t HtHtHtHtHtHt^RIt^RIHt^RIt^RIHtHt^RIHt^RIHt^RIH t ^R I!H"t"H#t#H$t$H%t%^RI&H't'^R I(H)t)^R I*H+t+^RI,t^R I-H.t.H/t/H0t0^R I1H2t2H3t3^RI4H5t5H6t6^RI7H8t8H9t9^RI:H;t;HH?t?]PP^8tB]PR8H;'d] P!4R8HtDRR.tEERbRltFRtGRtH!RR4tIERcRltJRtK]PPR.ERdO4R4tN!RR 4tO!R!R"4tP!R#R$4tQ!R%R&4tR!R'R(4tS!R)R*4tT!R+R,4tU!R-R.4tV!R/R04tW!R1R24tX!R3R44tY!R5R64tZ!R7R84t[!R9R:4t\!R;R<4t]!R=R>4t^!R?R@4t_!RARB4t`!RCRD4ta!RERF4tb!RGRH4tc!RIRJ4td!RKRL4te!RMRN4tf!RORP4tg!RQRR4th!RSRT4ti!RURV4tj!RWRX4tk!RYRZ4tl!R[R\4tm!R]R^4tn!R_R`4to!RaRb4tp!RcRd4tq!ReRf4tr!RgRh4ts!RiRj4tt!RkRl4tu!RmRn4tv!RoRp4tw!RqRr4tx!RsRt4ty!RuRv4tz!RwRx4t{!RyRz4t|!R{R|4t}!R}R~4t~!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t^^]EP !^^]EP ,, 4,^ERe]EP !^^]EP ,, 4,^ERf]EP !^^]EP ,, 4,^ERg]EP !^^]EP ,, 4,^iERh]EP !^^]EP ,, 4,. 3R]EP !^^e]EP ,, 4^ERi]EP !^^e]EP ,, 4,^R]EP !^^e]EP ,, 4,R, ^R]EP !^^e]EP ,, 4,R, ^iR]EP !^^e]EP ,, 4,R, . 3ERjERj]EP !^]EP ,4, ^ERk^ ]EP !^]EP ,4,, ^ERl^d]EP !^]EP ,4,, ^ERm^]EP !^]EP ,4,, ^iERnR]EP !^]EP ,4,, RERoR]EP !^]EP ,4,, RERpR]EP !^]EP ,4,, R.3.t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4tRt!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4tRt!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4t!RR4tRt]PEPm]BRR7R4tRtRtRtRtRtRtRtRt!RR4tRtRtERtERtERtERtERtERt]PPERER]P4!ERER .43ER ]P4!ER ER .43ER ]P4!ERqERr.43ER]P4!ERER.43.4ER4tERtERtERtERt]PPER.ERsO4ER4t]PPER.ERtO4ER4t]PPER.ERuO4ER4tERt]PPER.ERvO4ER4tERt!ERER ]'EP4t!ER!ER"]'EP4t!ER#ER$]'EP4t!ER%ER&]'EP4t!ER'ER(4t!ER)ER*4t]PEPm]BER+R7ER,4tER-tER.tER/tER0tER1tER2tER3tER4tER5tER6t]PPER.ERwO4ER74t]PPER8ERxERy.4ER94t]PPER:^^.ERzO3^^ .ERzO3^^.ER{O3.4ER;4tER<tER=tER>t!ER?ER@4tERAt!ERBERC4t!ERDERE4t!ERFERG4t!ERHERI4tERJt]PPERK]6]3,4ERL4tERMtERNt]PPERER|ER}.4ERO4t]PPER.ER~O4ERP4tERQtERRtERSt!ERTERU4t!ERVERW4t!ERXERY4t!ERZER[4t!ER\ER]4t!ER^ER_4Et]PPER`.ERO4ERa4EtR#(z! Test functions for stats module N)Path) assert_equalassert_array_equalassert_almost_equalassert_array_almost_equalassert_allcloseassert_assert_array_lessassert_array_max_ulp)raises) typecodesarray)rec_append_fields)special)check_random_state)IntegrationWarningquad trapezoidcumulative_trapezoid) argsreduce)_XMAX)xlogy polygammaentr)distcont invdistcont) distdiscreteinvdistdiscrete) FitDataError _argus_phi)rootfmindifferential_evolution)productdarwinx86_64 tukeylambdapearson3cHVfV RV 2p\\W4VR7R#)Nz does not have attribute msg)rhasattr)abr*s&&&b/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/stats/tests/test_distributions.py_assert_hasattrr/5s& {,QC0 GAMs#cN\\PPR4R#)f_genN)r/scipystats distributionsr0r.test_api_regressionr7;sEKK--w7r0cB\\PPP4p\ Uu.uF q^,NK pp\ Uu.uF q^,NK pp.ROpW#,V,p\\RV44pW8XgQhR#uupiuupi)c@\V4PR4'*#)<)str startswithss&r..test_distributions_submodule..JsA(9(9#(>$>r0N) rv_discrete rv_continuous rv_histogramentropy)setr3r4r5__all__rrfilter)actualdist continuousdiscreteotherexpecteds r.test_distributions_submodulerO@s **22 3F&./hdq''hJ/$01LDQLH1 E$u,H6>IJH   01s BBc a]tRt^OtoRt]P PR.RO4]P PR^^]P^ ^d.4R44t Rt Rt ]P PR.RO4R4t ]P PR .R O4R 4tR t]P PR .R!O4R 4tRt]P P$]P PR^^.4]P PR.R"O4]P PRRR.4]P PRRR.4R44444t]P P(R4t]P PRR#^.4R4tRtRtRtRtVtR#)$ TestVonMisescN\PPR4VnR#)lExqNnprandom default_rngrngselfs&r. setup_methodTestVonMises.setup_methodP99((4r0kxcRpRpV!V^^V4V!V^^V4V!V^^ V4V!V^^V4V!V^^V4V!V^^ V4R#)c\P!WVR7p\VPV4VPV^\P ,V,,44R#locscaleN)r4vonmisesrpdfrTpir]Lr?r^vms&&&& r.check_vonmises_pdf_periodicHTestVonMises.test_vonmises_periodic..check_vonmises_pdf_periodicVs>2B q 266!q255y1}2E+F Gr0c\P!WVR7p\VPV4^,VPV^\P ,V,,4^,4R#ra)r4rercdfrTrgrhs&&&& r.check_vonmises_cdf_periodicHTestVonMises.test_vonmises_periodic..check_vonmises_cdf_periodicZsK2B q A "qAIM': ;a ? Ar0Nr6)rYr]r^rkros&&& r.test_vonmises_periodic#TestVonMises.test_vonmises_periodicSsd H A $Aq!Q/#Aq!Q/#Aq"a0#Aq!Q/#Aq!Q/#Aq"a0r0c\\PP\P )4\\PP \P 4R#N)rr4 vonmises_liner,rTrgr-rXs&r.test_vonmises_line_support'TestVonMises.test_vonmises_line_supportgs8U((**RUUF3U((**BEE2r0ch\P!R4p\VP^4R4R#) ?N)r4rerrn)rYrjs& r.test_vonmises_numerical$TestVonMises.test_vonmises_numericalks" ^^C BFF1Is+r0zx, kappa, expected_pdfc^\PPW4p\WCRR7R#V瞯<rtolN)r4rerfr)rYr^kappa expected_pdfrfs&&&& r.test_vonmises_pdfTestVonMises.test_vonmises_pdfys"nn  *6r0zkappa, expected_entropyc^\PPV4p\W2RR7R#vIh%<=rN)r4rerEr)rYrexpected_entropyrEs&&& r.test_vonmises_entropy"TestVonMises.test_vonmises_entropys"..((/>r0cpRp\PPV4p\PPV4p\PPV4p\P!^^^R7P VR7p\P!^^\P ,^R7P VR7p\P!^^^\P ,\V4, ^,R7P VR7p\WVRR7\WWRR7R#)i@}rb random_stateratolN) rTrUrVr4rervsrgabsr)rYseedrng1rng2rng3rvs1rvs2rvs3s& r.test_vonmises_rvs_gh4598%TestVonMises.test_vonmises_rvs_gh4598syy$$T*yy$$T*yy$$T*~~aQa044$4G~~aQruuWA6:::M~~aQ%&ruuWSY%6q%8;;>3D3;Q //r0zx, kappa, expected_logpdfc^\PPW4p\WCRR7R#r~)r4relogpdfr)rYr^rexpected_logpdfrs&&&& r.test_vonmises_logpdf!TestVonMises.test_vonmises_logpdfs"&&q0e.Ar0c^#rr6rs&r.r@rrr0c<\P!RV,4#)y?)rTexprs&r.r@rsBFF2a4Lr0 complex_funcN) rTrUrVr4reexpectr issubdtypedtypefloatingrganglecomplexfloating)rYrWrcrlbresboundss& r.test_vonmises_expect!TestVonMises.test_vonmises_expectsNii##$78A+Bnn299+FQ}}SYY 4444!bee)^#nn299+OOQ}}SYY 4444!bee)^#nn299:PS;ASPQS sag7}}SYY(:(:;;;;r0rvs_loc rvs_shapefix_locTF fix_shapecvV'dV'd\P!R4\PP R4p\ P PVRVVR7pR^/pV'dWR&V'dW'R&\\ P V\ P P3/VBR#)zNothing to fit.rsizercrfscaleflocf0N) pytestskiprTrUrVr4rer_assert_less_or_close_loglikennlf)rYrrrrrWdatakwdss&&&&& r.test_fit_MLE_comp_optimizer(TestVonMises.test_fit_MLE_comp_optimizers  KK) *ii##$78~~!!)$G/2"4!} "L "J%ennd&+nn&9&9 C=A Cr0cp.ROp\P!V4pR\P,p\PP WR7wr4pV\P !\4P8XgQh\\PV\PP^VR7R#)g!*K?r)rrN)g!*Kg4,%OԿgZ۵?g ge_@g-8gPghn?grNg d?)r3r4rerrTrgrXs&r.test_vonmises_fit_bounds%TestVonMises.test_vonmises_fit_boundssT    !WA 6    "%%'9"5!6Q ?r0rWN)皙?re))r{Gz?g|65?)r9@g?U?)rryg"?)@rgDfI?)rrg1<)rry))rgA ?)g,eޞ?)dgBb9d22)rg G)g ))rrg EJ?)rrgoι?)rryg0,)rrgdty)rrgʹw[A)rryg)rrחA)__name__ __module__ __qualname____firstlineno__rZrmark parametrizerTrgrqrvr{rrrrrxslowrslowrrrrr__static_attributes____classdictcell__ __classdict__s@r.rQrQOs5 [[S-0 [[S1aC"891:11$3, [[5/0707 [[6;< ? < ? 0  [[8BC=C=<4 [[ [[YA/ [[[-8 [[Yu 6 [[[4-8C9790 C$ [[ O O [[Vb!W- (. ( Q9 @ @r0rQc Vf VPpVP!V3/VBp\\V4V`!V3/VBpV'g!\P !WV8g4'gQhV!WQ4pV!Wa4pWx8:g!\P !WxRR7'gQhRV9dVR,VR,8XgQhRV9dVR,VR,8XgQhR#R#)aF This utility function checks that the negative log-likelihood function (or `func`) of the result computed using dist.fit() is less than or equal to the result computed using the generic fit method. Because of normal numerical imprecision, the "equality" check is made using `np.allclose` with a relative tolerance of 1e-15. Nrrrrr)rrsupertyperTanyallclose) rJrfuncmaybe_identicalrmle_analytical numerical_optll_mle_analyticalll_numerical_opts &&&&, r.rrs |yyXXd+d+N$t*d/==M vvn56666^2M0  1 KK)% H HJ I ~b!T&\1114b!T(^333r0c RR.pVP'd3\VPPR44pV.R ORV, p\\ V\ P !\V4444p.R Op\P!\RR7;_uu_4VP!V3/VBRRR4\P!\RR7;_uu_4VP\ P.4RRR4\P!\RR7;_uu_4VP\ P.4RRR4\P!\RR7;_uu_4VPV^R7RRR4\P!\R R7;_uu_4VP!V.^.\V4^, ,O5!RRR4R# +'giELF;i +'giEL ;i +'giL;i +'giL;i +'giR#;i) rr,N3All parameters fixed. There is nothing to optimize.matchz#The data contains non-finite valueszUnknown keyword arguments:) extra_keywordzToo many positional arguments.)rf1f2r)shapeslensplitdictziprTarangerr RuntimeErrorr ValueErrornaninf TypeError)rJparamnshapes all_fixedrs& r.assert_fit_warningsr0>s X E {{{dkk'',- #HW--S #e* 567I D |& ' ' ## ' zB D D "&& D zB D D "&& D y(D E E Q' F y(H I I -SZ!^,- J I ' ' ' D D D D D F E I I Is<#G4#!H0!H=H/=-I4 H  H  H, / H?  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]]&&t, "4 #6#(==66:) C%G-"++f38u#F#F FF#Fr0c\P!.RO4p\PP V^R7wr#\ V^RRR7\PP V^R7wr#\ V^RRR7R#)rSrrrr#N)rSrSr rTrr=)rTr r4rrr)rYrrcrds& r.test_fit_simple_non_random_data+TestLaplace.test_fit_simple_non_random_data scxx78]]&&t!&4 qu59]]&&tA&6 QU7r0cNRp\PPV)4pVR8XgQh\PPV4pVR8XgQh\PPV4pVR8XgQh\PPV)4pVR8XgQhR#)rrrSN)r4rrnr)rYr^p0p1s& r.test_sf_cdf_extremes TestLaplace.test_sf_cdf_extremes s  ]]  r "Syy]]  q !Syy ]]  a Syy]]  qb !Syyr0c^p\PPV4p\V\P !V)4^, RR7R#)rrrN)r4rrrrTr)rYr^rzs& r.rTestLaplace.test_sf s5  MM  Q 2661":a66"++e&6&6&<& r6Nrr r!r)rzrSr)rg @) rrrrrrrrrrrrrr s@r.rr sDE [[S,/O0O [[S/2 [[\L>: [[WtUm4 [[[4-8F95;3Fr0rc a]tRtRto]P P RRR.4R4t]P!RR7R4t ]P P R.RO4]P P R.RO4]P P R .RO4]P P R ] !R R .^R 7Uu.uFpR V9gK VNK up4R4444t Rt Rt RtRtVtR#uupi) TestPowerlawi zx, a, sfc\\\PPW4VRR7R#r~)rr4powerlawr)rYr^r,rs&&&&r.rTestPowerlaw.test_sf s ))!/%@r0rMrNc@\PPR4#rQrRrXs&r.rWTestPowerlaw.rngrTr0rrrrwTFrxcJ\PP^WW7R7p\4p V'dWR&V'd8\P !VP 4\P)4V R&V'dW9R&\\PV3/V BRR/BR#))rr,rcrdrrrrrTN) r4rrr%rT nextafterrr+rr~s &&&&&&&& r.r(TestPowerlaw.test_fit_MLE_comp_optimizer s~~!!si(1"Ev "J << RVVG)rrzrrr rZr[)rrrrrrrrr\rWr#rrrrrrrs0@r.rr s [[Z1HJKAKA ^^*%+&+ [[[*=> [[Y 3 [[[*5 [[<)0$q)I-)IA!&! a)I-.<.64? <$ D4666{-s  C>C>rc@a]tRtRto]P P R.R O4R4t]P P RR R .4R4t]P P R.R O4R4t ]P P R.RO4R4t Rt Vt R #)TestPowerLogNormiSz x, c, s, refc^\\PPWV4VRR7R#r)rr4 powerlognormrrYr^rr?rs&&&&&r.rTestPowerLogNorm.test_sfds# **--aA6%Hr0z q, c, s, refc^\\PPWV4VRR7R#)g|=rN)rr4rr)rYrrr?rs&&&&&r.rTestPowerLogNorm.test_isfns# **..qQ75Ir0c^\\PPWV4VRR7R#)gt =rN)rr4rrnrs&&&&&r.rZTestPowerLogNorm.test_cdfts# **..qQ75Ir0c^\\PPWV4VRR7R#)gAfc=rN)rr4rrfrs&&&&&r.rPTestPowerLogNorm.test_pdfs# **..qQ75Ir0r6N))rrQrga!R()r2rQrg;?)r2rrgE?)MDrrg=)g?rrr)gR4 -rQrr))rrrg?)rrrgv6)rrrg+ 94|7)rrrg?))rrrgS^Ռe 9)@xDr2rg 0g;)g\)c=Hr2rg7H7) rrrrrrrrrrZrPrrr s@r.rrSs" [[^EF I F I  [[^ACEFJFJ [[^AB J B J [[^GHJ HJr0rca]tRtRto]P P R.R O4R4t]P P R.R O4R4t]P P R.R O4R4t Rt Vt R#) TestPowerNormirc\\\PPW4VRR7R#r)rr4 powernormrrs&&&&r.rTestPowerNorm.test_sfs **10#EBr0rsc\\\PPW4VRR7R#rrN)rr4rrrws&&&&r.rTestPowerNorm.test_isfs ++A13UCr0c\\\PPW4VRR7R#r)rr4rrnrs&&&&r.rZTestPowerNorm.test_cdfs ++A13UCr0r6N))rZrg|<)rQr ge()rrg%!@6)rrgT;-))rrQgĿ)rHrg!X)r rg缂U)rjrgͫ1@)rr gD@)Jz5rgU!zYr@))irZg.u T9)r rZ?)rrZgsK-)rrgk8>)rrg^u1-) rrrrrrrrrrZrrr s@r.rrs [[[CD C D C [[[=>D>D [[[BC D C Dr0rca]tRtRtoRtRtRtRtRt] PPRR R .4R4t R t VtR #) TestInvGammaic*\P!4;_uu_4\P!R\4\P P RRR7p.R Op\ W4.R Op\P P VRR7p.R O\PRR.\PRR.\P\PR.3p\W4FwrE\WE4K R R R 4R # +'giR #;i) rwg(\O3@rr\g^Yb?g,r?gOD@g2*Z@gFN8@N)g~?gCX&?g*7gS?gBqFq@)rR@gffffff@)rg Ey?gў3oz?) r{r|r}r~r4rrrTr+r*r&r)rYrrNr,r^rs& r.test_invgamma_inf_gh_1866&TestInvGamma.test_invgamma_inf_gh_1866s $ $ & &  ! !'> :>>''%'@D%H D +A>>''!V'!5I9>!#/>>s )B8 BcR\PP^ RRR7wrr4\\P!V44\\P!V44\\P!V44\\P!V4'*4R#)r@rrN)r4r$rrTrrds& r.test_f_momentsTestF.test_f_momentssaWW]]2sF]; a A A ABKKN"#r0c\P!4;_uu_4\P!R\4\P P ^ .^,.RORR7RRR4R# +'giR#;i)rwrdfndfdrN)r rrr)r{r|r}r~r4r$rXs&r.test_moments_warningsTestF.test_moments_warningssL  $ $ & &  ! !'> : GGMMrd1f,M G' & & &s AA00 B c\P!^.^ ..4p\P!^ ^ .4p\PPWRR7wr4rVW"^, , .^,p\ W74^V^,,W,^, ,V, V^, ^,, V^, , p\ WH4^V,V,^, \P !^V^, ,4,V^, \P !WV,^, ,4,, p \ WY4^ V^V,^, ,W,^, ,V^, V^, ^,,,,p W^, ,V^, ,W,^, ,p W, p \ Wl4R#)r!rr1N)rTr r4r$rr) rYr2r3r rGr?r]rhv2s2k2numk2denk2s & r.test_stats_broadcastTestF.test_stats_broadcast"sYhhbT{#hhBx WW]]sV]D a1Wo q  aZ39q= )C /37Q, >#' Jus{Q"''!S1W+"66a2773c A #6779cQsURZ(CIM:Qw37Q,./0Qw37+sy1}= ]r0r6N) rrrrrr.r4r<rrr s@r.r"r" s0$H r0r"c a]tRtRtoRtRtRt]PPRRR.4R4t ]PPR.RO4]PPR^^.^^.^^..RO.RO.^^.^^..^.^...4R 44t ]PPR^^.^^.^^..RO.RO.^^.^^..^.^...4R 4t R t ]PPR .RO4R 4tRtVtR#) TestStudentTi4c`\\PP^^.4RR.4R#)rg?g?N)rr4rrrXs&r.test_rvgeneric_stdTestStudentT.test_rvgeneric_std5s"!%''++q!f"5 J7OPr0c\\PP^RR7\P\P \P \P 34\\PPRRR7R\P\P \P 34\\PP^RR7R\P\P \P 34\\PPRRR7RR \P \P34\\PP^RR7\P \P34\\PPRRR7R\P34\\PP^RR7R\P34\ \PPRRR7R R R 7R #)rr)rr)\(?rgGz@r[gGz@g ףp= @r rNg i@)rgq@)rr4rrTr+r*rrXs&r.test_moments_tTestStudentT.test_moments_t9s]UWW]]a]8VVRVVRVVRVV4 6UWW]]dF];"&&"&&"&&1 3UWW]]a]8"&&"&&"&&1 3UWW]]dF];/266266: <UWW]]a]68HIUWW]]dD]9C=IUWW]]a]6bff F t <>U" $r0cl.ROp.ROp\\PPV4VRR7R#)rrrN)rr rr)g?@gTM]?ggY?U?rr4rrE)rYrrNs& r.test_t_entropyTestStudentT.test_t_entropyIs' ;+XEBr0zv, refc\\\PPV4VRR7R#rrI)rYrGrs&&&r.test_t_extreme_entropy#TestStudentT.test_t_extreme_entropyPs *Ceggoo!o4ZZ''AQ'7 ww"[/qJ S_j1S%|4r0c.ROp.ROp.ROp.ROp\\PPW4VRR7\\PP W4VRR7R#)rr rN)rrrbr)rd~QJrr)gZ_2g 9g!ǟuIgdg)g73?r9gմFhAW;gm0_?)rr4rrrf)rYr^r logpdf_refpdf_refs& r.test_logpdf_pdfTestStudentT.test_logpdf_pdfsO  #@ >q-zF A*G%@r0 x, df, refc\PPW4p\WCRR7\PP V)V4p\WSRR7R#r)r4rrrr)rYr^rrrrs&&&& r.rTestStudentT.test_logcdf_logsfs@ &%0 qb"%/r0r6N)rrH)rrc)rfrrnrrr)r9rr9)rrr))gRrguSaG)r9rr)R@rgGn`?)rrrrrArErJrrrrMr^rdrjrrrr s@r.r?r?4sWQ$ C [[X68:; =; = [[Z*<= [[\QFQFQF-6 ,B./VaV,<./S1#J,89C 9= C  [[\QFQFQF-6 ,B./VaV,<./S1#J,895 95& A [[\CD0 D0r0r?cha]tRtRtoRtRtRtRtRtRt Rt R t R t R t R tR tRtVtR#)TestRvDiscreteicN\PPR4VnR#)i}NrSrXs&r.rZTestRvDiscrete.setup_methodr<r0c.ROp.R OpRp\P!RW3R7pVPW0PR7p\ V\ P 4'gQh\W4F9wrg\\WV8H4\V4, V, 4R8dK9Qh VPVPR7p\ P!\V4\ P4'gQhR#) rrsample)rvaluesrrjrN)rr9rr r!r)rrrrrr)r4rBrrWrArTrer&rrprrrinteger)rYstates probabilitysamplesrr^r?rzs& r.rGTestRvDiscrete.test_rvss$4    8V4I J EEwXXE 6!RZZ((((,DAs16{5>1A56= ==- EEtxxE (}}T!Wbjj1111r0c>\P!.RO4p\P!.ROV3R7p\ \ W44)pVP 4p\WC4\P!.RO.RO3R7pVP 4p\VR4R#)rorvrN)ror_rr)rSr9r9) rTr r4rBrprrErr)rYr.rzrrrss& r.rtTestRvDiscrete.test_entropysu*+   i%7 8%-.. IIK&   i%= > IIKQr0c.R Op.R Op\P!W3R7pRR.R^..p\VPV4RR.RR..R R 7R #)rrzrrwr}rSr3r rr rNrrzrrw)r4rBrrN)rYxkpkrr^s& r.rlTestRvDiscrete.test_pmfs[     rh /"X!W q sc$*/ 1r0c.ROp.ROp\P!W3R7p.ROp.ROp\VPV4VRR7\VUu.uFqcPV4NK upVRR7R#uupi) rr}r rNrr)r rSrRrrr rr)r9rzrzrzrrrr)r4rBrrn)rYrrrx_valuesrNrs& r.rZTestRvDiscrete.test_cdfsf     rh /55x((? h7hh7 u .7A4c.ROp.ROp\P!W3R7p.ROp.ROp\VPV4VRR7\VUu.uFqcPV4NK upVRR7R#uupi) rr}r rNrr)rrzr`rrrS)rrr r rr)r4rBrr)rYrrrq_valuesrNrs& r.rTestRvDiscrete.test_ppfsf     rh /0%x((? H5HqH5 u .5rc .RO.RO3p\P!VR7p\VPVP VP RR4R,4VP R,4R#)rr}Nrr,)rr rr)rrwrrrr)r4rBrrrnr)rYrErs& r.test_cdf_ppf_next TestRvDiscrete.test_cdf_ppf_nextsS!:;   d +266"&&s"4t";<559 &r0cT\P!^ 4PR4p\P!.RO.RO.RO.4p\P !W3R7p\ VP4\P!VPVP,4RR7R#)rr}r rN)r!r)rrrrj)rrrjrj) rTr'rr r4rBrrrprrrYrrrs& r.test_multidimension"TestRvDiscrete.test_multidimensionsq YYr] " "6 * XX---/0  rh / RVVBEEBEEM%:Gr0c.ROpRR.p\\\P3/\ W3R7B.ROp\\\P3/\ W3R7B.ROp.ROp\\\P3/\ W3R7B.ROp.ROp\\\P3/\ W3R7B^^.pRR.p\\\P3/\ W3R7BR#)rrzr}Nr)rz333333?gffffff濩rr r!rr)rrrrr)rr)r4rBr%rYrrs& r.test_bad_inputTestRvDiscrete.test_bad_inputs 3Zj%"3"3MtB87LM j%"3"3MtB87LM  j%"3"3MtB87LM  'j%"3"3MtB87LMV3Zj%"3"3MtB87LMr0cr\P!^4PR4\P!RR4r!\ \ \ P3/\W3R7B\P!^4PR4\P!RR4r!\ \ \ P3/\W3R7B\P!^4PR4\P!RR4r!\\ P!W3R7P^4R4R#)rr}Nr r r r!gUUUUUU?r!r ) rTr'rrrr)r4rBr%rrNrs& r.test_shape_rv_sample#TestRvDiscrete.test_shape_rv_samples1%%f-rwwvs/CBj%"3"3MtB87LM1%%f-rwwvs/CBj%"3"3MtB87LM1%%f-rwwvs/CBU&&rh7;;A>Dr0c.ROp.ROp\P!W3R7p\VP4\P !VP VP,4RR7R#)rr}r rN)rr rrrr)rrwrwrwrwr)r4rBrrrTrprrrs& r. test_expect1TestRvDiscrete.test_expect1sE  +   rh / RVVBEEBEEM%:Gr0c .RNRNRNRNRNRNRNRNRNR NR NR NR NR NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.Np.R/NR0NR1NR2NR0NR0NR3NR4NR0NR0NR0NR5NR6NR7NR8NR9NR:NR;NRNR?NR@NR0NRANRBNRCNRDNRENRFNRGNRHNR0NR0NRINRJNR6NRKNR0NRLNR0NRMNR0NR0NRNNRONR0Np\P!W3RP7p\VP4VP 4RQRR7\VP4\ RS\ W444RQRR7\VPRT4\ RU\ W444RQRR7RV#)Wgi@gr@gy@g@@g@g@@g @rg0@g@gP@g@gp@g@g@g @g@rNgh@g0@g@g@g@gP@g@g@g@rOg8@g@gȩ@g@gX@g @g@g@gx@g@@g@gh@g̰@g0@g@g@g\@g@g-C6:?rgF%uk?g:vz?g.nr?g|гY?g@6*?g4U0*C?g@ +?gC6z?gnr?g ?gOjM?g n?g1w-!?g:pΈ?gףp= ?g_Le?g^)p?g~jtx?gJ4q?gGzt?gJ4q?gMb@?g@Psׂ?g@^)ˀ?gN@s?g1w-!_?gൄ|г?gH}}?g F%u?g^)ˀ?gv?r}r rc36"TFwrW,xK R#5irtr6.0rGws& r. .TestRvDiscrete.test_expect2..Es9jdaAEEjscV^,#r r6rs&r.r@-TestRvDiscrete.test_expect2..HAqDr0c3F"TFwrV^,V,xK R#5i)r Nr6rs& r.rrIs<AqD1HHs!N)r4rBrrrrpr&)rYrpyrs& r. test_expect2TestRvDiscrete.test_expect2&s =U =E =5 =% = = =u =e =V =  = =# =%+ =-3 =5; ==C =EK =  = =# =%+ =-3 =5; ==C =EK = = =$ =&, =.4 =6< =>D =FL =  =  =$  =&,  =.4  =6<  =>D  =FL  =   =   = $  = &,  = .4  = 6<  =?f?c?6?#7??c?"?$*?,/?14?69?$?&;?#?%9?$ ?&: ? " ? $7 ? 9M ? # ? %8 ? :O ??)?+??$?&;?$?&;?#?%9???.?0E?$?&9?;>?#?%(?*>?@C?EH?#?%9?;>?   qg .  RWWYU; 9c!j99 G  .1<Q<<5 Jr0rN)rrrrrZrGrtrlrZrrrrrrrrrr s@r.rqrqsL4 2  1 . .&HN( EH#J#Jr0rqc,a]tRtRtoRtRtRtVtR#)TestSkewCauchyiLc\P!R^^d4p\\PP V^R7\P P V44\\PPV^R7\P PV44\\PPV^R7\P PV44R#rrZNr) rTrWrr4 skewcauchyrfrrnrrs& r. test_cauchyTestSkewCauchy.test_cauchyMs KKAs #!%"2"2"6"6qA"6">"',,"2"21"5 7!%"2"2"6"6qA"6">"',,"2"21"5 7!%"2"2"6"6qA"6">"',,"2"21"5 7r0c\PP^4pVP^ 4^,^, pVP^ 4^ ,^, p.ROp.ROp\ \ P PW24V4\ \ P PW24V4\ \ P PWR4V4R#)r9N) 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?) rTrUrErandrr4rrfrnr)rYrWr,r^rfrns& r.test_skewcauchy_R TestSkewCauchy.test_skewcauchy_RVs&ii##A& HHRL1 q  HHRL2  !%$ ((,,Q2C8((,,Q2C8((,,S4a8r0r6N)rrrrrrrrr s@r.rrLs7 9 9r0rca]tRtRtoRt]P R4t]PPR.RO4R4t Rt Vt R#) TestJFSkewTiyc^;rV^,p.ROp.ROp\P!W4p\P!V4p\VP V4VP V44\VP V4VP V44\VP V4VP V44\VPR4VPR44R#)rrN)rrrSr)rrrorrrS)r4 jf_skew_trrrfrnr)rYr,r-rr^rjfrs& r.test_compare_tTestJFSkewT.test_compare_tzs  U ! - __Q " GGBKq 1558,q 1558,q 1558,(!''&/:r0c \P!\\4PR, 4p\P P VRR7#)atSample 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)rTloadr__file__parentrec fromarraysr$s& r.gamlss_pdf_dataTestJFSkewT.gamlss_pdf_datasAww N ! !$H H vv  [ 99r0za,bc VVR,V8HVR,V8H,,pVR,VR,re\V\P!W#4PV4RR7R#)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-r^rfrrN)rr4rrf)rYrr,r-rr^rfs&&&& r.test_compare_with_gamlss_r&TestJFSkewT.test_compare_with_gamlss_rs[  S !Q &?3+?1+D E cDK3U__Q266q9Fr0r6N)r)rr)r ) rrrrrrr\rrrrrrr s@r.rrysK;  ^^ : : [[U$>? 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NN ! !! $ NN  # FF1I ]]1  r0c\P!R^4p\PP V4p\PP V4p\ W4R#r)rTrWr4r^rrrrs& r.ruTestGumbelL.test_sf_isfsB KKQ  NN  a  ^^   "r0rcc\PP^dWPR7p\PP W!R7wr4\ W14R#)rrrN)r4r^rrWrr)rYrcr fitted_locrs&& r.test_fit_fixed_param TestGumbelL.test_fit_fixed_paramsB~~!!s((!K**4*: Z%r0rNr)rrrrrZrrrurrrr rrr s@r.r{ r{ msB5   [[URG,&-&r0r{ c,a]tRtRtoRtRtRtVtR#) TestGumbelRic\\\PP^24RRR7R#)r=?~T}%m;r rN)rr4r]rrXs&r.rTestGumbelR.test_sfs# ))"-/E" $r0c\\\PPR4RRR7R#)rBr< r rN)rr4r]rrXs&r.rTestGumbelR.test_isfs# **513D" $r0r6N)rrrrrrrrr s@r.r r s$$$r0r c a]tRtRtoRt]P !RR7R4t]P R4t]P R4t ]P R4t ]PP]PPR ]P!^24]P!R ]PPR 7.4]PPR R R.4]PPR.R:O4]PPRR;R<.4R44444t]PP ]PPRR^.4R44tRt]PP'RR7]PPRR=R>.4]PPRR R.4R444tRtRtRt]PP]PPR]P!.R?O.R@O.RBO4]P!.RCO.RDO.REO]PPR 7]P!.RFO]P2!R ^^4]P2!RA^^4]PP R 7.4R!44t]PPR]P!.R?O.R@O.RBO4]P!.RCO.RDO.REO]PPR 7]P!.RFO]P2!R ^^4]P2!RA^^4]PP R 7.4R"4t]PPR#^^.4]PPR$R%R&.4R'44t]PPR(R)^.R*^..4R+4t]PPR,RG^]P<]P>]P>3.RHRI..4R-4t ]PPR..RJO4]PPR/]!PDPFR]P2!RK^^ 4R03]!PDPHR]P2!RK^^ 4R03]!PDPFRL]P2!^^^ 4R3]!PDPHRL]P2!^^^ 4R03.4R144t%]PPR2.RMO4R34t&]PP&]PPR2.RNO4R444t']P R54t(R6t)R7t*R8t+Vt,R9#)OTestLevyStableicN\PPR4VnR#)lYNrSrXs&r.rZTestLevyStable.setup_methodr\r0T)autousec R\PnR\PnR\Pn\P P \PnR#)z2Setup default parameters for levy_stable generatorS1 piecewiseN)r4rparameterizationcdf_default_methodpdf_default_method _levy_stable _QUAD_EPSquad_epsrXs&r.reset_levy_stable_params'TestLevyStable.reset_levy_stable_paramssH.2*/:,/:,%*%7%7%A%A"r0c \P!\\4PR, 4p\P P VPRR7pV#)a{Sample data points for pdf computed with Nolan's stablec See - http://fs2.american.edu/jpnolan/www/stable/stable.html There's a known limitation of Nolan's executable for alpha < 0.2. The data table loaded below is generated from Nolan's stablec with the following parameter space: alpha = 0.1, 0.2, ..., 2.0 beta = -1.0, -0.9, ..., 1.0 p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5, and the equivalent for the right tail Typically inputs for stablec: stablec.exe << 1 # pdf 1 # Nolan S equivalent to S0 in scipy .25,2,.25 # alpha -1,-1,0 # beta -10,10,1 # x 1,0 # gamma, delta 2 # output file z.data/levy_stable/stable-Z1-pdf-sample-data.npyx,p,alpha,beta,pctrrTrrrrrrTr$s& r.nolan_pdf_sample_data$TestLevyStable.nolan_pdf_sample_datasL6ww N ! ! < = vv  /C D r0c \P!\\4PR, 4p\P P VPRR7pV#)aSSample data points for cdf computed with Nolan's stablec See - http://fs2.american.edu/jpnolan/www/stable/stable.html There's a known limitation of Nolan's executable for alpha < 0.2. The data table loaded below is generated from Nolan's stablec with the following parameter space: alpha = 0.1, 0.2, ..., 2.0 beta = -1.0, -0.9, ..., 1.0 p = 0.01, 0.05, 0.1, 0.25, 0.35, 0.5, and the equivalent for the right tail Ideally, Nolan's output for CDF values should match the percentile from where they have been sampled from. Even more so as we extract percentile x positions from stablec too. However, we note at places Nolan's stablec will produce absolute errors in order of 1e-5. We compare against his calculations here. In future, once we less reliant on Nolan's paper we might switch to comparing directly at percentiles (those x values being produced from some alternative means). Typically inputs for stablec: stablec.exe << 2 # cdf 1 # Nolan S equivalent to S0 in scipy .25,2,.25 # alpha -1,-1,0 # beta -10,10,1 # x 1,0 # gamma, delta 2 # output file z.data/levy_stable/stable-Z1-cdf-sample-data.npyr rr r$s& r.nolan_cdf_sample_data$TestLevyStable.nolan_cdf_sample_datasMJww N ! ! < = vv  /C D r0c n\P!\\4PR, 4pV#)zSample data where loc, scale are different from 0, 1 Data extracted in similar way to pdf/cdf above using Nolan's stablec but set to an arbitrary location scale of (2, 3) for various important parameters alpha, beta and for parameterisations S0 and S1. z1data/levy_stable/stable-loc-scale-sample-data.npy)rTrrrrr$s& r.nolan_loc_scale_sample_data*TestLevyStable.nolan_loc_scale_sample_datas/ww N ! ! ? @  r0 sample_sizerimarksr S0r z alpha,betarSrzz gamma,deltacV\Pn\P!W#WER7p\P!VP W`P R7VP 4wrV R8gQhR#))rr rdrcrrjN)r4rr rmrrWrn) rYr rr rrr lsrrzs &&&&&&& r.rGTestLevyStable.test_rvs s^(.>*   % || FF ((F ;RVV 4xxr0r c  RpRpRp\PPW!W4RVPR7p\P!VRW!W43R7wrgVR8gQhR #) z3Additional test cases for rvs for alpha equal to 1.rSrzrrwrrrrN)r4rrrWrm)rYr rrcrdr^statrzs&& r.test_rvs_alpha1TestLevyStable.test_rvs_alpha1*sc    ! !%3'+$(( " D,,q-%*#$=?4xxr0c|.R Op\PPV4wr#rE\VR^RR7\ VR ^4\ VR^4\ VR^4V.R O,p\PPV4wrxr\ V^4\ VR 4\ V R^4\ V R^4R#) gwg?67',?Gz?rrhgۧ1?g9]c?gv?N)wgr rrrr羼u?r r r r r r r r r tA}˜.?r r r r )\(̿)r r r r r r)r4rrrrr rYr^alpha1beta1loc1scale1ralpha2beta2rrs & r.r TestLevyStable.test_fit7s  ',&7&7&A&A!&D#t148E4+FGQ/ '1 9 9&+&7&7&A&A"&E#tVQUBFFA.D&!,r0zUnknown problem with fitstart.rzalpha,beta,delta,gammaparametrizationc  V\Pn\PPWW4RVPR7p\PP V4pVwrr\ WW4.WW.RR7R#)z7Test that fit agrees with rvs for each parametrization.rrrrN)r4rr rrWrr) rYrr rrr rr alpha_obsbeta_obs delta_obs gamma_obss &&&&&& r. test_fit_rvsTestLevyStable.test_fit_rvsOsw-<)  $$ Ue$((% ))$/471 Y % ' ) 7 r0cF\P!.RO4p\PP V4wr#rE\PP V)4wrgr\ V^4V^8wgQh\ Wb4\ Ws)4\ W)4\ W4R#rN) rrr!r!rbrbrbrrrr)rTr r4rrrr) rYr^r r r r r r rrs & r.test_fit_beta_flip!TestLevyStable.test_fit_beta_fliphs HH? @&+&7&7&A&A!&D#t&+&7&7&A&A1"&E#tUAqyyF+E6*D%(F+r0c:^p\P!.RO4p\PP V)4wr4rV\PP V)V,4wrxr\ Ws4\ W4\ WV,4\ W4R#r )rTr r4rrr) rYSHIFTr^r r r r r r rrs & r.test_fit_delta_shift#TestLevyStable.test_fit_delta_shifttsx HH? @&+&7&7&A&A1"&E#t&+&7&7&A&A1"u*&M#tF+E)D,/F+r0cz.ROp\PPV4wr#rEV^8g QRV 24hV\V48gQR\V4 RV 24h.ROp\PPV4wrxrV^8g QRV 24hV \ V48gQR\ V4 RV 24hR#) rzExpected alpha < 1, got zExpected loc < z, got zExpected alpha > 1, got zExpected loc > N) rrr!r!rbrbrbrrr ) rrr!r!rbrbrbrrr )r4rrrr&r s & r.test_fit_loc_extrap"TestLevyStable.test_fit_loc_extraps 6&+&7&7&A&A!&D#tz>5fX>>zc!f}DAxvdVDD} 7&+&7&7&A&A"&E#tz>5fX>>zc"g~FR vFF~r0z pct_range,alpha_range,beta_rangerc JaaaaTp\P!4pVPR8H;'dVPR8HoRP VPVPVP .4pRRVVV3Rl.RRVVV3R l.RRVVVV3R l.RR VVV3R l.R RVVV3Rl.R RVVV3Rl..p\ V4EFwp wrp V \Pn V eW\!V4,MTp Rp\P!4;_uu_4\P!RV\4\PPV R,V R,V R,^^R7p\P !RR7;_uu_4\#V .R#OV\P$!WR,, 4\P$!WR,, 4\P$!V R,4, .4pRRR4XVR,V 8\P&!V4,,pRV RV RV RVP(P* R V 2 p\-VV R,V VR!R"7RRR4EK R# +'giL;i +'giEK;i)$z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnirGc > <\P!VR,S4\P!VR,S4,\P!VR,S4,VR,^8HVR,R8H,VR,R8VR,R8,VR,R8H,,VR,R8*\P!VR,RR.4,,VR,R 8*\P!VR,R R .4,,VR,R 8*\P!VR,R R.4,,VR,R 8H\P!VR,RR.4,\P!\P!VR,4.RO4,,VR,R 8H\P!VR,R.4,\P!\P!VR,4R .4,,VR,R 8H\P!VR,RR.4,\P!\P!VR,4.RO4,,VR,R 8HVR,R8H,VR,R8H,,VR,R 8HVR,R8H,VR,R8H,,VR,R 8HVR,R 8H,VR,R8H,,VR,R8H\P!VR,R.4,\P!\P!VR,4.RO4,,VR,R8H\P!VR,RR.4,\P!\P!VR,4.RO4,,VR,R8H\P!VR,RR.4,\P!\P!VR,4RR .4,,VR,R8,(,#)pctrr rzrr( rrrrrjrrwrrorffffff??rSrR)rzr`ra333333ӿ)gٿr rrrzrrwrr)rrrSr)rTisinrr alpha_range beta_range pct_ranges&r.r@7TestLevyStable.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,EHr0r rc<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,R8,VR,R8g,#)r rr rwrSrTr r s&r.r@r siGGAeHi0GGAgJ 45GGAfIz23wZ#%'wZ2% 'r0c<VR,R8HS'*,\P!VR,S4,RS9,\P!VR,S4,#)rrSr r r )rr r is_linux_32r s&r.r@r sXwZ2%$_&GGAeHi01;&(GGAfIz2 3r0g& .=c<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,R8*,#)r rr rwr r s&r.r@r sVGGAeHi0GGAgJ 45GGAfIz23wZ3&(r0 fft-simpsonrc<VR,R8\P!VR,S4,\P!VR,S4,\P!VR,S4,#)rrr r r r s&r.r@r sVwZ3&GGAeHi01GGAgJ 45GGAfIz23r0rc<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,^8,VR,R8,#)r rr rr r s&r.r@r (shGGAeHi0GGAgJ 45GGAfIz23wZ!^%wZ#% 'r0Nz0Density calculations experimental for FFT methodrzr^rr rdrcrrelerrrzz pdf test  failed with method 'z ' [platform: z]  Ferr_msgverbosecalcabserrr )platformunamesystemmachinejoin processorrLr4rr r{r|rr~rfrTrrrisnanrrr)rYr r r r rr platform_desctestsixdefault_methodr filter_funcsubdatar*rzsubdata2failuresmessager s&&fff @r.test_pdf_nolan_samples%TestLevyStable.test_pdf_nolan_sampless4% llg-II%--62I  \\5==%// :< tJL ^U% U% W' t& t& kC L"+5!1 B3AE   0 + 7;t,=A DC((**''#~F%%))CLG$FO *[[h//04FF1s|#34FF1s|#34rvvgcl7KK H0$H%-((1+  t#88HI""/HNN4H4H3IH:W CL#! 9+* "20/+**s'A5JA7I= .~sGGAeHi0GGAgJ 45GGAfIz23 wZ2-GGAfI/ABCuX-/ wZ2-GGAfI?@uX-/  r0rjc<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,R8H\P!VR,.RO4,VR,R8H,,VR,R8H\P!VR,.RO4,VR,R8H,,#r r r s&r.r@r sGGAeHi0GGAgJ 45GGAfIz237r)& +=>?5T)+ 7r)& ?;<5T)+ r0r rc<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,R8,#)r rr 333333?r r s&r.r@r sVGGAeHi0GGAgJ 45GGAfIz23wZ#%'r0rc<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,R8,VR,R8*,#)r rr rr r r s&r.r@r iGGAeHi0GGAgJ 45GGAfIz23wZ#%'wZ3& (r0r2c<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,R8,VR,R8*,#)r rr rg rr r s&r.r@r r r0rc<\P!VR,S4\P!VR,S4,\P!VR,S4,VR,R8,VR,R8*,#)r rr rSrg r r s&r.r@r r r0NrzzZCumulative density calculations experimental for FFT method. Use piecewise method instead.r^rr r rr rzz cdf test r z' r Fr r )rLr4rr r{r|rr~rnrTrrrr rrr)rYr r r r rr r r rr r rzr r r s&&fff r.test_cdf_nolan_samples%TestLevyStable.test_cdf_nolan_samplesas 2%U% ,T$ &t& t& t& t& GL \"+5!1 B3AE   0 + 7;t,=A ((**''>" $ %%))CLG$FO *[[h//04FF1s|#34FF1s|#34rvvgcl7KK H0$H%-((1+'rd*??Os&nn2232hZACL#! ;+* "2"0/+**s'A5HA7H A/H HH H. r-r@rfrnc \P!4pVPR8H;'d R\P!4^,9pV'dVR8Xd\P !R4TpR\ PnR\ Pn WfR,V8H,pRV 2\ Pn VR9gQhVR8Xd\ PPM\ PPpV!VR,VR ,VR ,^^R 7p \WV,R 4R #)zGTests for pdf and cdf where loc, scale are different from 0, 1 r 32bitrfz4Test unstable on some platforms; see gh-17839, 17859r r-Sr^rr r rN)rfrn)r r r architecturerrr4rr r r rfrnr) rYr r-r@r r rr rMr$s &&&& r.test_location_scale"TestLevyStable.test_location_scales llg-WW'X=R=R=TUV=W2W  45= KKN O*0;,/:,G}-./0[*~%%%%)U]E   ! !8I8I8M8M  CL''*GFO1!  DM40r0zmethod,decimal_placesr r c  D\P!.RO4p\P!.RO4p\P!.R O4p\P!RR7;_uu_4\P!4;_uu_4\P !R\ RR7V\Pn \PPV^V^^R7p\WdW!4RRR4RRR4R# +'giL;i +'giR#;i) zwsample points extracted from Tables and Graphs of Stable Probability Density Functions - Donald R Holt - 1973 - p 187. rzrzDensity calculation unstable.*)categoryr r N)r9r9r9r9rrrrr r r r r!r!r!r!rrrr)gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g ?gDioɴ?g r?gH?g+?gHPs?gX?g&?g 0*?gv/?ga2U0*?)r9rorzrr9rorzrr9rorzrr9rorzrr9rorzr) rTr rr{r|rr~r4rr rfr)rYrdecimal_placesxsdensitybetasrfs&&& r.'test_pdf_alpha_equals_one_beta_non_zero6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerosXX H ((     [[X & &(?(?(A(A  # #H'8 4:E   0##''AuA1'EC n )B & &(A(A & & &s%(DA#C; )D; D D D zparams,expectedc\PPV^,V^,V^,V^,RR7p\W24R#)r9rraN)r4rr)rYrrNobserveds&&& r.rTestLevyStable.test_stats;sE$$** 1IvayfQivay+  H/r0rzfunction,beta,points,expectedrc ^Tu;8d ^8gQhQh\V!WAVR7\P!\V4V44R#)a4Ensure the pdf/cdf routines do not return nan outside support. This distribution's support becomes truncated in a few special cases: support is [mu, infty) if alpha < 1 and beta = 1 support is (-infty, mu] if alpha < 1 and beta = -1 Otherwise, the support is all reals. Here, mu is zero by default. rr N)rrTrr#)rYrrMr rWrNs&&&&&&r.!test_distribution_outside_support0TestLevyStable.test_distribution_outside_supportIs>P5}1}}} Vt 4 GGCK * r0zx,alpha,beta,expectedc R\Pn\\PP WVR7V4R#)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=r3 Nr4rr rrfrYr^rr rNs&&&&&r.test_x_equal_zeta TestLevyStable.test_x_equal_zetaws7Z&-"    ! !!t ! <  r0c R\Pn\\PP WVR7V4R#)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 r7 r3 Nr8 r9 s&&&&&r.test_x_near_zetaTestLevyStable.test_x_near_zetas7D&-"    ! !!t ! <  r0c,\P!4#rt) threadingLockrXs&r.levy_stable_lockTestLevyStable.levy_stable_locks~~r0c r\PPp\RRRRR7p\P p\P !R /VBpT;_uu_4RVnRVnVP!R /VBR^ RV!R 4/BpVP^ V!R 4R 7p\P!Wv8H4'dQhRVnRVnVP!R /VBR^ RV!R 4/BpVP^ V!R 4R 7p \W4\W4R R R 4R # +'giR #;i) rrrrSrr rcrdr r rr rNr6) rTrUrVr%r4rr rrr rYrB rWr"unfrozenfrozen unfrozen_afrozen_a unfrozen_bfrozen_bs && r.$test_frozen_parameterization_gh208213TestLevyStable.test_frozen_parameterization_gh20821sii##Ccs#>$$"",V,  (,H %&*F #!UURUc)nUJzzrIzGHvvh455 55(,H %&*F #!UURUc)nUJzzrIzGH  .  .   s CD%% D6 c B\PPp\RRRRR7p\P pV;_uu_4RVn\P !R /VBpVP!R /VBR^ RV!R4/BpVP^ V!R4R 7p\Wv4R Vn\P !R /VBpVP!R /VBR^ RV!R4/BpVP^ V!R4R 7p \W4R R R 4R # +'giR #;i) rrrrSrE r rrrF rr Nr6) rTrUrVr%r4rr rrrG s && r.%test_frozen_parameterization_gh20821b4TestLevyStable.test_frozen_parameterization_gh20821bsii##Ccs#>$$  (,H %&&00F!UURUc)nUJzzrIzGH  .(,H %&&00F!UURUc)nUJzzrIzGH  .   s B?D  D rN))rSr9)rSr)rr9)rrzrr9r)rrr r!)rSrr r!)rrzr)rrr r)rr9r)rrjrzrr)rrzrrr )grr9rr`r) rrjrror rzr rrrr)r r r9r)r rrbr)rbrr9r9)rorzrrf r))r9/iZ?s0?gz5F?)r9~H?|/mg>m?)r9.d5 ?L ,ٿg깃\?)r9>?ЀjoؿgA]4?)r9pa2?Յ пgqQ?) )rrT rU gz¶?)rrV rW gV?)rrX rY gRE)3\?)rrZ r[ gB?)rr\ r] g/^?)-C6rT rU gH?)r^ rV rW gn?)r^ rX rY gx\?)r^ rZ r[ gVM%?)r^ r\ r] gm?)-rrrrrZrr\r r r r rrrr-rGrr r xfailr r r r rTrWr r r$ r- r+r*rr4rrnrfr4 r: r= rB rN rQ rrr s@r.r r s5 ^^D!B"B ^^B ^^))V ^^   [[ [[ LL fll4v{{7G7GH   [[/$> [[C [[]VV,<=>? $ [[ [[Vc1X. / -0 [[>? 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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)) rrN)rS)rzrrr)r)gUUUUUU?r g^cQg333333)r4rr)rr, exact_mvskrs r.test_powerlaw_statsrC !s>>, = ?E ~~##Av#6!$3r0c^\PP^^4p\VR4R#)r9rN)r4rrrrzs r.test_powerlaw_edgerF !s" a#ACr0cx\PP^^4p\VR4\PP ^.RO4p\V\ P RR.4\PP^.RO4p\V\ P R\ P ).4R#)r9rrSN)rorSr)r4rrrrfrTr+rE s r.test_exponpow_edgerH !s a#AC 1./ARVVS#&' a!12ARVVS266'*+r0ca]tRtRtoRt]P PR.R O4R4tRt Rt Rt Rt Vt R #) TestGenGammai!c`\PP^^^4p\VR4R#)r9rSN)r4gengammarfrrs& r.test_gengamma_edgeTestGenGamma.test_gengamma_edge!s$ NN  q!Q 'Qr0za, c, ref, tolcZ\\PPW4W4R7R#r)rr4rL rE)rYr,rrrs&&&&&r.test_gengamma_extreme_entropy*TestGenGamma.test_gengamma_extreme_entropy!s" ..q4cDr0c\PP^^R4pVR8XgQh\PP^^R4pV\P )8XgQhR#)r9rNr)r4rL rfrrTr+)rYrzrs& r.!test_gengamma_endpoint_with_neg_c.TestGenGamma.test_gengamma_endpoint_with_neg_c "sO NN  q!R (Cxx~~$$Q2.wr0c\PPR^R4p\VR4\PPR^ R4p\VR4R#)r rSNr g>gqq?)r4rL r5rrs& r.test_gengamma_munpTestGenGamma.test_gengamma_munp"sF NN S" -Az* NN R ,Av&r0c\\PP.RO^R4\P )RR.4R#)r9N)r9rrr)rr4rL rrTr+rXs&r.)test_gengamma_logpdf_broadcasting_gh245746TestGenGamma.test_gengamma_logpdf_broadcasting_gh24574"s,--iB?266'2rARSr0r6N))g`6Arg2j!@r)r rggA@r)rrrN r)rOrg#@r)g`FArbgI~mr)gl$W}Lr|g.I#Ur)rrrrrM rrrrP rS rV rY rrr s@r.rJ rJ !sP  [[-NO EO E 'TTr0rJ c \P!.R!NRNRNRNR"NR#NRNRNRNRNRNR$NR NR%NR&NR NR NR NR NRNRNRNRNRNRNRNRNRNR'NR(NR)NR*NRNR+NRNR,NR-NR.NRNR/NR0NR1NRNR2NR3NR4NRNR5N4p\P!RR7;_uu_4\P!4;_uu_4\P !RR\ 4\P !RR\4\PPV4R R R 4R R R 4R # +'giL;i +'giR #;i)6g>X*?gPix#?g=?g&^?gO_ZQ?g\?g~?g)/?gRܶ?gH߃[g?g7k?g#BF?g KU= ?gT?gZg[Qs?g2?g6Hwƭ8?g*- ?ga]?g'?g޻?g?J_?g~sw?g&zM?g F?gTzy?g 't?g,?rzr{z:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integerNg>X*ȿgoϿg뵏˿g핚οg S"gm_ пg0FfͿgg"@ӿg?%:˿g?Gg~,g HgW2ҿgwm ǿg@gW=ֿg".v1glg.Hꮿg*˿) rTr rr{r|rrr~r4r"r)r\ s r.test_ksone_fit_freezer\ "sZ  / /j /* /j /) /  / /!+ /-7 /9B /  /  /", /.9 /;F /  / /!+ /-7 /9C /  / /!+ /-7 /9B /  /  / ", / .9 / ;F /  / " / $- / /: / B""1biiS&91= #  BKK  # # %&  " "g~6UZZ^^E1b115 ))%B79KL # " # " # " "sBE>A2F> F  F" zmethod, expectedrng u%>g ;Q=rfggRz\R>rrgfHu@ge:@cj\\PV4!R^^.^ R7p\W!RR7R#)r)rw rrrN)r2r4rr r)rrNrs&& r.test_ncx2_zero_ncry "s+ UZZ (!QB ?FF51r0c\PP^ ^^R7p\PP^ ^R7p\ WRR7R#)rb)rrw r)rrrrN)r4rr rrl r)rrNs r.test_ncx2_zero_nc_rvsr{ "s<ZZ^^raa^ 8Fzz~~!~4HF51r0c^ \P!^^ 4,p\\PP R^VR7^4R#)rbrrrw N)rTr'rr4rr rn)rw s r.test_ncx2_gh12731r~ "s4 RYYq"  Bb115r0c\P!.RO4p^Rr!\PP WVR7p.ROp\ W4RR7R#)ю] @gh?8@r} rrN) r gj%@gb y/7@gH@gIZ@g Xl@g'/2?8@gݰmА@gU @gy]`'@g@g*\@g48c@) rSrSrSrSrSg?gy[qD?rrrrrr)rTr r4rr rr)r^nurWr sf_expecteds r.test_ncx2_gh8665r "sH " #A $ qC (B'K B%0r0c RpRp\P!\PP RW4\PP RW4RR7p\PP W V4p\P P W V,\P!^V,^V,,44p\W4RR7R#) i,ir2rrrn rrN) rTrWr4rr rrfr8rr)rrw r^ncx2_pdf gauss_approxs r.test_ncx2_gh11777r "s B B EJJNN5"1JJNN5"1u >Azz~~aR(H::>>!"Wbgga"fq2vo.FGLH6r0zx, c, expectedc\\PPW4p\W2R4R#r)N)r4 foldcauchyrrr^rrNrs&&& r.test_foldcauchy_sfr #s$     Q "BB%(r0rkc\\PPV4p\W!R4R#r )r4rrr)r^rNrs&& r.test_halfcauchy_sfr #s$     Q BB%(r0z p, expectedcZ\PPV4p\W!4R#rt)r4rrr)rzrNr^s&& r.test_halfcauchy_isfr *#s" QAA r0cl\P!^^R7p\VP^4^4R#)r9r^N)r4rrrn)rs r.test_foldnorm_zeror 6#s$  #BAr0c\\PPW4p\W2R4R#)r N)r4rrrr s&&& r.test_foldnorm_sfr J#s"   1 BB%(r0c\PP.RO^R4p\PPRR.^R4p\;QJd.RV4FNK 5M !RV44p\W 4\PP.RO4p\PP^R.4p\;QJd.RV4FNK 5M !RV44p\W 4R#) rrzrSc3p"TF,p\P\PV3,xK. 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[((!,[''-jj:$,,.CA r0c\RR7p\VP^4\VPR4\P !RVP 4p\\V4^8H4R#)r r'rz!logpdf\(x, a, b, loc=0, scale=1\)N) r rr/r"r0r1rQrr#r2s& r.test_signature_inspection_2args7TestSubclassingNoShapes.test_signature_inspection_2args$sX"w/ [((!,[''0jj=$,,.CA r0c2\\\RR7R#)r r'N)rr,r rXs&r.0test_signature_inspection_2args_incorrect_shapesHTestSubclassingNoShapes.test_signature_inspection_2args_incorrect_shapes$si7;r0cn!RR\P4p\\V3/\ RR7BR#)c*a]tRtRtoRRltRtVtR#)>TestSubclassingNoShapes.test_defaults_raise.._dist_geni%$c^*#r r6r s&&&r.r CTestSubclassingNoShapes.test_defaults_raise.._dist_gen._pdf&$r0r6Nr r r s@r.r r=%$s  r0r r r'Nr4rCrr,r%rYr s& r.test_defaults_raise+TestSubclassingNoShapes.test_defaults_raise#$* ++  iAd.@Ar0cn!RR\P4p\\V3/\ RR7BR#)c&a]tRtRtoRtRtVtR#)>TestSubclassingNoShapes.test_starargs_raise.._dist_geni,$c^*#r r6)rYr^r,r4s&&&*r.r CTestSubclassingNoShapes.test_starargs_raise.._dist_gen._pdf-$r@r0r6Nr r s@r.r rH,$  r0r r r'NrArBs& r.test_starargs_raise+TestSubclassingNoShapes.test_starargs_raise*$rEr0cn!RR\P4p\\V3/\ RR7BR#)c&a]tRtRtoRtRtVtR#)._dist_geni3$c^*#r r6)rYr^r,rs&&&,r.r ATestSubclassingNoShapes.test_kwargs_raise.._dist_gen._pdf4$r@r0r6Nr r s@r.r rP3$rKr0r r r'NrArBs& r.test_kwargs_raise)TestSubclassingNoShapes.test_kwargs_raise1$rEr0r6N)rrrrr(r+rrrDOCSTRINGS_STRIPPEDr3r6r9rCrLrSrrr s@r.r$r$#s28  [[+4HIJ [[+4HIJ<BBBBr0r$r-c2.ROp\PF~p\\V4p\V\P\P ,4'gKJVF.p\ \P!W2P4RJ4K0 K R#),\s*,N)rWz\(\s*,z^\s*:) r4rGr2rArBrCrr0searchrQ)badonesdistnamerJregexs r.rl rl 9$sc-GMMuh' dU..1D1DD F F  %6$>?!"r0c\\PP\P ^ ^ 4^4\\P P\P ^R4^4R#)rbrN)rr4rrrTr+rr r r6r0r.test_infinite_inputr]C$sB ((R8!< 37;r0c\PP\PPR^4^4p\ VR4R#r{)r4lomaxrrnrrE s r.test_lomax_accuracyr`H$s/  2A6AAvr0c\PP\PPR^4^4p\ VR4R#r{)r4rrrnrrE s r.test_truncexpon_accuracyrbN$s7 U--11&!>,,Q2A6A3+r0c\P!RR7;_uu_4p\P!R4\PP R^4\PP R^4\PPR^4\PP\P)R4\V4p\V^4RRR4R# +'giR#;i)zregression test for gh-6219T)recordalwaysrzrN) r{r|r}r4rrnrfrrrTr+r#r)rnumber_of_warnings_throwns r. test_genextreme_give_no_warningsriZ$s   - -h' R# R# R# -$'F!.2 . - - -s B=C'' C8 c~\P!\PPR\P^R.RR74p\P p\P ^,^, p^ \P!^4,\P!^4,\P ^,, pRpWW4.p\P.^,;rg.ROp\VR ,VRR7\VR ,V4\VR ,VRR7\VR ,V4R#) rrrr rNrr)r9rr r)rr9)rr)rr )rr!) rTrr4rr* euler_gammargrrzetarr) rrrrrref_0ref_1ref_3ref_2s r.test_moments_gh22400rqh$s **U%%++S"&&!T,BF+S TC >>D %%(Q,C  ?W\\!_ ,ruuax 7D D  #EVVHQJE ECIu51TE"CIu51TE"r0cRp\PPR4p\V^V,^,RR7\PP^4p\W^,RR7\PPR4p\ V^4\PPR^ R7p\W^,\ P !^ 4,^,RR7\PP^ 4p\VRV,^,RR7\PPR 4p\V^ V,^,RR7R#) gox?rSr rr^Nrrrgr)r4rrErrrTr)rkrss r.test_genextreme_entropyrs~$s$K   &AAq}q(u5   #AAQU3   %AA   R 0AA1}rvvbz1A5EB   $AAr+~)6   %AAr+~)6r0cRp\PPVR4p\VR4\PP VR4p\W 4Rp\PPVR4p\VR4\PP VR4p\W 4Rp\PPV^4p\VR4\PP V^4p\W 4R#)rrg'b%4gQ@gؗҜ;g.l6?Nr)r4rrrr)r^r?rs r.test_genextreme_sf_isfru$s2 A Av&AA-.     a (BB A Au%AA()     a 'BB A Aq!AA-.     a #BBr0cdRp\PPV^^4p\VR4R#)rgH&8>N)r4r rr)probrs r.test_burr12_ppf_small_argrx$s, D||a+HH45r0cRRlp\P!.R O4p\PP V^VR7wr#p\ VRRR7V^8XgQh\ VRRR7R#) a Test fitting invweibull to data. Here is a the same calculation in R: > library(evd) > library(fitdistrplus) > x = c(1, 1.25, 2, 2.5, 2.8, 3, 3.8, 4, 5, 8, 10, 12, 64, 99) > result = fitdist(x, 'frechet', control=list(reltol=1e-13), + fix.arg=list(loc=0), start=list(shape=2, scale=3)) > result Fitting of the distribution ' frechet ' by maximum likelihood Parameters: estimate Std. Error shape 1.048482 0.2261815 scale 3.099456 0.8292887 Fixed parameters: value loc 0 c  \WW#RRR7#)r)r4dispxtolftol)r!)rx0r4r{s&&&&r.r&test_invweibull_fit..optimizer$sD4UKKr0)rrg`?rrg [@N)r6r9)rrPr rrYr!rrrrrbr@c)rTr r4 invweibullrr)rr^rrcrds r.test_invweibull_fitr$s].L HIA$$((i(HMAEAxd+ !8O8E8$/r0c^\PPW4p\W2RR7R#r~)r4rrr)r^rrNrs&&& r.test_invweibull_sfr$s$ ""1(HHU3r0zp, c, expectedc^\PPW4p\W2RR7R#r~)r4rrr)rzrrNrs&&& r.test_invweibull_isfr$s$##A)HHU3r0z df1,df2,xc>^p\PPW V4p\PPW W4p\ WERR7\PP W V4p\PP W W4p\ WgRR7R#)r9r rrN)r4r$rnr rrf)df1df2r^rw expected_cdfcalculated_cdfrcalculated_pdfs&&& r.test_ncf_edge_caser%so B77;;qs+LYY]]133NLu=77;;qs+LYY]]133NLt@g&4I,)?)decimalsN)r4r rnrrTround) scipy_val check_vals r.test_ncf_cdf_spotcheckr%%s6  b!R.IIIrxx A>?r0c \P!^^R4pRV^&Rp\PP!V.VO5!pVUu.uF%p\PP!V.VO5!NK' pp\ W$4R#uupi)r9rrN)rr rr9r)rTrWr4r rr)r^parrxiq0s r.test_ncf_ppf_issue_17026r/%sl Aq#A AaD C a#A,- .Ab%))-- !S !AB .A /s+BcDa]tRtRtoRtRtRtRtRtRt Rt Vt R #) TestHistogrami9%cx\PPR4Vn\P!.RO^R7p\ P !V4Vn\ PPRRRVPR7p\P!V^2R7p\ P !V4Vn R#)l&'binsrSrrrN)rr r r!r!r!rrrrrrrrrrrrrrrrrrrZ) rTrUrVrW histogramr4rDtemplater8r norm_template)rYrrnorm_histograms& r.rZTestHistogram.setup_method:%s99((4LL"@FGI **95 zz~~#Su488~Td4"//?r0c \P!.R O4p\P!.R O4p\VPP V4V4\ VPP R4R 4\ VPP R4R 4\ VPP R4R4\ VPP R4R4\P!R^^ 4p\VPP V4\PP VRRR7RR 7R #)rrSrr!@r4rrbrrNrrzrSrrrr rr3rrT@rVr-r. rYrrr4rQ?)rrrKrK{Gz?rrr{Gz?rrwrwrrrrrrrrr ) rTr rrrrfrrWrr4r8)rYrv pdf_valuesr^s& r.rPTestHistogram.test_pdfJ%sMNZZ!IJ  ))&1:> DMM--c2H=DMM--c2H= DMM--c2H=DMM--d3X> KKAr "**..q1 qc=C Ir0c \P!.RO4p\P!.R O4p\VPP V4V4\VPP V^R 4V^R 4\P!RR^d4p\VPP VPP V44V4\P!RR^d4p\VPP VPP V44V4\P!R ^^ 4p\VPP V4\PP VRRR7RR7R#) rrSrr4rbrrNr)rrrrrKrr ףp= ?Q?{Gz?rrzr`(\?RQ?= ףp=?)\(?rk rSrSrr ) rTr rrrrnrrWrr4r8)rYrv cdf_valuesr^s& r.rTestHistogram.test_cdf_ppfd%s)MNZZ!MN  ))&1:> ))*Qr*:;VAb\J KKS# & ))$--*;*;A*>?C KKS# & ))$--*;*;A*>?C KKAr "**..q1 qc=C Ir0cbRpVPPWPR7p\\P !VR84R4\ \P !VR8*4RV,RR7\ \P !VR8*4RV,RR7\ \P !VR8*4RV,R R7\ \P !VR 8*4RV,R R7\ \P !VR 8*4RV,R R7\ \P !VR 8*4RV,R R7\ \P !VR8*4RV,RR7\ \P !VR8*4RV,RR7\ \P !VR 8*4R V,RR7\ \P !VR8*4R!V,RR7\ \P !VR8*4R"V,RR7\ \P !VR8*4R#V,RR7\ \P !VR8*4R$V,RR7\ \P !VR8*4R%V,RR7\ \P !VR8*4RV,RR7\ \P !VR8*4RV,RR7\\P !VR84R4R#)&rrrSrrrwrrr rrrr3rVrrTrjrr-r. rYrr4NrKrrrrrrrzr`rrrrrk )rrrWrrTrpr)rYrLrus& r.rGTestHistogram.test_rvsz%s  """ARVVFSL)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/r0c\^4FNp\VPPV4\P !RR4P V4RR7KP R#)rrSrrjrN)rrrr5r4r8rrs& r.r- TestHistogram.test_munp%sGqA D..44Q7!JJsC077: Gr0c\VPP4\PPRRR7RR7R#)rSrrbrjrN)rrrEr4r8rXs&r.rtTestHistogram.test_entropy%s5**224 **s#*>T Kr0)rrWrN) rrrrrZrPrrGr- rtrrr s@r.rr9%s.@ I4I,0,G KKr0rc^^..R Or\P!W3RR7p\PP VP R^.4RR.4VP 4^8XgQh\P!W3RR7p\PP VP R^.4R 4VP 4R 8XgQhRp\P!\VR7;_uu_4\P!W34pVP 4R 8XgQhRRR4\P!V.R O34pVP 4^8XgQhR# +'giLC;i) rF)r+ rzrTz(Bin widths are not constant. Assuming...rN)r9rrg'^P?gH@r) r4rDrTrIrrfrrrM r~)countsrrJr s r.test_histogram_non_uniformr%sFLD   vne \PPR4p\PP R^RVR7p\PP W1R7wrErgV^8XgQh\PP V^VR7wrErgV^8XgQhR#)rrrrrrN)rTrUrVr4rrr)rYrrWrr,r-rcrds&& r.test_fit_override TestLogUniform.test_fit_override%sii##K0""33"G ++///Cczz ++//Af/Mczzr0c\PPR4pRRr2\P!W#4pVP ^^RR7p\ VPVPV44V4VPRVR7p\ VPVPV44V4R\P!R ^4,pVPV4p\ VRR VR,, ^ 4W2, \P!V4\P!V4, , p \ VP4V 4R#) leVi PgN~hrrrTrrNr,i8r)rTrUrVr4rrrrnrrr'rfrr) rYrWr,r-rJrnrr^rfrs & r. test_overflowTestLogUniform.test_overflow%sii##$78u1%kk!QTk*#/5hhDsh3#/5 4% %hhqkCRR("-q BFF1I-. T*r0r6N) rrrrrrrrrrrrr s@r.rr%s=4" [[Xt}5 6 ++r0rca]tRtRtoRt]P PRRR.R^.R^..4R4t]P PR R R .4R 4t ]P PR .RO4R4t ]P PR.RO4R4t ]P PR.RO4R4t ]P PR.RO4R4t ]P PR.R O4R4t]P PR.R!O4R4t]P PR.R"O4R4t]P PR.R#O4R4tRtVtR#)$ TestArgusi%c\PP^2RRR7p\\P!^24P 4VP 4^R7R#)r=rErrUN)r4argusrrrrs& r.test_argus_rvs_large_chi"TestArgus.test_argus_rvs_large_chi%s= KKOOBSsO ;EKKO002AFFHaHr0zchi, random_staterrrg rc\PPVRVR7p\P!VRV34wrE\ VR84R#)rrrrjNr4rrrmr)rYrrr^rrzs&&& r.rGTestArgus.test_rvs%s> KKOOCc O E||Aw0Dr0rrrc\PPVRRR7p\P!VR4wr4\ VR84R#)rie rc>^^V^,, R,, #)rrr6rs&r.r@.TestArgus.test_rvs_small_chi..%sa!Q$h#->)>r0rjNr)rYrrrrzs&& r.test_rvs_small_chiTestArgus.test_rvs_small_chi%s; KKOOCcO ?||A>?Dr0zchi, expected_meancb\PPV^R7p\W2RR7R#)rr^rrN)r4rrr)rYr expected_meanr s&&& r.rTestArgus.test_mean&s' KK  S  *u5r0zchi, expected_var, rtolcb\PPV^R7p\WBVR7R#)rr^rN)r4rrr)rYr expected_varrrGs&&&& r.rTestArgus.test_var &s$ KKOOCqO )d3r0zchi, expected, rtolc2\\V4W#R7R#r)rr)rYrrNrs&&&&r.test_argus_phi_small_chi"TestArgus.test_argus_phi_small_chi&s  3=r0z chi, expectedc\P!.RO4p\\PP W14VRR7R#)rrrNrrzr)rTr rr4rrfrYrrNr^s&&& r.test_pdf_small_chiTestArgus.test_pdf_small_chi$&+ HH_ % /Fr0c\P!.RO4p\\PP W14VRR7R#)rr rNr)rTr rr4rrrs&&& r.test_sf_small_chiTestArgus.test_sf_small_chi3&s+ HH_ % q.uEr0zx, chi, expectedc^\PPW4p\WCRR7R#r)r4rrr)rYr^rrNrs&&&& r.test_sf_near_1TestArgus.test_sf_near_1B&s [[^^A #51r0c\P!.RO4p\\PP W14VRR7R#)rrrNr)rTr rr4rrnrs&&& r.test_cdf_small_chiTestArgus.test_cdf_small_chiM&rr0cb\PPVRR7p\WBVR7R#)rJrrN)r4rr)rYrrNrrFs&&&& r.test_stats_small_chiTestArgus.test_stats_small_chi\&s'kkT2D1r0r6N))rgщi?)rbg.憃?)rg\paP?)rg ?)rg,6?))rgLH'B?r)rbgo$?r)rg =>r)rg2W>r)rgb~P>r))rgwM?r )rzgj?r )rgHEA`!?r )rgc ف>r)r2gF=r )rg߹Q#B=r )rg0ޟ)rrg=~L]=)rrgD,G '=))rz)g+&?gk?gμm/?)rw)g?CL\f?g^N?g]AͭR?)r)ga>$?g;Lf?gaW?)r)gx?g43n?gwY?)r2)go7🤎?g +-oGn?gIQ9‹Y?)r)g T?gGn?g@̋Y?)r)gU?g{Gn?giG͋Y?)r)gDU?g{Gn?gH͋Y?))rz)g Q)?g6{?r)gB`"۹?)g?g8%?r)r)g388?gV%?r)r)g*j?gRS%?r)r2)g! |?gZ%?r)r)gy[|?gG%?r)r)g"3|?gW%?r)r)g!3|?gW%?r)rrrrrrrrrGrrrrrrrrrrrr s@r.rr%sI  [[0 #J #J #J3      [[UT4L12 [[189 6 9 6  [[6BC 4 C 4  [[2DE>E> [[ M NG NG  [[ N OF OF  [[ 67 2 7 2  [[ P QG QG  [[ C D2 D2r0rca]tRtRtoRtRtRtRtRt] PPR.RO4R4t ] PPR.RO4R 4t R t] PPR .RO4R 4t] PP!R R7] PPR.RO4] PPR.RO4] PPR.RO4R4444t] PPR.RO4] PPR.RO4R44tRtVtR#) TestNakagamiik&cN\PPR4VnR#)li{NrSrXs&r.rZTestNakagami.setup_methodl&r\r0cdRp^p\PPW!4p\VR4R#)rNgM+)r4nakagamirr)rYr r^rs& r.rTestNakagami.test_logpdfo&s- ~~$$Q+12r0cRpRp\PPW!4p\VRRR7\PP W14p\WBRR7R#)rrTg"S+:rrN)r4rrrr)rYr r~rrs& r.ruTestNakagami.test_sf_isf&sM  ^^  r &1> ^^   'U+r0cj^pRpRp\PPW4p\WCRR7R#)rrzrrNgU iּ)r4rrr)rYr^r rrs& r.rTestNakagami.test_logcdf&s/  %&&q-%0r0cjRp^ pRp\PPW4p\WCRR7R#)rjrrNgD&`U)r4rrr)rYr^r rrs& r.rTestNakagami.test_logsf&s/  %$$Q+/r0zm, refc\\\PPV4VRR7R#)g^~z=rNrr4rrErYr rs&&&r.rtTestNakagami.test_entropy&s ..q13WEr0cX\\PPV4V4R#rtr r s&&&r.test_extreme_nuTestNakagami.test_extreme_nu&s ..q137r0c\P!\PP R44'gQh\P!\PP R44'gQhR#)rr|N)rTrr4r_entropyrXs&r.test_entropy_overflow"TestNakagami.test_entropy_overflow&sJ{{5>>2259::::{{5>>226:;;;;r0znu, refc\\\PPV4VRR7R#r)rr4rr)rYr rs&&&r.rTestNakagami.test_mean&s ++B/5Ar0z+Fit of nakagami not reliable, see gh-10908.rr rcrdca a ^do \PPS WW0PR7o \PP S 4wrEp\ WARR7\ WRRR7\ WcRR7V 3RlpV V 3RlpV V 3Rlp \ V!WEV4^RR7\ V!WEV4^RR7\ V !WEV4^RR7R #) rrr rcrdrrwrc<RV,^,\P!^SV, , 4,^V,V^,, \P!SV, 4,,#r r rTrp)r rcrdrzs&&&r. dlogl_dnu(TestNakagami.test_fit..dlogl_dnu&sPUQY"&&GcM):";;d5!8mbffWs]&;;< =r0cV<S^\P!V4,\^V4, ,^\P!\P!SV, V, 44,,\P!SV, V, ^,4, #r)rTrrrpr rcrdrLrzs&&&r. dlogl_dloc)TestNakagami.test_fit..dlogl_dloc&spRVVBZ)Ar*::;rvvw}&=>??@ffw}59:; .dlogl_dscale&sF!GbL5("fuz)BFFGcMa3G,HHI Jr0r2rN)r4rrrWrr) rYr rcrdnu_estloc_est scale_estrr r#rLrzs &&&& @@r.r TestNakagami.test_fit&s ..$$!+0xx%I%*^^%7%7%@"-3/ s3 = <  J  &9=qtL 6I>M Vi@!$Or0cRp^dp\PPWCVW PR7p\PP WSR7wrgp\ P !V4p \ P!\ P!WW, ^,44p \WcRR7\WyRR7\WRR7R#)rzrrwrGrN) r4rrrWrrTrrrr) rYrcrdr ryrzr%r&r'loc_theo scale_theos &&& r. test_fit_nuTestNakagami.test_fit_nu&s  ..$$!+0xx%I%*^^%7%7%7%G"66'?WWRWWg&7A%=>? .5 D9r0rN))rg|Bd븿)rzr)rbg/ۿ))r|g}Ô%I)rgq_)gScAgB4U)gcAgu1U)rgb >%)rgWҙ\))rg2H?)rg:U?)rg>)r( rr)rrbr")rrrQ)rrrrrZrrurrrrrrtrrrr_ r r,rrr s@r.rrk&s[53",&10 [[X %& F & F [[X DE8 E8< [[Y>?B ?B [[KL [[T?3 [[UN3 [[Wk2P344MP8 [[UN3 [[Wk2:34:r0rc |a]tRtRtoRtRtRtRt]PPRRR.4]PPR RR] P,] P)^] P^] P,^d.4]PPR .RO4R 444t R tVtR #)TestWrapCauchyi'cN\PPR4VnR#)l3R"NrSrXs&r.rZTestWrapCauchy.setup_method'r\r0c\P!RR.RR..4p\P!R.R..4p\PP W!4pVP R 8XgQh\P !W!34UUu.uF$wrE\PP WE4NK& ppp\VP4VRR7R#uuppi) Q?rorzrrSr3rrNr) rTr r4 wrapcauchyrnr?nditerrrc )rYrr^rzrrg scalar_valuess& r.test_cdf_shape_broadcasting*TestWrapCauchy.test_cdf_shape_broadcasting's HHtTlS$K0 1 HHsecU^ $     &ww&   )+A6):<):Xb))--b5): < =u=?!a"))Brvvbeebdl/C,C"DRUU"JJKr0rrrrcrdc\PPWVRVPR7p\P !V^84'gQh\P !V^\P ,8*4'gQhR#)r)rrcrdrrN)r4r4rrWrTrrg)rYrrcrdr^s&&&& r.test_rvs_lie_on_circle%TestWrapCauchy.test_rvs_lie_on_circle'sd    1U&* ! Cvva1f~~~vva1ruu9n%%%%r0rNrr )rrr)rrrrrZr7r:rZrrrrTrgrBrrr s@r.r/r/'s5 >,L [[S5$-0 [[UT2bee8beeVQqwPS$TU [[W&67&8V1&r0r/c!RR\P4pV!RR7p\PP R4p\ \ RR7;_uu_4VPVR7RRR4R# +'giR#;i) c&a]tRtRtoRtRtVtR#)/test_rvs_no_size_error..rvs_no_size_geni*'c^#rr6rXs&r._rvs4test_rvs_no_size_error..rvs_no_size_gen._rvs+'sr0r6N)rrrrrHrrr s@r.rvs_no_size_genrF*'s  r0rJ rvs_no_sizer'i_Oz_rvs\(\) got (an|\d) unexpectedrrN)r4rCrTrUrVrr,r)rJrKrWs r.test_rvs_no_size_errorrL('s`%--"}5K ))   +C y(J K KS) L K K Ks A88 B zdistname, argscV\9d\P!RV R24\\V4p\ V\P 4'd\V4^8wdGVP!V!wr4\V\P4\V\P4^RreVP!.VOVNVN5!wrx\V\P4\V\P4R#VP!V!wr\V \P4\V \P4R#)z6skipping test for the support method for distribution .Nr) $skip_test_support_gh13294_regressionrrr2r4rArCr#r rrTr*) rZr4rJa0b0r r a1b1r,r-s && r.test_support_gh13294_regressionrT4's77 $$,:Q0 1 5( #D$++,, t9>\\4(FB RVV $ RVV $ "f2t2T262R R ||T"QQr0c\PP.RO.RO4wr\P!\P )\P )\P )\P .4p\P!\P \P \P \P .4p\W4\W4VPVP8XgQhVPVP8XgQh\PP..4wrE\P!.4\P!.4rv\WF4\WW4VPVP8XgQhVPVP8XgQh\PP.ROR.4wr\P!^\P .,4p \P!^\P .,4p \W4\W4VPV P8XgQhV PV P8XgQhR#)r9N)r9r9r9rr)rrrr) r4r8r rTr r+r*rr?) rPrQex_a0ex_b0rRrSex_a1ex_b1rr ex_a2ex_b2s r.,test_support_broadcasting_gh13294_regressionr\O's ZZ   m ># % + +v 55 5r0c\\PPV4V4\\PP V)4V4R#rt)rr4cosinernr)r^rNs&&r.test_cosine_cdf_sfrav's6ELL$$Q'2ELLOOQB'2r0c\\PPV4V4\\PP V4V)4R#rt)rr4r`rr)rzrNs&&r.test_cosine_ppf_isfrc~'s8 ELL$$Q'2ELL$$Q'(3r0c\PP\P)\P.4p\ VR4R#)grB@NgrB)r4r`rrTrgr )rs r.test_cosine_logpdf_endpointsre's1 <<   /Dd./r0cN\UUu0uFwr\V\4'gKVkK! ppp\UUu0uFwrVkK pppW#8XgQh\UUu0uFwrVkK ppp\ UUu0uFwrVkK pppWE8XgQhR#uuppiuuppiuuppiuuppirt)rrAr<rrr)rrdiscrete_distnamesinvdiscrete_distnamescont_distnamesinvcont_distnamess r.test_distr_params_listsrk's/;4l74'c2$l41@AgdTA  66 6*23(wtd(N3-89['$[9  .. .4A49sBB B B5 B!c\PP^RR7\PP^^R7R8XgQh\PP ^^4R8XgQhR#)r9r]r\)rr,r N)r4r_statsrr5r6r0r.test_moment_order_4rn's` NNAs+ >> qA .# 55 5 >>  1 % ,, ,r0c :a]tRtRto]P R4t]PPR.RO4R 4t ]PPR .RO4R 4t ]PP]PPR ]P!RR]PPR7]P!RR]PPR7]P!RR ]PPR7.4R44tRtVtR#)TestRelativisticBWi'c \P!\\4PR, 4p\P P VPRR7pV#)zSample data points for pdf computed with CERN's ROOT See - https://root.cern/ Uses ROOT.TMath.BreitWignerRelativistic, available in ROOT versions 6.27+ pdf calculated for Z0 Boson, W Boson, and Higgs Boson for x in `np.linspace(0, 200, 401)`. z-data/rel_breitwigner_pdf_sample_data_ROOT.npyzx,pdf,rho,gammarr r$s& r.ROOT_pdf_sample_data'TestRelativisticBW.ROOT_pdf_sample_data'sLww N ! ! ; < vv  /@ A r0zrho,gamma,rtolqVEB@gj+@‰FC@Gz@ND@_LU?c VVR,V8HVR,V8H,,pVR,VR,rv\V\PPWbVR7VR7R#)rhorr^rfr^rN)rr4rel_breitwignerrf)rYrrr{rrrr^rfs&&&&& r.test_pdf_against_ROOT(TestRelativisticBW.test_pdf_against_ROOT'sc$ !% (C /#G,5 7 cDK3 &&**1*?d r0zrho, Gamma, rtolcRp\P!RR^ 4p\PP WQVR7p\PP WaVR7pV!WaV,V4p\ WxVR7R#)c\P!V^,V^,V^,,,4p^\P!^4,V,V,V,\P\P!V^,V,4,, pW@^,V^,, ^,V^,V^,,,, #r)rTrrg)ErGammarr]s&&& r.rfFTestRelativisticBW.test_pdf_against_simple_implementation..pdf'sGGAqDAqD5!8O45ERWWQZ!#e+e3EEBGGAqD5L113AA1q(1a4q=89 9r0rjrr^rN)rTrWr4r|rrfr) rYr{rrrfrzr^rrs &&&& r.&test_pdf_against_simple_implementation9TestRelativisticBW.test_pdf_against_simple_implementation'sk : KKdB '  ! ! % %aE % :##''e'<!Y&t,r0z rho,gammar c Rp\PPV4p\PP WRVR7p\PP V^R7p\V^,V^,3W3RR7V^,^8XgQh\PP V^VR7p\V^,VRR7V^,V^,3^V38XgQhR #) z`Tests fit for cases where floc is set. `rel_breitwigner` has special handling for these cases. ls ; rl#rrcrrwrrrN)rTrUrVr4r|rrr)rYr{rrrWrrs&&& r. test_fit_floc TestRelativisticBW.test_fit_floc's&#ii##D)$$(( 4c) ##''1'5QQ(3,TB1v{{##''1U'CA$/AAAu:---r0r6N))rtrur)rvrwr )rxryrt))rtrurt)rvrwrt)rxryg& .>)rrrrrr\rrrrr}rrr-rrrrr s@r.rprp's  ^^$ [[    [[/2  -  - [[ [[ LL"F&++2B2B  LL!5 0A0A  LL & 0A0A    . .r0rpcha]tRtRto]P P RRR.4R4tRtVt R#) TestJohnsonSUi (r@c|\PP!VR,RR/p\W!R,RR7R#):NrNrr:rNNr rN)r4rr)rYr@rs&& r.test_moment_gh18071!TestJohnsonSU.test_moment_gh18071 (s/oo##T"X>v>"XE2r0r6N)rd rRrrg={?g?5mV>gn?g\}\1@)g`fo@g$ں _@r9rgvUg N#2QsV )=>r0rTFrrlrcJ\PPR4pR wrgr\P!WgWR7p V P RVR7p /p V'dWR&V'dWR&V'dWlR&V'dW|R&V'dkV'dcV'd[V'dSRp \ P!\V R 7;_uu_4\PP!V 3/V BR R R 4R #\\PV 3/V BR # +'giR #;i) lZ #LmrbrrrrrrrrN)rrrr) rTrUrVr4rrrr r(rr)rYrrrlrrWr-rrcrdrJrrr s&&&&& r.r TestTruncPareto.test_fit:(s ii##$78+c  3<xxSsx3 L "N J J yUuKG|7;;!!%%d3d3<; *%*;*;T JT J<;;s "D D" r6N) rrrrrPrrrrr rrr s@r.rr(s"?. 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