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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)rVloadr__file__parentrec fromarraysr*s r0gamlss_pdf_dataTestJFSkewT.gamlss_pdf_datasAww N ! !$H H vv  [ 99r2za,b)r)rr)re cUUSU:HUSU:H-nUSUSpe[U[R"X#5RU5SS9 g)zCompare the pdf with a table of reference values. The table of reference values was produced using R, where the Jones and Faddy skew t distribution is available in the GAMLSS package as `ST5`. r.r/rbrlrrN)rr6rrl)r[rr.r/rrbrls r0test_compare_with_gamlss_r&TestJFSkewT.test_compare_with_gamlss_rs[  S !Q &?3+?1+D E cDK3U__Q266q9Fr2r8N) rrrrrrrcrrrrr r8r2r0rrysH;  ^^ : : [[U$>? 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NN ! !! $ NN  # FF1I ]]1  r2c[R"SS5n[RR U5n[RR U5n[ X5 g)Nrr)rVrhr6rerrrr s r0ryTestGumbelL.test_sf_isfsB KKQ  NN  a  ^^   "r2rhrrc[RRSXRS9n[RR X!S9up4[ X15 g)Nrdrr)r6rerrYrr)r[rhr fitted_locrs r0test_fit_fixed_param TestGumbelL.test_fit_fixed_paramsB~~!!s((!K**4*: Z%r2rN) rrrrr\rrryrrrr r r8r2r0r r ms?5   [[URG,&-&r2r c \rSrSrSrSrSrg) TestGumbelRicT[[RRS5SSS9 g)NrJ?~T}%m;rr)rr6rdrrZs r0rTestGumbelR.test_sfs# ))"-/E" $r2cT[[RRS5SSS9 g)NrNr@ rr)rr6rdrrZs r0rTestGumbelR.test_isfs# **513D" $r2r8N)rrrrrrr r8r2r0r r s $$r2r c \rSrSrSr\R "SS9S5r\R S5r\R S5r \R S5r \RR\RRS \R"S 5\R"S \RRS 9/5\RRS SS/5\RRS/SQ5\RRSSS/5S55555r\RR \RRSSS/5S55rSr\RR'SS9\RRSSS/5\RRS SS/5S!555rS"rS#rS$r\RR\RRS%\R"/S&Q/S'Q/S(Q5\R"/S)Q/S*Q/S+Q\RRS 9\R"/S,Q\R2"S-S.S/5\R2"S0SS15\RR S 9/5S255r\RRS%\R"/S&Q/S'Q/S(Q5\R"/S)Q/S*Q/S+Q\RRS 9\R"/S,Q\R2"S-S.S/5\R2"S0SS15\RR S 9/5S35r\RRS4S5S/5\RRS6S7S8/5S955r\RRS:S;S5r\RRS?S@S5\R<\R>\R>4/SASB//5SC5r \RRSD/SEQ5\RRSF\!RDRFSG\R2"SHS5SI5SJ4\!RDRHSG\R2"SHS5SI5SJ4\!RDRFSK\R2"S5SLSI5SG4\!RDRHSK\R2"S5SLSI5SJ4/5SM55r%\RRSN/SOQ5SP5r&\RR&\RRSN/SQQ5SR55r'\R SS5r(STr)SUr*SVr+gW)XTestLevyStableicL[RRS5Ulg)NlYrUrZs r0r\TestLevyStable.setup_methodr^r2T)autousecS[RlS[RlS[Rl[R R [Rlg)z2Setup default parameters for levy_stable generatorS1 piecewiseN)r6rparameterizationcdf_default_methodpdf_default_method _levy_stable _QUAD_EPSquad_epsrZs r0reset_levy_stable_params'TestLevyStable.reset_levy_stable_paramssH.2*/:,/:,%*%7%7%A%A"r2c[R"[[5RS- 5n[R R URSS9nU$)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,pctrrVrrrrrrTr*s r0nolan_pdf_sample_data$TestLevyStable.nolan_pdf_sample_datasL6ww N ! ! < = vv  /C D r2c[R"[[5RS- 5n[R R URSS9nU$)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 r0nolan_cdf_sample_data$TestLevyStable.nolan_cdf_sample_datasMJww N ! ! < = vv  /C D r2cf[R"[[5RS- 5nU$)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)rVrrrrr*s r0nolan_loc_scale_sample_data*TestLevyStable.nolan_loc_scale_sample_datas/ww N ! ! ? @  r2 sample_sizerJrxmarksr S0r z alpha,beta))rcr)rcr)rr)rrz gamma,deltarrrcU[Rl[R"X#XES9n[R"UR X`R S9UR 5upU S:deg)N)r0rrirhrry)r6rr r|rrYrt) r[r r0rrrr lsrrs r0rWTestLevyStable.test_rvs s^(.>*   % || FF ((F ;RVV 4xxr2rrrc SnSnSn[RRX!X4SURS9n[R"USX!X44S9upgUS:deg ) z3Additional test cases for rvs for alpha equal to 1.rcrrrsrrrrN)r6rrrYr|)r[rr0rhrirbstatrs r0test_rvs_alpha1TestLevyStable.test_rvs_alpha1*sc    ! !%3'+$(( " D,,q-%*#$=?4xxr2cl/SQn[RRU5up#pE[USSSS9 [ USS5 [ USS 5 [ US S5 U/S Q-n[RRU5upxp[ US5 [ US 5 [ U S S 5 [ U SS 5 g)N)wgr rrrr羼u?r r r r 67',?r r r r tA}˜.?r r r r Gz?rrrx)\(̿rjgۧ1?rg9]c?)r r r r r rgv?r )r6rr!rrr r[rbalpha1beta1loc1scale1ralpha2beta2rrs r0r&TestLevyStable.test_fit7s  ',&7&7&A&A!&D#t148E4+FGQ/ '1 9 9&+&7&7&A&A"&E#tVQUBFFA.D&!,r2zUnknown problem with fitstart.rzalpha,beta,delta,gamma)rrrjr)rcrrjrparametrizationc U[Rl[RRXX4SURS9n[RR U5nUupp[ XX4/XX/SS9 g)z7Test that fit agrees with rvs for each parametrization.r#rrrN)r6rr rrYr!r) r[r0rrrr rr alpha_obsbeta_obs delta_obs gamma_obss r0 test_fit_rvsTestLevyStable.test_fit_rvsOsw-<)  $$ Ue$((% ))$/471 Y % ' ) 7 r2cB[R"/SQ5n[RR U5up#pE[RR U*5upgp[ US5 US:wde[ Xb5 [ Xs*5 [ X*5 [ X5 g)N rrrrrcrcrcrHrHrdrdrr)rVrr6rr!rr) r[rbr r r r r r rrs r0test_fit_beta_flip!TestLevyStable.test_fit_beta_fliphs HH? @&+&7&7&A&A!&D#t&+&7&7&A&A1"&E#tUAqyyF+E6*D%(F+r2c(Sn[R"/SQ5n[RR U*5up4pV[RR U*U-5upxp[ Xs5 [ X5 [ XU-5 [ X5 g)Nrr )rVrr6rr!r) r[SHIFTrbr r r r r r rrs r0test_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+r2cp/SQn[RRU5up#pEUS:d SU35eU[U5:dS[U5SU35e/SQn[RRU5upxpUS:d SU35eU [ U5:dS[ U5SU 35eg) N) rrrrrcrcrcrHrHr rzExpected alpha < 1, got zExpected loc < z, got ) rrrrrcrcrcrHrHr zExpected alpha > 1, got zExpected loc > )r6rr!rr+r s r0test_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~r2z pct_range,alpha_range,beta_range)rrr)r`rrj)rrr)rryrrr)r`rrrrj)grrrrr) rryr`rffffff?r?rrrrr`rjrArrc^^^^Un[R"5nURS:H=(a URS:HmSR URURUR /5nSSUUU4Sj/SSUUU4S j/SSUUUU4S j/SS UUU4S j/S SUUU4Sj/S SUUU4Sj//n[ U5GHfun upn U [Rl U b X\"U5OUn Sn[R"5 [R"SU[5 [RRU SU SU SSSS9n[R "SS9 [#U /SQU[R$"XS- 5[R$"XS- 5[R$"U S5- /5nSSS5 WUSU :[R&"U5-nSU S U S!US"UR(R*S#U3 n[-UU SU US$S%9 SSS5 GMi g!,(df  Ns=f!,(df  GM=f)&z2Test pdf values against Nolan's stablec.exe outputLinuxi686/dnirZc >[R"UST5[R"UST5-[R"UST5-USS:HUSS:H-USS:USS:-USS:H--USS:*[R"USS S /5--USS :*[R"USS S /5--USS:*[R"USSS/5--USS:H[R"USSS/5-[R"[R"US5/SQ5--USS:H[R"USS/5-[R"[R"US5S/5--USS:H[R"USSS/5-[R"[R"US5/SQ5--USS:HUSS:H-USS:H--USS:HUSS:H-USS:H--USS:HUSS :H-USS:H--USS:H[R"USS/5-[R"[R"US5/SQ5--USS:H[R"USSS/5-[R"[R"US5/SQ5--USS:H[R"USS S /5-[R"[R"US5SS/5--USS:-)-$)Npctr0rrrrr/ rrrrryrrr`rr)rrrr r )gٿ333333ӿrrrr rcr`rrr)rrrcrrB)rVisinrr alpha_range beta_range pct_ranges r0rE7TestLevyStable.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,EHr2r rc>[R"UST5[R"UST5-[R"UST5-USS:-USS:g-$)Nr r0rrrcrVr r s r0rEr siGGAeHi0GGAgJ 45GGAfIz23wZ#%'wZ2% 'r2c>USS:HT(+-[R"UST5-ST;-[R"UST5-$)Nr0rcr rr )rr r is_linux_32r s r0rEr sXwZ2%$_&GGAeHi01;&(GGAfIz2 3r2g& .=c>[R"UST5[R"UST5-[R"UST5-USS:*-$)Nr r0rrr r s r0rEr sVGGAeHi0GGAgJ 45GGAfIz23wZ3&(r2 fft-simpsonrc>USS:[R"UST5-[R"UST5-[R"UST5-$)Nr0rr rr r s r0rEr sVwZ3&GGAeHi01GGAgJ 45GGAfIz23r2rc>[R"UST5[R"UST5-[R"UST5-USS:-USS:-$)Nr r0rrrr r s r0rEr (shGGAeHi0GGAgJ 45GGAfIz23wZ!^%wZ#% 'r2Nz0Density calculations experimental for FFT methodrrbr0rrrrirhrcalcabserrrelerrrr z pdf test  failed with method 'z ' [platform: z]  Ferr_msgverbose)platformunamesystemmachinejoin processorrSr6rr rrrrrlrVrrrisnanrrr)r[r r r r rr platform_desctestsixdefault_methodr filter_funcsubdatar,rsubdata2failuresmessager s ``` @r0test_pdf_nolan_samples%TestLevyStable.test_pdf_nolan_samplesss4% llg-I%--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'AH:AH)[R"UST5[R"UST5-[R"UST5-USS:H[R"US/SQ5-USS:H-USS:H[R"US/SQ5-USS:H--)-$ Nr r0rrc)r rrrr`rrrr r s r0rE7TestLevyStable.test_cdf_nolan_samples..~sGGAeHi0GGAgJ 45GGAfIz23 wZ2-GGAfI/ABCuX-/ wZ2-GGAfI?@uX-/  r2ryc`>[R"UST5[R"UST5-[R"UST5-USS:H[R"US/SQ5-USS:H--USS:H[R"US/SQ5-USS:H--$r r r s r0rEr sGGAeHi0GGAgJ 45GGAfIz237r)& +=>?5T)+ 7r)& ?;<5T)+ r2r rc>[R"UST5[R"UST5-[R"UST5-USS:-$)Nr r0r333333?r r s r0rEr sVGGAeHi0GGAgJ 45GGAfIz23wZ#%'r2r c>[R"UST5[R"UST5-[R"UST5-USS:-USS:*-$)Nr r0rrr r r s r0rEr iGGAeHi0GGAgJ 45GGAfIz23wZ#%'wZ3& (r2rGc>[R"UST5[R"UST5-[R"UST5-USS:-USS:*-$)Nr r0rrb rr r s r0rEr r r2rc>[R"UST5[R"UST5-[R"UST5-USS:-USS:*-$)Nr r0rrcrb r r s r0rEr r r2NrzZCumulative density calculations experimental for FFT method. Use piecewise method instead.rbr0rrrr rr rr z cdf test r z' r Fr )rSr6rr rrrrrtrVrrrr rrr)r[r r r r rr r r rr r rr r r s ``` r0test_cdf_nolan_samples%TestLevyStable.test_cdf_nolan_samplesas2%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'AG-AF6 AG6 G G G r,rrLrlrtc:[R"5nURS:H=(a S[R"5S;nU(aUS:Xa[R "S5 UnS[ RlS[ Rl XfSU:HnSU3[ Rl US ;deUS:Xa[ RRO[ RRnU"US US US S SS9n [XUS5 g)zGTests for pdf and cdf where loc, scale are different from 0, 1 r 32bitrrlz4Test unstable on some platforms; see gh-17839, 17859r r,S)rlrtrbr0rrjrr rN)r r r architecturerrr6rr r r rlrtr) r[r r,rLr r rr rTr-s r0test_location_scale"TestLevyStable.test_location_scales llg-W'X=R=R=TUV=W2W  45= KKN O*0;,/:,G}-./0[*~%%%%)U]E   ! !8I8I8M8M  CL''*GFO1!  DM40r2zmethod,decimal_placesr rr c [R"/SQ5n[R"/SQ5n[R"/SQ5n[R"SS9 [R"5 [R "S[ SS9 U[Rl [RRUSUSS S 9n[XdX!5 S S S 5 S S S 5 g !,(df  N=f!,(df  g =f) zwsample points extracted from Tables and Graphs of Stable Probability Density Functions - Donald R Holt - 1973 - p 187. )rrrrrrrrrjrjrjrjrrrrrrrr)gtF_?gܵ|?gQ?g@?gec]?gHP?gPkw?g!rh?gTN?g ?gDioɴ?g r?gH?g+?gHPs?gX?g&?g 0*?gv/?ga2U0*?)rrrrrrrrrrrrrrrrrrrrrrzDensity calculation unstable.*)categoryr rrr N) rVrrrrrrr6rr rlr)r[rdecimal_placesxsdensitybetasrls r0'test_pdf_alpha_equals_one_beta_non_zero6TestLevyStable.test_pdf_alpha_equals_one_beta_non_zerosXX H ((     [[X &(?(?(A  # #H'8 4:E   0##''AuA1'EC n )B & &(A(A & &s%C23AC!C2! C/ +C22 Dzparams,expected)r r rr)rjrrcr)rcrrrct[RRUSUSUSUSSS9n[X25 g)Nrrrjrrrg)r6rr)r[r"rOobserveds r0rTestLevyStable.test_stats;sE$$** 1IvayfQivay+  H/r2r0)rrrzfunction,beta,points,expectedrcr^ rcrrrcSUs=:aS:de e[U"XAUS9[R"[U5U55 g)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. rrr0rN)rrVrr")r[r0rTrr[rOs r0!test_distribution_outside_support0TestLevyStable.test_distribution_outside_supportIs>P5}1}}} Vt 4 GGCK * r2zx,alpha,beta,expected))r/iZ?s0?gz5F?)r~H?|/mg>m?)r.d5 ?L ,ٿg깃\?)r>?ЀjoؿgA]4?)rpa2?Յ пgqQ?c~S[Rl[[RR XUS9U5 g)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=r8 Nr6rr rrlr[rbr0rrOs r0test_x_equal_zeta TestLevyStable.test_x_equal_zetaws7Z&-"    ! !!t ! <  r2) )r r; r< gz¶?)r r= r> gV?)r r? r@ gRE)3\?)r rA rB gB?)r rC rD g/^?)-C6r; r< gH?)rK r= r> gn?)rK r? r@ gx\?)rK rA rB gVM%?)rK rC rD gm?c~S[Rl[[RR XUS9U5 g)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. 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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)) )rc)rrrr)r)gUUUUUU?r g^cQg333333rrN)r6rr)rr. exact_mvskrs r0test_powerlaw_statsrH !s>>, = ?E ~~##Av#6!$3r2c\[RRSS5n[US5 g)Nrrr)r6rrrrs r0test_powerlaw_edgerK !s" a#ACr2cv[RRSS5n[US5 [RR S/SQ5n[U[ R SS/5 [RRS/SQ5n[U[ R S[ R */5 g)Nrrr)rrcrrc)r6rrrrlrVr*rJ s r0test_exponpow_edgerM !s a#AC 1./ARVVS#&' a!12ARVVS266'*+r2c^[RRSSS5n[US5 g)Nrrrc)r6gengammarlrrJ s r0test_gengamma_edgerP !s$ 1a#ACr2za, c, ref, tol))g`6Arg2j!@r)r' rggA@r)rrrL r)rSrg#@r)g`FArgI~mr)gl$W}Lrg.I#UrcR[[RRX5X#S9 gr)rr6rO r>)r.rrrs r0test_gengamma_extreme_entropyrR !s"ENN**10#@r2c[RRSSS5nUS:Xde[RRSSS5nU[R *:Xdeg)Nrrrr)r6rO rlrrVr*)rrs r0!test_gengamma_endpoint_with_neg_crT "sO 1a$A 8O8 >> Ar *D BFF7??r2c[RRSSS5n[US5 [RRSSS5n[US5 g)Nr rrcg>rcgqq?)r6rO rHrrJ s r0test_gengamma_munprV "sF Rb)A:& RR(A6"r2c[R"/SQ5n[R"SS9 [R"5 [R "SS[ 5 [R "SS[5 [RRU5 SSS5 SSS5 g!,(df  N=f!,(df  g=f)N)0g>X*ȿgPix#?g=?g&^?goϿg뵏˿gO_ZQ?g\?g~?g)/?gRܶ?g핚οgH߃[g?g S"gm_ пg7k?g#BF?g KU= ?gT?gZg[Qs?g2?g6Hwƭ8?g*- ?ga]?g'?g޻?g?J_?g~sw?g0FfͿgg"@ӿg?%:˿g&zM?g?Gg F?g~,g HgW2ҿgTzy?gwm ǿg@gW=ֿg 't?g".v1glg.Hꮿg,?g*˿rrz:The maximum number of subdivisions .50. has been achieved.z-floating point number truncated to an integer) rVrrrrrrrr6r+r)r` s r0test_ksone_fit_freezerX "s  / 0A X &  $ $ &  # #L"   # #?  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