M/PhqSdZddlmZddlZddlmZddlmZddl m Z dZ d?d Z d ZeZdZdZdZdZdZiZeeeeeeeded<dZdddded<deied<GddZd@d ZdAd!ZdBd#ZdCd$ZGd%d&Zed'kriej1d1e%DZ2e"d2d33e%e"d4e2d5k4d0e"d6e2d7k4d0e"d8e2d9k4d0ed:d,d";d"Z+dZ5eedz8e9Z:e"e6e:dSdS)DatMore Goodness of fit tests contains GOF : 1 sample gof tests based on Stephens 1970, plus AD A^2 bootstrap : vectorized bootstrap p-values for gof test with fitted parameters Created : 2011-05-21 Author : Josef Perktold parts based on ks_2samp and kstest from scipy.stats (license: Scipy BSD, but were completely rewritten by Josef Perktold) References ---------- )lmapN) distributions)cache_readonly) kolmogorovcttj||f\}}|jd}|jd}t |}t |}tj|}tj|}tj||g}tj||dd|zz }tj||dd|zz }tjtj ||z }tj ||zt||zz } t|dzd|z z|z} n #d} YnxYw|| fS)aA Computes the Kolmogorov-Smirnof statistic on 2 samples. This is a two-sided test for the null hypothesis that 2 independent samples are drawn from the same continuous distribution. Parameters ---------- a, b : sequence of 1-D ndarrays two arrays of sample observations assumed to be drawn from a continuous distribution, sample sizes can be different Returns ------- D : float KS statistic p-value : float two-tailed p-value Notes ----- This tests whether 2 samples are drawn from the same distribution. Note that, like in the case of the one-sample K-S test, the distribution is assumed to be continuous. This is the two-sided test, one-sided tests are not implemented. The test uses the two-sided asymptotic Kolmogorov-Smirnov distribution. If the K-S statistic is small or the p-value is high, then we cannot reject the hypothesis that the distributions of the two samples are the same. Examples -------- >>> from scipy import stats >>> import numpy as np >>> from scipy.stats import ks_2samp >>> #fix random seed to get the same result >>> np.random.seed(12345678) >>> n1 = 200 # size of first sample >>> n2 = 300 # size of second sample different distribution we can reject the null hypothesis since the pvalue is below 1% >>> rvs1 = stats.norm.rvs(size=n1,loc=0.,scale=1) >>> rvs2 = stats.norm.rvs(size=n2,loc=0.5,scale=1.5) >>> ks_2samp(rvs1,rvs2) (0.20833333333333337, 4.6674975515806989e-005) slightly different distribution we cannot reject the null hypothesis at a 10% or lower alpha since the pvalue at 0.144 is higher than 10% >>> rvs3 = stats.norm.rvs(size=n2,loc=0.01,scale=1.0) >>> ks_2samp(rvs1,rvs3) (0.10333333333333333, 0.14498781825751686) identical distribution we cannot reject the null hypothesis since the pvalue is high, 41% >>> rvs4 = stats.norm.rvs(size=n2,loc=0.0,scale=1.0) >>> ks_2samp(rvs1,rvs4) (0.07999999999999996, 0.41126949729859719) rright)side?Q?)\(?) rnpasarrayshapelensort concatenate searchsortedmaxabsolutesqrtfloatksprob) data1data2n1n2data_allcdf1cdf2denprobs i/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/distributions/gof_new.pyks_2sampr$s4P UEN33LE5 QB QB UB UB GENNE GENNE~uUm,,H ?5w 7 7 7R @D OE( 8 8 83r6 BD r{49%%&&A BuRU||# $ $Br$wtBw)** d7Ns $EE two_sidedapproxc Lt|trL|r||kr5tt|j}tt|j}nt dt|trtt|j}t|rd|i}tj ||i|}n#tj |}t|}||g|R}|dvrXtj d|dz|z |z } |dkr"| tj | |fS|dvrU|tj d||z z } |d kr"| tj | |fS|d krtj | | g} |d kr6| tj| tj|zfS|d krtj| tj|z} |d ks| d|dzdz z kr6| tj| tj|zfS| tj | |dzfSdSdS)a Perform the Kolmogorov-Smirnov test for goodness of fit This performs a test of the distribution G(x) of an observed random variable against a given distribution F(x). Under the null hypothesis the two distributions are identical, G(x)=F(x). The alternative hypothesis can be either 'two_sided' (default), 'less' or 'greater'. The KS test is only valid for continuous distributions. Parameters ---------- rvs : str or array or callable string: name of a distribution in scipy.stats array: 1-D observations of random variables callable: function to generate random variables, requires keyword argument `size` cdf : str or callable string: name of a distribution in scipy.stats, if rvs is a string then cdf can evaluate to `False` or be the same as rvs callable: function to evaluate cdf args : tuple, sequence distribution parameters, used if rvs or cdf are strings N : int sample size if rvs is string or callable alternative : 'two_sided' (default), 'less' or 'greater' defines the alternative hypothesis (see explanation) mode : 'approx' (default) or 'asymp' defines the distribution used for calculating p-value 'approx' : use approximation to exact distribution of test statistic 'asymp' : use asymptotic distribution of test statistic Returns ------- D : float KS test statistic, either D, D+ or D- p-value : float one-tailed or two-tailed p-value Notes ----- In the one-sided test, the alternative is that the empirical cumulative distribution function of the random variable is "less" or "greater" than the cumulative distribution function F(x) of the hypothesis, G(x)<=F(x), resp. G(x)>=F(x). Examples -------- >>> from scipy import stats >>> import numpy as np >>> from scipy.stats import kstest >>> x = np.linspace(-15,15,9) >>> kstest(x,'norm') (0.44435602715924361, 0.038850142705171065) >>> np.random.seed(987654321) # set random seed to get the same result >>> kstest('norm','',N=100) (0.058352892479417884, 0.88531190944151261) is equivalent to this >>> np.random.seed(987654321) >>> kstest(stats.norm.rvs(size=100),'norm') (0.058352892479417884, 0.88531190944151261) Test against one-sided alternative hypothesis: >>> np.random.seed(987654321) Shift distribution to larger values, so that cdf_dgp(x)< norm.cdf(x): >>> x = stats.norm.rvs(loc=0.2, size=100) >>> kstest(x,'norm', alternative = 'less') (0.12464329735846891, 0.040989164077641749) Reject equal distribution against alternative hypothesis: less >>> kstest(x,'norm', alternative = 'greater') (0.0072115233216311081, 0.98531158590396395) Do not reject equal distribution against alternative hypothesis: greater >>> kstest(x,'norm', mode='asymp') (0.12464329735846891, 0.08944488871182088) Testing t distributed random variables against normal distribution: With 100 degrees of freedom the t distribution looks close to the normal distribution, and the kstest does not reject the hypothesis that the sample came from the normal distribution >>> np.random.seed(987654321) >>> stats.kstest(stats.t.rvs(100,size=100),'norm') (0.072018929165471257, 0.67630062862479168) With 3 degrees of freedom the t distribution looks sufficiently different from the normal distribution, that we can reject the hypothesis that the sample came from the normal distribution at a alpha=10% level >>> np.random.seed(987654321) >>> stats.kstest(stats.t.rvs(3,size=100),'norm') (0.131016895759829, 0.058826222555312224) 5if rvs is string, cdf has to be the same distributionsize)r'greaterr r,)r'lessr.r'asympr(j 皙?333333?@@N) isinstancestrgetattrrcdfrvsAttributeErrorcallabler rrarangerksonesf kstwobignr) r:r9argsN alternativemodekwdsvalscdfvalsDplusDminDpval_twos r#kstestrL}sf#sZ Z---1C---1CC !XYY Y#s.mS))-}}qzwssD(4(())ws|| IIc$G...3!$$Q&05577 ) # #--00q999 9+++")C++A--2244 & ,//Q777 7k!! 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For the Kolmogorov-Smirnov test the tests as given in scipy.stats are also available as options. design: I might want to retest with different distributions, to calculate data summary statistics only once, or add separate class that holds summary statistics and data (sounds good). r%r&ct|trL|r||kr5tt|j}tt|j}nt dt|trtt|j}t|rd|i}tj ||i|}n#tj |}t|}||g|R}||_ ||_ ||_ dS)Nr*r+)r6r7r8rr9r:r;r<r rrrW vals_sortedrG)selfr:r9rArBrErFrGs r#__init__z GOF.__init__s c3   ^ ^SCZZmS115mS115$%\]]] c3   2---1C C== 1:D733,t,,--DD73<>C#7!";;; rMc|j}|j}d}td|D]@}|||d|z }|dk}d||z ||<||z }A|dz d|z |zz }|S)Nrr-rg@rt)rWrGrangerS)rrWrGmsumjmjmaskr{s r#r{zGOF.asy,q  Agbqbk)BHD2d8|BtH BFFHH DD 2IT D( (rMc |j}|j}dtjd|dzzdz tj|tjd|dddz zz |z |z }|S)z4Stephens 1974, does not have p-value formula for A^2rtr r-N)rWrGr r=logrS)rrWrGasqus r#rzGOF.asqusy,ryT!V,,,q026!GDDbDM/#:#::=>AceeDDHIKOP rMr r|ct||}|dkr#t||||j|fSt||||jS)z r|)r8 gof_pvalsrW)rtestidpvalsrVs r#get_testz GOF.get_tests[ tV$$ O # #U#F+D$)<ctj fdt D}tdd t td |d k dtd |d k dtd |dk ddS)Nr defaultdictir|r-c g|] }| Sr%r%).0tiresultss r# zgof_mc..s666rwr{666rM  at 0.01:{Gz?at 0.05:rfat 0.10:rm) collectionsrlistrrall_gofsappendrr rTprintjoinr) randfndistrrWrir:goftrresarrrs @r#gof_mcrsM''''''k$G 4[[IIfTll3 I IB BK  t}}RAA!DQG H H H H IX6666X666 7 7F +x}}X../// *v}**1--... *v}**1--... *v|))!,,-----rMc t|j}|j|}tdg|z}dg|z}td||<tddd||<dtjd|dzt |zdz tj|tjd|t |z zz|z | |z }|S)z.vectorized Anderson Darling A^2, Stephens 1974Nrrtr r-)rrslicer r=tuplerrS)rGaxisndimrW slice_reverseislicers r#asquarers w}  D = D4[[MD(MVd]F;;F4LdB//M$29Ra((v77!; VG__rvam0D0D(E&EFF FHHLMNQcRVii X D KrMcF||tdttj|t |z }d}t |D]}|j|fid||fi} || d} td| } tj | | | d} t| d} || |k z }|t ||zz S|j|fid||fi} || d} td| } tj | | | d} t| d} |tj | } | S| |k S) aMonte Carlo (or parametric bootstrap) p-values for gof currently hardcoded for A^2 only assumes vectorized fit_vec method, builds and analyses (nobs, nrep) sample in one step rename function to less generic this works also with nrep=1 Nzusing batching requires a valuerr+r-rc,tj|dSNr-r expand_dimsxs r#rzbootstrap..;sBN1a$8$8rMc,tj|dSrrrs r#rzbootstrap..Dsq! 4 4rM) ValueErrorintr ceilrrr:fit_vecrrr9rrSr)rrArWnrepvalue batch_sizen_batchcountirepr:paramsrGrV stat_sorteds r# bootstraprs, =>?? ?bgd5#4#445566'NN + +D%)D@@VZ,>$?@@C]]3Q]//F88&AAFgeiiV441===G7+++D dem((** *EEuWz12222ei66t 566s++44f=='%))C00q999wQ''' ='$--K EM'')) )rMcd}t|D]i}|j|fid|i}||}tj|||} t | d} || |kz }j|dz|z S)zMonte Carlo (or parametric bootstrap) p-values for gof currently hardcoded for A^2 only non vectorized, loops over all parametric bootstrap replications and calculates and returns specific p-value, rename function to less generic rr+rr )rr:rr rr9r) rrrArWrrrr:rrGrVs r# bootstrap2rOs$ Ed !!ei.. ..s##'%))C0011wQ''' $%-  2: rMc&eZdZdZddZdZdZdS)NewNormz-just a holder for modified distributions rcV||||fSr)rstd)rrrs r#rzNewNorm.fit_vecps!vvd||QUU4[[((rMc^tj||d|dS)Nrr-)locscale)rnormr9)rrrAs r#r9z NewNorm.cdfss(!%%aT!WDG%DDDrMcn|d}|d}||tj|zzS)Nrr-r+)rrr:)rrAr+rrs r#r:z NewNorm.rvsvs8 G1gU]/333>>>>>rMNr)rrrrrr9r:r%rMr#rrlsS))))EEE?????rMr__main__)statsrz scipy kstestr)r rvrwrxryrzr{z Is it correctly sized?rr-c(g|]}t|Sr%)r)rrs r#rrs666rwr{666rMrrrrrrfrrmcDtjd|S)Nrr)rtr:rWs r#rrs AD 11rMr)rr-)rArWrr)gGz?gffffff?rs)r%r&r'r()rr)r%rrNN)r%rr);rstatsmodels.compat.pythonrnumpyr scipy.statsrstatsmodels.tools.decoratorsr scipy.specialrrr$rLr\dminus_st70_uppr_rdrkrqrurr~rrrrrrrrrrr:rrrrrrrrrrWrrrandomrandnrrTrrrrbtfloorastyper quantindexr%rMr#rs&+*****%%%%%%777777......ZZZ~Y8Y8Y8Y8|'''!'''''''''''''''        /888RQNN L L '  .~=~=~=~=~=~=~=~=N...."    ..*.*.*.*d: ? ? ? ? ? ? ? ?& z '++ac+ " "C E. 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