M/Ph&dZddlmZddlZddlmZddlmZddl m Z m Z m Z ddl mZd Zdd ZddZed ZedZdZddZeZeZeedZdS)u Implements Lilliefors corrected Kolmogorov-Smirnov tests for normal and exponential distributions. `kstest_fit` is provided as a top-level function to access both tests. `kstest_normal` and `kstest_exponential` are provided as convenience functions with the appropriate test as the default. `lilliefors` is provided as an alias for `kstest_fit`. Created on Sat Oct 01 13:16:49 2011 Author: Josef Perktold License: BSD-3 pvalues for Lilliefors test are based on formula and table in An Analytic Approximation to the Distribution of Lilliefors's Test Statistic for Normality Author(s): Gerard E. Dallal and Leland WilkinsonSource: The American Statistician, Vol. 40, No. 4 (Nov., 1986), pp. 294-296 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/2684607 . On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown Hubert W. Lilliefors Journal of the American Statistical Association, Vol. 62, No. 318. (Jun., 1967), pp. 399-402. --- Updated 2017-07-23 Jacob C. Kimmel Ref: Lilliefors, H.W. On the Kolmogorov-Smirnov test for the exponential distribution with mean unknown. Journal of the American Statistical Association, Vol 64, No. 325. (1969), pp. 387–389. )partialN)stats) string_like)critical_valuesasymp_critical_values PERCENTILES) TableDistcfd}|S)a& Generates an asymptotic distribution callable from a param matrix Polynomial is a[0] * x**(-1/2) + a[1] * x**(-1) + a[2] * x**(-3/2) Parameters ---------- params : ndarray Array with shape (nalpha, 3) where nalpha is the number of significance levels ctjdtj|tj|dzg}tj|jS)Nr)nparraylogexpdotT)npolyparamss ]/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/stats/_lilliefors.pyfz$_make_asymptotic_function..fAsKxBF1IIrvayyA~677vdhhvx(())))rrs` r_make_asymptotic_functionr4s#***** Hr two_sidedrc$tt|}t|tr t t j|j}n t|drt |d}tj |}||g|R}tj d|dz|z |z }|tj d||z z }|dkr|S|dkr|Stj ||gS)a Calculate statistic for the Kolmogorov-Smirnov test for goodness of fit This calculates the test statistic for a test of the distribution G(x) of an observed 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 ---------- x : array_like, 1d array of observations cdf : str or callable string: name of a distribution in scipy.stats callable: function to evaluate cdf alternative : 'two_sided' (default), 'less' or 'greater' defines the alternative hypothesis (see explanation) args : tuple, sequence distribution parameters for call to cdf Returns ------- D : float KS test statistic, either D, D+ or D- See Also -------- scipy.stats.kstest 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). In contrast to scipy.stats.kstest, this function only calculates the statistic which can be used either as distance measure or to implement case specific p-values. cdfg?rggreaterless) floatlen isinstancestrgetattrr distributionsrhasattrrsortarangemax)xr alternativeargsnobscdfvalsd_plusd_mins rksstatr2HsX Q==D#s"e)3//3 e  "c5!!  Ac!mdmmmGiTAX&&-7 < < > >F ryd++d2 2 7 7 9 9Ei    665/ " ""rnormcNdtjtdz z }|ddd}|dkrdn|}|tvrt dt|t |tjt t}tjfd t D}|dddddf}tjfd t D}t|ddd}t|||| }|S) a Generates tables for significance levels of Lilliefors test statistics Tables for available normal and exponential distribution testing, as specified in Lilliefors references above Parameters ---------- dist : str distribution being tested in set {'norm', 'exp'}. Returns ------- lf : TableDist object. table of critical values rY@Nr3normalz/Invalid dist parameter. Must be 'norm' or 'exp')dtypec g|] }| Srr).0keycv_datas r z(get_lilliefors_table..s@@@ @@@rc g|] }| Srr)r:r;acv_datas rr=z(get_lilliefors_table..sFFFcHSMFFFr) asymptotic) rrr r ValueErrorrsortedr!rr ) distalphasizecrit_lf asym_paramsasymp_fnlfr?r<s @@rget_lilliefors_tablerJs(( %%- -E $$B$KEv~~884D ?""JKKKd#G$T*H 8F7OO5 1 1 1Dh@@@@w@@@AAGaaa2gG(FFFFVH5E5EFFFGGK(TTrT):;;H 5$H = = =B Ir)rCrc|dkr ||dz dzz}d}tjd|dzz|dzzd|ztj|dzzzdz d tj|z zd |z z}|S) a` Approximate pvalues for Lilliefors test This is only valid for pvalues smaller than 0.1 which is not checked in this function. Parameters ---------- d_max : array_like two-sided Kolmogorov-Smirnov test statistic n : int or float sample size Returns ------- p-value : float or ndarray pvalue according to approximation formula of Dallal and Wilkinson. Notes ----- This is mainly a helper function where the calling code should dispatch on bound violations. Therefore it does not check whether the pvalue is in the valid range. Precision for the pvalues is around 2 to 3 decimals. This approximation is also used by other statistical packages (e.g. R:fBasics) but might not be the most precise available. References ---------- DallalWilkinson1986 dr5g\(\?gwT r gvT5A=@gHȰ@g`80C?g}%/?g-9(?)rrsqrt)d_maxrpvals rpval_lfrPsD 3ww !d(t##  6(UaZ'1w;7eObga'k&:&::;=EFrwqzz)*,3aK8 9 9D Krtablec>t|dd}tj|}|jdkr|jddkr |dddf}n|jdkrt dt |}|d krG||z |d z }tj j }t}nG|d kr2||z }tj j }t}d }nt d |d krdnd}||kr#t d||t!||d}|dkr-t#||} | dkr|||} n|||} || fS)a Test assumed normal or exponential distribution using Lilliefors' test. Lilliefors' test is a Kolmogorov-Smirnov test with estimated parameters. Parameters ---------- x : array_like, 1d Data to test. dist : {'norm', 'exp'}, optional The assumed distribution. pvalmethod : {'approx', 'table'}, optional The method used to compute the p-value of the test statistic. In general, 'table' is preferred and makes use of a very large simulation. 'approx' is only valid for normality. if `dist = 'exp'` `table` is always used. 'approx' uses the approximation formula of Dalal and Wilkinson, valid for pvalues < 0.1. If the pvalue is larger than 0.1, then the result of `table` is returned. Returns ------- ksstat : float Kolmogorov-Smirnov test statistic with estimated mean and variance. pvalue : float If the pvalue is lower than some threshold, e.g. 0.05, then we can reject the Null hypothesis that the sample comes from a normal distribution. Notes ----- 'table' uses an improved table based on 10,000,000 simulations. The critical values are approximated using log(cv_alpha) = b_alpha + c[0] log(n) + c[1] log(n)**2 where cv_alpha is the critical value for a test with size alpha, b_alpha is an alpha-specific intercept term and c[1] and c[2] are coefficients that are shared all alphas. Values in the table are linearly interpolated. Values outside the range are be returned as bounds, 0.990 for large and 0.001 for small pvalues. For implementation details, see lilliefors_critical_value_simulation.py in the test directory. pvalmethod)approxrQ)optionsr rNrzXInvalid parameter `x`: must be a one-dimensional array-like or a single-column DataFramer3)ddofrrQz/Invalid dist parameter, must be 'norm' or 'exp'z:Test for distribution {} requires at least {} observationsr)r,rTg?)rrasarrayndimshaperAr"meanstdrr3rlilliefors_table_normexponlilliefors_table_exponformatr2rPprob) r+rCrSr.ztest_dlilliefors_tablemin_nobsd_ksrOs r kstest_fitrhsXZ)%8:::J 1 Av{{qwqzQ aaadG 1DEE E q66D v~~ \QUUU]] *0  L1 JKKKFNNqqH h((.tX(>(>@@ @ !V 5 5 5DXtT"" #::#((t44D$$T400 :r)rr)r3)r3rQ)__doc__ functoolsrnumpyrscipyrstatsmodels.tools.validationr_lilliefors_critical_valuesrrr tabledistr rr2rJr^r`rPrh lilliefors kstest_normalkstest_exponentialrrrrssM&&N4444447777777777!    (=#=#=#=#@$$$$N-,&999--5999(((VSSSSl  WZe444r