p7]c@sdZddlmZddlmZddlZddlmZddl m Z ddd Z d d Z e d d Z e d d ZdZd ddZeZeZeed d ZdS(s 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. 294-296Published by: American Statistical AssociationStable 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. i(tpartial(t string_typesN(tstatsi(t TableDistt two_sidedc Cstt|}t|tr9ttj|j}n!t|drZt|d}nt j |}|||}|dkrt j d|d||j }|dkr|Sn|d kr|t j d||j }|dkr|Snt j ||g}|S( s 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 : string 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. tcdfRtgreaterg?itlessg(RR(RR( tfloattlent isinstanceRtgetattrRt distributionsRthasattrtnptsorttarangetmax( txRt alternativetargstnobstcdfvalstDplustDmintD((s<lib/python2.7/site-packages/statsmodels/stats/_lilliefors.pytksstat-s"- $    tnormc Cs|dkrtjddddddgddd }tjd d d d ddddddddddddddddddd gt}tjd!d"d#d$d%d&gd'd!d(d)d*d+gd,d-d.d/d0d1gd2d3d4d5d6d7gd8d9d:d;d<d=gd>d?d2d@dAdBgdCdDdEdFd5dGgdHdIdJdKdLdMgdNdOdPdQd-dRgdSdTdUdVdWdXgdYdZdHd[dFd\gd]d^d_d`dadbgdcdddedfdgdhgdidjd^dkdldmgdndodpdTdVdqgdrdsd]dtdDdugdvdwdcdxdydzgd{d|dvd}d_d~gddddvdpdCgddddddgddddddgddddddgddddddggddddd fd}d}tjdddddddddNdddddddgt}tj|jd|jddg}x:tt|D]&}|||||ddf900). Values in the table are linearly interpolated. Values outside the range will be returned as bounds, 0.2 for large and 0.001 for small pvalues. For exponential: 'table' uses the table from Lilliefors 1967, available for pvalues between 0.01 and 0.2. Values outside the range will be returned as bounds, 0.2 for large and 0.01 for small pvalues. Returns ------- ksstat : float Kolmogorov-Smirnov test statistic with estimated mean and variance. pvalue : float If the pvalue is lower than some threshold, e.g. 0.05, then we can reject the Null hypothesis that the sample comes from a normal distribution Notes ----- Reported power to distinguish normal from some other distributions is lower than with the Anderson-Darling test. could be vectorized RtddofiR ttables4Invalid dist parameter. dist must be 'norm' or 'exp'RRR6g?(RtasarrayR tmeantstdRRRtlilliefors_table_normtexpontlilliefors_table_exponR&RR5tprob( RR't pvalmethodRtzttest_dtlilliefors_tabletd_ksR4((s<lib/python2.7/site-packages/statsmodels/stats/_lilliefors.pyt kstest_fits(/            ((t__doc__t functoolsRtstatsmodels.compat.pythonRtnumpyRtscipyRt tabledistRRR2R<R>R5REt lillieforst kstest_normaltkstest_exponential(((s<lib/python2.7/site-packages/statsmodels/stats/_lilliefors.pyt$s I n ,K