3.11.11.1.2. statsmodels.stats.lilliefors.ksstat

statsmodels.stats.lilliefors.ksstat(x, cdf, alternative='two_sided', args=())

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.