Kolmogorov-Smirnov test for beta distribution

Description

Performs Kolmogorov-Smirnov goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The Kolmogorov-Smirnov test compares the empirical distribution function with the theoretical cumulative distribution function of the beta distribution.

Hypothesis of Beta Distribution The null hypothesis is that the data comes from a beta distribution with positive shape parameters alpha and beta on the interval \([0, 1]\).

Test Statistic The statistic is based on the maximum distance between the empirical distribution function and the beta cumulative distribution function.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovBetaGofStatistic,
)


test_statistic = KolmogorovSmirnovBetaGofStatistic(alpha=2, beta=5)
statistic_result = test_statistic.execute_statistic([0.08, 0.14, 0.22, 0.31, 0.38, 0.46, 0.57])
print(statistic_result)

Arguments

alpha - first positive shape parameter of the beta distribution. Default value is 1.

beta - second positive shape parameter of the beta distribution. Default value is 1.

alternative_type - alternative hypothesis type used by the Kolmogorov-Smirnov statistic.

mode - calculation mode passed to the Kolmogorov-Smirnov statistic. Default value is auto.

rvs - array-like sample data passed to execute_statistic.

Details

The observations are sorted and transformed with the reference beta cumulative distribution function

\[ F_0(x) = I_x(\alpha, \beta), \quad 0 \le x \le 1. \]

The transformed values are passed to the common Kolmogorov-Smirnov statistic implementation.

Author(s)

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, Alexey Mironov

References

Kolmogorov, A.N. (1933): Sulla determinazione empirica di una legge di distribuzione. - Giornale dell'Istituto Italiano degli Attuari, vol. 4, pp. 83-91.

Smirnov, N.V. (1948): Table for estimating the goodness of fit of empirical distributions. - Annals of Mathematical Statistics, vol. 19, pp. 279-281.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovBetaGofStatistic,
)


test_statistic = KolmogorovSmirnovBetaGofStatistic(alpha=2, beta=5)
statistic_result = test_statistic.execute_statistic([0.08, 0.14, 0.22, 0.31, 0.38, 0.46, 0.57])
print(statistic_result)