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Kuiper test for beta distribution

Description

Performs Kuiper goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The statistic combines the largest positive and negative empirical distribution deviations.

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 \([0, 1]\).

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KuiperBetaGofStatistic,
)


test_statistic = KuiperBetaGofStatistic(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.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation computes

\[ V = D^+ + D^- \]

where \(D^+\) and \(D^-\) are the one-sided deviations between empirical plotting positions and beta CDF values.

Author(s)

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, Alexey Mironov

References

Kuiper, N.H. (1960): Tests concerning random points on a circle. - Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, vol. 63, pp. 38-47.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    KuiperBetaGofStatistic,
)


test_statistic = KuiperBetaGofStatistic(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)