Pearson chi-squared test for beta distribution

Description

Performs Pearson's chi-squared goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The implementation compares observed histogram bin counts with expected counts under the reference 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 \([0, 1]\).

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    Chi2PearsonBetaGofStatistic,
)


test_statistic = Chi2PearsonBetaGofStatistic(alpha=2, beta=5, lambda_=1)
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.

lambda_ - power-divergence parameter passed to the common chi-squared statistic implementation. Default value is 1.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation uses approximately \(\sqrt n\) bins on \([0, 1]\). Expected frequencies are computed from beta CDF differences at the bin edges.

Author(s)

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, Alexey Mironov

References

Pearson, K. (1900): On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. - Philosophical Magazine, vol. 50, pp. 157-175.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    Chi2PearsonBetaGofStatistic,
)


test_statistic = Chi2PearsonBetaGofStatistic(alpha=2, beta=5, lambda_=1)
statistic_result = test_statistic.execute_statistic([0.08, 0.14, 0.22, 0.31, 0.38, 0.46, 0.57])
print(statistic_result)