Entropy test for beta distribution

Description

Performs entropy-based goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The statistic compares a spacing-based sample entropy estimate with the theoretical entropy 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 \([0, 1]\).

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    EntropyBetaGofStatistic,
)


test_statistic = EntropyBetaGofStatistic(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.

m - optional window size for the spacing-based entropy estimator, passed to execute_statistic. Default value is n // 4.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation uses a Vasicek-style spacing entropy estimator on the sorted sample. It compares this estimate with the theoretical beta entropy computed from betaln and digamma terms.

Author(s)

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, Alexey Mironov

References

Vasicek, O. (1976): A test for normality based on sample entropy. - Journal of the Royal Statistical Society, Series B, vol. 38, pp. 54-59.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    EntropyBetaGofStatistic,
)


test_statistic = EntropyBetaGofStatistic(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)