Skewness-kurtosis test for beta distribution

Description

Performs skewness-kurtosis goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The statistic compares sample skewness and kurtosis with the theoretical beta distribution values.

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 (
    SkewnessKurtosisBetaGofStatistic,
)


test_statistic = SkewnessKurtosisBetaGofStatistic(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 sample skewness and kurtosis and compares them with the theoretical values for the beta distribution. The squared differences are combined in a Jarque-Bera-like statistic.

Author(s)

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, Alexey Mironov

References

The statistic follows the implementation in pysatl_criterion.statistics.goodness_of_fit.beta.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    SkewnessKurtosisBetaGofStatistic,
)


test_statistic = SkewnessKurtosisBetaGofStatistic(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)