Ratio test for beta distribution

Description

Performs ratio goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The statistic compares the sample ratio of geometric mean to arithmetic mean with the theoretical beta distribution ratio.

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 (
    RatioBetaGofStatistic,
)


test_statistic = RatioBetaGofStatistic(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 sample statistic is the ratio of the geometric mean to the arithmetic mean. The theoretical ratio uses

\[ E[X] = \frac{\alpha}{\alpha + \beta} \]

and

\[ E[\log X] = \psi(\alpha) - \psi(\alpha + \beta), \]

where \(\psi\) is the digamma function.

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 (
    RatioBetaGofStatistic,
)


test_statistic = RatioBetaGofStatistic(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)