Moment-based test for beta distribution¶

Description¶

Performs moment-based goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The statistic compares sample mean and sample variance with the theoretical beta distribution moments.

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 (
    MomentBasedBetaGofStatistic,
)


test_statistic = MomentBasedBetaGofStatistic(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¶

For a beta distribution,

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

and

\[ Var(X) = \frac{\alpha\beta}{(\alpha + \beta)^2(\alpha + \beta + 1)}. \]

The implementation combines squared standardized differences for the sample mean and sample variance.

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 (
    MomentBasedBetaGofStatistic,
)


test_statistic = MomentBasedBetaGofStatistic(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)