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Watson test for beta distribution

Description

Performs Watson goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The Watson statistic is a centered modification of the Cramer-von Mises statistic.

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 (
    WatsonBetaGofStatistic,
)


test_statistic = WatsonBetaGofStatistic(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 a Cramer-von Mises statistic from beta CDF values and subtracts the Watson correction term

\[ n\left(\bar F_0 - \frac{1}{2}\right)^2. \]

Large values indicate stronger deviation from the beta model.

Author(s)

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, Alexey Mironov

References

Watson, G.S. (1961): Goodness-of-fit tests on a circle. - Biometrika, vol. 48, pp. 109-114.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    WatsonBetaGofStatistic,
)


test_statistic = WatsonBetaGofStatistic(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)