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Watson test for gamma distribution

Description

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

Hypothesis of Gamma Distribution The null hypothesis is that the data comes from a gamma distribution with positive shape parameter alpha and positive rate parameter beta.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    WatsonGammaGofStatistic,
)


test_statistic = WatsonGammaGofStatistic(alpha=2, beta=1)
statistic_result = test_statistic.execute_statistic([0.42, 0.77, 1.05, 1.48, 1.96, 2.34, 3.12])
print(statistic_result)

Arguments

alpha - positive shape parameter of the gamma distribution. Default value is 1.0.

beta - positive rate parameter of the gamma distribution. Default value is 1.0.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation computes Cramer-von Mises terms from gamma CDF values and subtracts the Watson centering correction. Large values indicate stronger deviation from the gamma model.

Author(s)

Sergey Golovachev, 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 (
    WatsonGammaGofStatistic,
)


test_statistic = WatsonGammaGofStatistic(alpha=2, beta=1)
statistic_result = test_statistic.execute_statistic([0.42, 0.77, 1.05, 1.48, 1.96, 2.34, 3.12])
print(statistic_result)