Likelihood-ratio test for gamma distribution

Description

Performs likelihood-ratio goodness-of-fit test for the hypothesis that the sample comes from a gamma distribution. The test is a G-test variant of the binned chi-squared family.

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 (
    LikelihoodRatioGammaGofStatistic,
)


test_statistic = LikelihoodRatioGammaGofStatistic(bins=4, 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

bins - number of equiprobable gamma bins. Default value is 8.

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 uses equiprobable gamma quantile bins and the power-divergence statistic with lambda = 0.

Author(s)

Sergey Golovachev, Alexey Mironov

References

Wilks, S.S. (1935): The likelihood test of independence in contingency tables. - Annals of Mathematical Statistics, vol. 6, pp. 190-196.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    LikelihoodRatioGammaGofStatistic,
)


test_statistic = LikelihoodRatioGammaGofStatistic(bins=4, 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)