Anderson-Darling test for gamma distribution

Description

Performs Anderson-Darling goodness-of-fit test for the hypothesis that the sample comes from a gamma distribution. The test gives additional weight to discrepancies in the tails.

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 (
    AndersonDarlingGammaGofStatistic,
)


test_statistic = AndersonDarlingGammaGofStatistic(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 evaluates gamma logcdf and logsf values for the ordered sample and passes them to the common Anderson-Darling statistic implementation.

Author(s)

Sergey Golovachev, Alexey Mironov

References

Anderson, T.W. and Darling, D.A. (1952): Asymptotic theory of certain goodness of fit criteria based on stochastic processes. - Annals of Mathematical Statistics, vol. 23, pp. 193-212.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    AndersonDarlingGammaGofStatistic,
)


test_statistic = AndersonDarlingGammaGofStatistic(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)