Kolmogorov-Smirnov test for gamma distribution

Description

Performs Kolmogorov-Smirnov goodness-of-fit test for the hypothesis that the sample comes from a gamma distribution. The statistic compares the empirical distribution function with the theoretical gamma cumulative distribution function.

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.

Test Statistic The statistic is based on the maximum distance between the empirical distribution function and the reference gamma cumulative distribution function.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovGammaGofStatistic,
)


test_statistic = KolmogorovSmirnovGammaGofStatistic(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.

alternative_type - alternative hypothesis type used by the Kolmogorov-Smirnov statistic.

mode - calculation mode passed to the Kolmogorov-Smirnov statistic. Default value is auto.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation evaluates the gamma cumulative distribution function using scale=1 / beta:

\[ F_0(x) = F_{\Gamma(\alpha, 1 / \beta)}(x). \]

The transformed ordered observations are passed to the common Kolmogorov-Smirnov statistic implementation.

Author(s)

Sergey Golovachev, Alexey Mironov

References

Kolmogorov, A.N. (1933): Sulla determinazione empirica di una legge di distribuzione. - Giornale dell'Istituto Italiano degli Attuari, vol. 4, pp. 83-91.

Smirnov, N.V. (1948): Table for estimating the goodness of fit of empirical distributions. - Annals of Mathematical Statistics, vol. 19, pp. 279-281.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovGammaGofStatistic,
)


test_statistic = KolmogorovSmirnovGammaGofStatistic(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)