Pearson chi-squared test for gamma distribution

Description

Performs Pearson chi-squared goodness-of-fit test for the hypothesis that the sample comes from a gamma distribution. The implementation bins observations using equiprobable gamma quantile bins.

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 (
    Chi2PearsonGammaGofStatistic,
)


test_statistic = Chi2PearsonGammaGofStatistic(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 bin edges are gamma quantiles, so each bin has equal theoretical probability under the null model. Observed bin counts are compared with equal expected counts.

Author(s)

Sergey Golovachev, Alexey Mironov

References

Pearson, K. (1900): On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. - Philosophical Magazine, vol. 50, pp. 157-175.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    Chi2PearsonGammaGofStatistic,
)


test_statistic = Chi2PearsonGammaGofStatistic(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)