Probability plot correlation test for gamma distribution

Description

Performs probability plot correlation coefficient goodness-of-fit test for the hypothesis that the sample comes from a gamma distribution. The statistic measures linear alignment between ordered sample values and theoretical gamma quantiles.

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 (
    ProbabilityPlotCorrelationGammaGofStatistic,
)


test_statistic = ProbabilityPlotCorrelationGammaGofStatistic(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 plotting positions, evaluates theoretical gamma quantiles, and returns one minus the correlation coefficient between the ordered sample and the expected quantiles. Values near zero indicate stronger linear alignment with the gamma model.

Author(s)

Sergey Golovachev, Alexey Mironov

References

Filliben, J.J. (1975): The probability plot correlation coefficient test for normality. - Technometrics, vol. 17, pp. 111-117.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    ProbabilityPlotCorrelationGammaGofStatistic,
)


test_statistic = ProbabilityPlotCorrelationGammaGofStatistic(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)