Lilliefors test for gamma distribution

Description

Performs Lilliefors-type goodness-of-fit test for the hypothesis that the sample comes from a gamma distribution. The implementation estimates gamma parameters from the sample before computing a Kolmogorov-Smirnov type statistic.

Hypothesis of Gamma Distribution The null hypothesis is that the data comes from a gamma distribution.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    LillieforsGammaGofStatistic,
)


test_statistic = LillieforsGammaGofStatistic(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 stored in the statistic hypothesis. Default value is 1.0.

beta - positive rate parameter stored in the statistic hypothesis. Default value is 1.0.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation estimates gamma parameters with

\[ \hat\alpha = \frac{\bar X^2}{S^2}, \quad \hat\theta = \frac{S^2}{\bar X}. \]

The sorted sample is then transformed by the estimated gamma cumulative distribution function.

Author(s)

Sergey Golovachev, Alexey Mironov

References

Lilliefors, H.W. (1967): On the Kolmogorov-Smirnov test for normality with mean and variance unknown. - Journal of the American Statistical Association, vol. 62, pp. 399-402.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    LillieforsGammaGofStatistic,
)


test_statistic = LillieforsGammaGofStatistic(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)