Moran test for gamma distribution¶

Description¶

Performs Moran log-spacing goodness-of-fit test for the hypothesis that the sample comes from a gamma distribution. The statistic is based on logarithms of spacings after the gamma probability integral transform.

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 (
    MoranGammaGofStatistic,
)


test_statistic = MoranGammaGofStatistic(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¶

For spacings \(D_i\) between consecutive gamma CDF values, the implementation returns

\[ M = -\sum_i \log(nD_i). \]

Spacings must be strictly positive.

Author(s)¶

Sergey Golovachev, Alexey Mironov

References¶

Moran, P.A.P. (1951): The random division of an interval. - Journal of the Royal Statistical Society, Series B, vol. 13, pp. 147-150.

Examples¶

from pysatl_criterion.statistics.goodness_of_fit import (
    MoranGammaGofStatistic,
)


test_statistic = MoranGammaGofStatistic(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)