Lilliefors test for beta distribution

Description

Performs Lilliefors-type goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The implementation reuses the common Lilliefors statistic calculation with beta cumulative distribution function values.

Hypothesis of Beta Distribution The null hypothesis is that the data comes from a beta distribution with positive shape parameters alpha and beta on the interval \([0, 1]\).

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    LillieforsTestBetaGofStatistic,
)


test_statistic = LillieforsTestBetaGofStatistic(alpha=2, beta=5)
statistic_result = test_statistic.execute_statistic([0.08, 0.14, 0.22, 0.31, 0.38, 0.46, 0.57])
print(statistic_result)

Arguments

alpha - first positive shape parameter of the beta distribution. Default value is 1.

beta - second positive shape parameter of the beta distribution. Default value is 1.

rvs - array-like sample data passed to execute_statistic.

Details

The sample is sorted and transformed with the reference beta cumulative distribution function. The transformed values are passed to the common Lilliefors statistic implementation.

Author(s)

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, 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 (
    LillieforsTestBetaGofStatistic,
)


test_statistic = LillieforsTestBetaGofStatistic(alpha=2, beta=5)
statistic_result = test_statistic.execute_statistic([0.08, 0.14, 0.22, 0.31, 0.38, 0.46, 0.57])
print(statistic_result)