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Kuiper test for Laplace distribution

Description

Performs Kuiper goodness-of-fit test for the hypothesis that the sample comes from a Laplace distribution. The statistic combines the largest positive and negative empirical distribution deviations.

Hypothesis of Laplace Distribution The null hypothesis is that the data comes from a Laplace distribution with location parameter t and positive scale parameter s.

Test Statistic The statistic is based on the sum of one-sided empirical distribution discrepancies after the Laplace probability integral transform.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KuiperLaplaceGofStatistic,
)


test_statistic = KuiperLaplaceGofStatistic(t=0, s=1)
statistic_result = test_statistic.execute_statistic([-1.7, -0.9, -0.35, 0.0, 0.42, 0.88, 1.64])
print(statistic_result)

Arguments

t - location parameter of the Laplace distribution. Default value is 0.0.

s - positive scale parameter of the Laplace distribution. Default value is 1.0.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation computes

\[ V = D^+ + D^- \]

where \(D^+\) and \(D^-\) are one-sided deviations between empirical plotting positions and Laplace CDF values.

Author(s)

Kirill Tahmazidi, Alexey Mironov

References

Kuiper, N.H. (1960): Tests concerning random points on a circle. - Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, vol. 63, pp. 38-47.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    KuiperLaplaceGofStatistic,
)


test_statistic = KuiperLaplaceGofStatistic(t=0, s=1)
statistic_result = test_statistic.execute_statistic([-1.7, -0.9, -0.35, 0.0, 0.42, 0.88, 1.64])
print(statistic_result)