Watson test for Laplace distribution

Description

Performs Watson goodness-of-fit test for the hypothesis that the sample comes from a Laplace distribution. The Watson statistic is a centered modification of the Cramer-von Mises statistic.

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 removes the squared mean deviation of the probability-transformed observations from the Cramer-von Mises statistic.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    WatsonLaplaceGofStatistic,
)


test_statistic = WatsonLaplaceGofStatistic(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 Cramer-von Mises terms from Laplace CDF values and subtracts the Watson centering correction. Large values indicate stronger deviation from the Laplace model.

Author(s)

Kirill Tahmazidi, Alexey Mironov

References

Watson, G.S. (1961): Goodness-of-fit tests on a circle. - Biometrika, vol. 48, pp. 109-114.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    WatsonLaplaceGofStatistic,
)


test_statistic = WatsonLaplaceGofStatistic(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)