Anderson-Darling test for Laplace distribution

Description

Performs Anderson-Darling goodness-of-fit test for the hypothesis that the sample comes from a Laplace distribution. The test gives additional weight to discrepancies in the distribution tails.

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 computed from the log cumulative distribution function and log survival function of the reference Laplace distribution.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    AndersonDarlingLaplaceGofStatistic,
)


test_statistic = AndersonDarlingLaplaceGofStatistic(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 evaluates Laplace logcdf and logsf values for the ordered sample and passes them to the common Anderson-Darling statistic implementation. Large values indicate stronger deviation from the Laplace model.

Author(s)

Kirill Tahmazidi, Alexey Mironov

References

Anderson, T.W. and Darling, D.A. (1952): Asymptotic theory of certain goodness of fit criteria based on stochastic processes. - Annals of Mathematical Statistics, vol. 23, pp. 193-212.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    AndersonDarlingLaplaceGofStatistic,
)


test_statistic = AndersonDarlingLaplaceGofStatistic(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)