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Greenwood test for Laplace distribution

Description

Performs Greenwood spacing goodness-of-fit test for the hypothesis that the sample comes from a Laplace distribution. The statistic measures squared spacings after transforming observations by the Laplace cumulative distribution function.

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 squared spacings between consecutive probability-transformed observations.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    GreenwoodLaplaceGofStatistic,
)


test_statistic = GreenwoodLaplaceGofStatistic(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 spacings \(D_i\) between consecutive Laplace CDF values after adding 0 and 1, and returns

\[ G = \sum_i D_i^2. \]

Large values indicate clustering or uneven spacing in the probability-transformed sample.

Author(s)

Kirill Tahmazidi, Alexey Mironov

References

Greenwood, M. (1946): The statistical study of infectious diseases. - Journal of the Royal Statistical Society, Series A, vol. 109, pp. 85-110.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    GreenwoodLaplaceGofStatistic,
)


test_statistic = GreenwoodLaplaceGofStatistic(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)