Kolmogorov-Smirnov test for uniformity

Description

Performs the Kolmogorov-Smirnov goodness-of-fit test for the hypothesis of uniformity on the interval \([a, b]\). The statistic measures the largest discrepancy between the empirical distribution function and the cumulative distribution function of the reference uniform distribution.

Hypothesis of Uniformity The null hypothesis is that the sample comes from a uniform distribution on the interval \([a, b]\). All observations passed to execute_statistic must lie inside this interval.

Test Statistic The statistic is based on the maximum vertical distance between the empirical cumulative distribution function and the theoretical uniform cumulative distribution function.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovUniformGofStatistic,
)


test_statistic = KolmogorovSmirnovUniformGofStatistic(a=0, b=1)
statistic_result = test_statistic.execute_statistic([0.12, 0.25, 0.41, 0.53, 0.77, 0.91])
print(statistic_result)

Arguments

a - left boundary of the uniform distribution. Default value is 0.

b - right boundary of the uniform distribution. Default value is 1.

alternative_type - alternative hypothesis type used by the Kolmogorov-Smirnov statistic.

mode - calculation mode passed to the Kolmogorov-Smirnov statistic. Default value is auto.

rvs - array-like sample data passed to execute_statistic.

Details

For ordered observations \(X_{(i)}\), the implementation evaluates

\[ F_0(X_{(i)}) = \frac{X_{(i)} - a}{b - a} \]

and passes these values to the common Kolmogorov-Smirnov statistic implementation. Large values indicate stronger deviation from the uniform model.

Author(s)

Aleksandr Podmarev, Alexey Mironov

References

Kolmogorov, A.N. (1933): Sulla determinazione empirica di una legge di distribuzione. - Giornale dell'Istituto Italiano degli Attuari, vol. 4, pp. 83-91.

Smirnov, N.V. (1948): Table for estimating the goodness of fit of empirical distributions. - Annals of Mathematical Statistics, vol. 19, pp. 279-281.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovUniformGofStatistic,
)


test_statistic = KolmogorovSmirnovUniformGofStatistic(a=0, b=1)
statistic_result = test_statistic.execute_statistic([0.12, 0.25, 0.41, 0.53, 0.77, 0.91])
print(statistic_result)