Kuiper test for uniformity

Description

Performs the Kuiper goodness-of-fit test for the hypothesis of uniformity on the interval \([a, b]\). The statistic combines the largest positive and negative deviations between the empirical and theoretical distribution functions.

Hypothesis of Uniformity The null hypothesis is that the sample comes from a uniform distribution on the interval \([a, b]\).

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KuiperUniformGofStatistic,
)


test_statistic = KuiperUniformGofStatistic(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.

rvs - array-like sample data passed to execute_statistic.

Details

After standardizing observations to \([0, 1]\), the implementation computes

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

where

\[ D^+ = \max_i\left(\frac{i}{n} - U_{(i)}\right), \quad D^- = \max_i\left(U_{(i)} - \frac{i - 1}{n}\right). \]

Large values indicate stronger deviation from the uniform model.

Author(s)

Aleksandr Podmarev, 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 (
    KuiperUniformGofStatistic,
)


test_statistic = KuiperUniformGofStatistic(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)