Zhang tests for uniformity

Description

Performs Zhang's goodness-of-fit tests for the hypothesis of uniformity on the interval \([a, b]\). The implementation supports three variants selected by test_type: A, C, and K.

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 (
    ZhangTestsUniformGofStatistic,
)


test_statistic = ZhangTestsUniformGofStatistic(a=0, b=1, test_type="A")
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.

test_type - Zhang statistic variant. Must be A, C, or K. Default value is A.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation standardizes ordered observations to \(U_{(i)} \in [0, 1]\) and computes one of the Zhang statistics using logarithmic transforms of \(U_{(i)}\) and \(1 - U_{(i)}\). Large values indicate stronger deviation from the uniform model.

Author(s)

Aleksandr Podmarev, Alexey Mironov

References

Zhang, J. (2002): Powerful goodness-of-fit tests based on the likelihood ratio. - Journal of the Royal Statistical Society, Series B, vol. 64, pp. 281-294.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    ZhangTestsUniformGofStatistic,
)


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