Stein test for uniformity

Description

Performs a Stein-type U-statistic test for the hypothesis of uniformity on the interval \([a, b]\). The implementation standardizes observations to \([0, 1]\) and computes a pairwise kernel statistic.

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 (
    SteinUniformGofStatistic,
)


test_statistic = SteinUniformGofStatistic(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

For standardized observations, the implementation computes a U-statistic with pairwise kernel

\[ h(x, y) = \frac{1}{2}\left(2\max(x, y) - 2x - 2y + x^2 + y^2\right). \]

The returned statistic is the average of this kernel over unordered pairs.

Author(s)

Aleksandr Podmarev, Alexey Mironov

References

Stein, C. (1972): A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. - Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 583-602.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    SteinUniformGofStatistic,
)


test_statistic = SteinUniformGofStatistic(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)