Neyman smooth test for uniformity

Description

Performs Neyman's smooth goodness-of-fit test for the hypothesis of uniformity on the interval \([a, b]\). The statistic uses orthonormal polynomial components on the unit interval.

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 (
    NeymanSmoothTestUniformGofStatistic,
)


test_statistic = NeymanSmoothTestUniformGofStatistic(a=0, b=1, k=4)
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.

k - number of smooth components. Default value is 4.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation standardizes observations to \([0, 1]\) and computes

\[ \sum_{j=1}^{k} V_j^2, \quad V_j = \frac{1}{\sqrt n}\sum_{i=1}^{n}\phi_j(U_i). \]

The first components are implemented explicitly, and higher-order components use Legendre polynomials.

Author(s)

Aleksandr Podmarev, Alexey Mironov

References

Neyman, J. (1937): Smooth test for goodness of fit. - Skandinavisk Aktuarietidskrift, vol. 20, pp. 149-199.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    NeymanSmoothTestUniformGofStatistic,
)


test_statistic = NeymanSmoothTestUniformGofStatistic(a=0, b=1, k=4)
statistic_result = test_statistic.execute_statistic([0.12, 0.25, 0.41, 0.53, 0.77, 0.91])
print(statistic_result)