Bickel-Rosenblatt test for uniformity¶

Description¶

Performs the Bickel-Rosenblatt density-based goodness-of-fit test for the hypothesis of uniformity on the interval \([a, b]\). The statistic compares a kernel density estimate of the standardized sample with the unit uniform density.

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 (
    BickelRosenblattUniformGofStatistic,
)


test_statistic = BickelRosenblattUniformGofStatistic(a=0, b=1, bandwidth="auto")
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.

bandwidth - kernel bandwidth or auto. Default value is auto.

rvs - array-like sample data passed to execute_statistic.

Details¶

The implementation standardizes observations to \([0, 1]\), evaluates a Gaussian kernel density estimate on a fixed grid, and approximates

\[ \int_0^1 \left(\hat f(x) - 1\right)^2 dx. \]

Large values indicate stronger deviation from the uniform density.

Author(s)¶

Aleksandr Podmarev, Alexey Mironov

References¶

Bickel, P.J. and Rosenblatt, M. (1973): On some global measures of the deviations of density function estimates. - Annals of Statistics, vol. 1, pp. 1071-1095.

Examples¶

from pysatl_criterion.statistics.goodness_of_fit import (
    BickelRosenblattUniformGofStatistic,
)


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