Pearson chi-squared test for uniformity

Description

Performs Pearson's chi-squared goodness-of-fit test for the hypothesis of uniformity on the interval \([a, b]\). The implementation bins the sample and compares observed bin counts with equal expected counts.

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 (
    Chi2PearsonUniformGofStatistic,
)


test_statistic = Chi2PearsonUniformGofStatistic(a=0, b=1, bins="sturges")
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.

lambda_ - power-divergence parameter passed to the common chi-squared statistic implementation. Default value is 1.

bins - number of bins or bin-selection rule. Supported string values include sturges, sqrt, and auto.

rvs - array-like sample data passed to execute_statistic.

Details

The sample is divided into bins over \([a, b]\). For \(m\) bins and sample size \(n\), each bin has expected count \(n / m\) under the uniform null hypothesis. The observed and expected counts are passed to the common chi-squared statistic implementation.

Author(s)

Aleksandr Podmarev, Alexey Mironov

References

Pearson, K. (1900): On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. - Philosophical Magazine, vol. 50, pp. 157-175.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    Chi2PearsonUniformGofStatistic,
)


test_statistic = Chi2PearsonUniformGofStatistic(a=0, b=1, bins="sturges")
statistic_result = test_statistic.execute_statistic([0.12, 0.25, 0.41, 0.53, 0.77, 0.91])
print(statistic_result)