Chi-square test for Student distribution

Description

Performs chi-square goodness-of-fit test for the hypothesis that the sample comes from a Student's t-distribution. The implementation bins standardized observations using equiprobable Student quantile bins.

Hypothesis of Student Distribution The null hypothesis is that the data comes from a Student's t-distribution with positive degrees of freedom df, location parameter loc, and positive scale parameter scale.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    ChiSquareStudentGofStatistic,
)


test_statistic = ChiSquareStudentGofStatistic(df=5, loc=0, scale=1, n_bins=4)
statistic_result = test_statistic.execute_statistic([-1.8, -0.9, -0.25, 0.0, 0.31, 0.95, 1.7])
print(statistic_result)

Arguments

df - positive degrees of freedom of the Student's t-distribution. Default value is 1.

loc - location parameter of the Student's t-distribution. Default value is 0.

scale - positive scale parameter of the Student's t-distribution. Default value is 1.

n_bins - number of equiprobable Student quantile bins. Default value is 10.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation standardizes observations, builds bin edges from Student quantiles, and compares observed bin counts with equal expected counts.

Author(s)

Dmitriy Rusanov, 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 (
    ChiSquareStudentGofStatistic,
)


test_statistic = ChiSquareStudentGofStatistic(df=5, loc=0, scale=1, n_bins=4)
statistic_result = test_statistic.execute_statistic([-1.8, -0.9, -0.25, 0.0, 0.31, 0.95, 1.7])
print(statistic_result)