Zhang Za test for Student distribution

Description

Performs Zhang Za goodness-of-fit test for the hypothesis that the sample comes from a Student's t-distribution. The statistic uses weighted logarithms of Student CDF and survival values.

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 (
    ZhangZaStudentGofStatistic,
)


test_statistic = ZhangZaStudentGofStatistic(df=5, loc=0, scale=1)
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.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation standardizes observations, evaluates clipped Student CDF values, and computes Zhang's \(Z_A\) statistic from weighted log-CDF and log-survival terms.

Author(s)

Dmitriy Rusanov, Alexey Mironov

References

Zhang, J. (2002): Powerful goodness-of-fit tests based on the likelihood ratio. - Journal of the Royal Statistical Society, Series B, vol. 64, pp. 281-294.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    ZhangZaStudentGofStatistic,
)


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