Kuiper test for Student distribution¶
Description¶
Performs Kuiper goodness-of-fit test for the hypothesis that the sample comes from a Student's t-distribution. The statistic combines the largest positive and negative empirical distribution deviations.
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.
Test Statistic The statistic is based on the sum of one-sided empirical distribution discrepancies after the Student probability integral transform.
Usage¶
from pysatl_criterion.statistics.goodness_of_fit import (
KuiperStudentGofStatistic,
)
test_statistic = KuiperStudentGofStatistic(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 computes
where \(D^+\) and \(D^-\) are one-sided deviations between empirical plotting positions and Student CDF values.
Author(s)¶
Dmitriy Rusanov, Alexey Mironov
References¶
Kuiper, N.H. (1960): Tests concerning random points on a circle. - Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, vol. 63, pp. 38-47.
Examples¶
from pysatl_criterion.statistics.goodness_of_fit import (
KuiperStudentGofStatistic,
)
test_statistic = KuiperStudentGofStatistic(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)