Anderson-Darling test for Student distribution

Description

Performs Anderson-Darling goodness-of-fit test for the hypothesis that the sample comes from a Student's t-distribution. The test gives additional weight to discrepancies in the distribution tails.

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 computed from the log cumulative distribution function and log survival function of the reference Student distribution.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    AndersonDarlingStudentGofStatistic,
)


test_statistic = AndersonDarlingStudentGofStatistic(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 the ordered observations and evaluates Student logcdf and logsf values. These values are passed to the common Anderson-Darling statistic implementation.

Author(s)

Dmitriy Rusanov, Alexey Mironov

References

Anderson, T.W. and Darling, D.A. (1952): Asymptotic theory of certain goodness of fit criteria based on stochastic processes. - Annals of Mathematical Statistics, vol. 23, pp. 193-212.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    AndersonDarlingStudentGofStatistic,
)


test_statistic = AndersonDarlingStudentGofStatistic(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)