Lilliefors test for Student distribution

Description

Performs Lilliefors-type goodness-of-fit test for the hypothesis that the sample comes from a Student's t-distribution. The implementation reuses the common Lilliefors statistic calculation with Student CDF 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.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    LillieforsStudentGofStatistic,
)


test_statistic = LillieforsStudentGofStatistic(df=5)
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.

rvs - array-like sample data passed to execute_statistic.

Details

The sorted sample is transformed with the Student cumulative distribution function using df degrees of freedom. The transformed values are passed to the common Lilliefors statistic implementation.

Author(s)

Dmitriy Rusanov, Alexey Mironov

References

Lilliefors, H.W. (1967): On the Kolmogorov-Smirnov test for normality with mean and variance unknown. - Journal of the American Statistical Association, vol. 62, pp. 399-402.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    LillieforsStudentGofStatistic,
)


test_statistic = LillieforsStudentGofStatistic(df=5)
statistic_result = test_statistic.execute_statistic([-1.8, -0.9, -0.25, 0.0, 0.31, 0.95, 1.7])
print(statistic_result)