Kolmogorov-Smirnov test for Weibull distribution

Description

Performs Kolmogorov-Smirnov goodness-of-fit test for the hypothesis that the sample comes from a Weibull distribution. The implementation uses the Weibull distribution utilities from pysatl_criterion.core.distributions.weibull where applicable.

Hypothesis of Weibull Distribution The null hypothesis is that the data comes from a Weibull distribution with parameters a and k. The observations passed to execute_statistic should be positive for statistics that use logarithms or Weibull probability plots.

Test Statistic The statistic is based on the maximum distance between the empirical distribution function and Weibull CDF values.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovWeibullGofStatistic,
)


test_statistic = KolmogorovSmirnovWeibullGofStatistic(a=1, k=2)
statistic_result = test_statistic.execute_statistic([0.42, 0.65, 0.88, 1.12, 1.43, 1.76, 2.05, 2.44, 2.91, 3.37])
print(statistic_result)

Arguments

a - Weibull distribution parameter. Default value is 1.

k - Weibull distribution parameter. Default value is 1 for most statistics; KolmogorovSmirnovWeibullGofStatistic defaults to 5.

alternative_type - alternative hypothesis type used by the Kolmogorov-Smirnov statistic.

mode - calculation mode passed to the Kolmogorov-Smirnov statistic. Default value is auto.

rvs- array-like sample data passed toexecute_statistic`.

Details

The implementation evaluates the Kolmogorov-Smirnov statistic for the supplied observations. For EDF-based statistics, observations are transformed with the Weibull cumulative distribution function. For spacing, probability plot, Laplace-transform, and moment-style statistics, the implementation follows the corresponding formulas in pysatl_criterion.statistics.goodness_of_fit.weibull.

Author(s)

Alexey Mironov

References

The statistic follows the implementation in pysatl_criterion.statistics.goodness_of_fit.weibull.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    KolmogorovSmirnovWeibullGofStatistic,
)


test_statistic = KolmogorovSmirnovWeibullGofStatistic(a=1, k=2)
statistic_result = test_statistic.execute_statistic([0.42, 0.65, 0.88, 1.12, 1.43, 1.76, 2.05, 2.44, 2.91, 3.37])
print(statistic_result)