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ST1 test for Weibull distribution

Description

Performs ST1 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 a smooth-test statistic based on skewness of transformed observations.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    ST1WeibullGofStatistic,
)


test_statistic = ST1WeibullGofStatistic(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.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation evaluates the ST1 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 (
    ST1WeibullGofStatistic,
)


test_statistic = ST1WeibullGofStatistic(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)