Doornik-Hansen test for log-normal distribution

Description

Performs Doornik-Hansen goodness-of-fit test for the hypothesis that the sample comes from a log-normal distribution. The implementation uses positive observations and either evaluates the log-normal model directly or applies a normality statistic to standardized logarithms.

Hypothesis of Log-Normal Distribution The null hypothesis is that the data comes from a log-normal distribution with positive shape parameter s and positive scale parameter scale. Observations passed to execute_statistic should be positive; tests that receive non-positive observations may return inf.

Test Statistic The statistic is based on the wrapped Doornik-Hansen normality statistic applied to standardized log observations.

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    DoornikHansenLogNormalGofStatistic,
)


test_statistic = DoornikHansenLogNormalGofStatistic(s=1, scale=1)
statistic_result = test_statistic.execute_statistic([0.42, 0.58, 0.76, 0.93, 1.12, 1.35, 1.61, 1.92, 2.28, 2.71, 3.23, 3.84])
print(statistic_result)

Arguments

s - positive shape parameter of the log-normal distribution. Default value is 1.

scale - positive scale parameter of the log-normal distribution. Default value is 1.

rvs - array-like sample data passed to execute_statistic.

Details

For dynamically generated log-normal tests, the implementation transforms observations with

\[ Z_i = \frac{\log X_i - \log(scale)}{s} \]

and applies the corresponding normality statistic to the standardized values. Explicit EDF and KL-based implementations use the formulas in pysatl_criterion.statistics.goodness_of_fit.log_normal.

Author(s)

Anton Dorosev, Alexey Mironov

References

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

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    DoornikHansenLogNormalGofStatistic,
)


test_statistic = DoornikHansenLogNormalGofStatistic(s=1, scale=1)
statistic_result = test_statistic.execute_statistic([0.42, 0.58, 0.76, 0.93, 1.12, 1.35, 1.61, 1.92, 2.28, 2.71, 3.23, 3.84])
print(statistic_result)