Anderson-Darling test for beta distribution¶

Description¶

Performs Anderson-Darling goodness-of-fit test for the hypothesis that the sample comes from a beta distribution. The test gives additional weight to discrepancies in the distribution tails.

Hypothesis of Beta Distribution The null hypothesis is that the data comes from a beta distribution with positive shape parameters alpha and beta on the interval \([0, 1]\).

Test Statistic The statistic is computed from the log cumulative distribution function and log survival function of the reference beta distribution.

Usage¶

from pysatl_criterion.statistics.goodness_of_fit import (
    AndersonDarlingBetaGofStatistic,
)


test_statistic = AndersonDarlingBetaGofStatistic(alpha=2, beta=5)
statistic_result = test_statistic.execute_statistic([0.08, 0.14, 0.22, 0.31, 0.38, 0.46, 0.57])
print(statistic_result)

Arguments¶

alpha - first positive shape parameter of the beta distribution. Default value is 1.

beta - second positive shape parameter of the beta distribution. Default value is 1.

rvs - array-like sample data passed to execute_statistic.

Details¶

For ordered observations \(X_{(i)}\), the implementation evaluates beta logcdf and logsf values and computes

\[ A_n^2 = -n - \sum_{i=1}^{n}\frac{2i - 1}{n}\left(\log F_0(X_{(i)}) + \log(1 - F_0(X_{(n+1-i)}))\right). \]

Large values indicate stronger deviation from the beta model.

Author(s)¶

Dmitry Deruzhinsky, Aleksei Tokarev, Vladimir Zakharov, 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 (
    AndersonDarlingBetaGofStatistic,
)


test_statistic = AndersonDarlingBetaGofStatistic(alpha=2, beta=5)
statistic_result = test_statistic.execute_statistic([0.08, 0.14, 0.22, 0.31, 0.38, 0.46, 0.57])
print(statistic_result)