The Biased Transformation and its Application in Goodness-of-Fit Tests for the Beta and Gamma Distribution
Résumé
The biased transformation is introduced for continuous random variables. It is proved in the paper that the biased transformation works for the generalized Pareto, the generalized extreme value and the normal distribution. The biased transformation works for continuous distributions of the exponential family as an approximation; this is demonstrated with the aid of simulations. The new transformation can be used for the Anderson-Darling test for the gamma and beta distribution. The power of the new test procedure is validated by simulations. The practical relevance of the new test for the beta distribution is demonstrated in an analysis of meteorological data.
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