Abstract
The beta distribution is used in different models of environmental research. The power of the test for beta distribution of Raschke [Biased transformation and its application in goodness-of-fit tests for the beta and gamma distribution. Commun. Statist. B–Computa. Simula. 38 (2009): 1870–1890] is researched here. The power of the Kolmogorov–Smirnov, Kuiper, Cramer-von Mises, Watson and Anderson–Darling tests are researched for different sample sizes, levels of significance and parameters of the beta distribution. The limitation to these tests is discussed including the differences between previous publications. The empirical behaviour is investigated by extensive Monte Carlo simulations. The most powerful test for the beta distribution is the Anderson–Darling test for the considered constellations of alternative distribution, contamination or scaling. The second best test is the Cramer-von Mises test, followed by the Watson test. The analysis of relative humidity data of meteorology and of runoff coefficients of the hydrology demonstrates the advantages of the new tests and the necessity to test an assumption of beta distribution.
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