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Discrimination test between the Halphen (A and B) and the gamma distributions

El Adlouni, S., Hammami, D., Bobée, B.
Stochastic environmental research and risk assessment 2015 v.29 no.1 pp. 13-26
computer software, decision support systems, hydrology, risk estimate
Hydrological frequency analysis is the most widely used method to estimate risk for extreme values. The most used statistical distributions to fit extreme value data in hydrology can be regrouped in three classes: class C of regularly varying distributions, class D of sub exponential and class E, Exponential depending on their tail behavior. The Halphen distributions (Halphen type A (HA), Halphen type B (HB)) are separated by the Gamma distribution; these three distributions belong to class D and can be displayed in the (δ₁, δ₂) moment-ratio diagram. In this study, a statistical test for discriminating between HA, HB and the Gamma distribution is developed. The methodology is based on: (1) the generation of N samples of different sizes n around the Gamma curve; (2) the determination of the confidence zones around the Gamma curve for each fixed couple (δ₁, δ₂) moment-ratios and finally; (3) the study of the power of the test developed and the calculation of the type 2 error β and the power of the test which is 1-β for a fixed significance level α. Results showed that the test is powerful especially for high coefficients of skewness. This test will be included in Decision Support System of the HYFRAN-PLUS software.