Assessment of modified Anderson–Darling test statistics for the generalized extreme value and generalized logistic distributions

Abstract

An important problem in frequency analysis is the selection of an appropriate probability distribution for a given sample data. This selection is generally based on goodness-of-fit tests. The goodness-of-fit method is an effective means of examining how well a sample data agrees with an assumed probability distribution as its population. However, the goodness of fit test based on empirical distribution functions gives equal weight to differences between empirical and theoretical distribution functions corresponding to all observations. To overcome this drawback, the modified Anderson–Darling test was suggested by Ahmad et al. (1988b). In this study, the critical values of the modified Anderson–Darling test statistics are revised using simulation experiments with extensions of the shape parameters for the GEV and GLO distributions, and a power study is performed to test the performance of the modified Anderson–Darling test. The results of the power study show that the modified Anderson–Darling test is more powerful than traditional tests such as the χ2, Kolmogorov–Smirnov, and Cramer von Mises tests. In addition, to compare the results of these goodness-of-fit tests, the modified Anderson–Darling test is applied to the annual maximum rainfall data in Korea.