Approximation of modified Anderson-Darling test statistics for extreme value distributions with unknown shape parameter

Jun Haeng Heo, Hongjoon Shin, Woosung Nam, Juseong Om, Changsam Jeong

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44 Citations (Scopus)


Studies of the goodness-of-fit test, which describes how well a model fits a set of observations with an assumed distribution, have long been the subject of statistical research. The selection of an appropriate probability distribution is generally based on goodness-of-fit tests. This test is an effective means of examining how well a sample data set agrees with an assumed probability distribution that represents its population. However, the empirical distribution function test gives equal weight to the differences between the empirical and theoretical distribution functions corresponding to all observations. The modified Anderson-Darling test, suggested by Ahmad et al. (1988), uses a weight function that emphasizes the tail deviations at the upper or lower tails. In this study, we derive new regression equation forms of the critical values for the modified Anderson-Darling test statistics considering the effect of unknown shape parameters. The regression equations are derived using simulation experiments for extreme value distributions such as the log-Gumbel, generalized Pareto, GEV, and generalized logistic models. In addition, power test and at-site frequency analyses are performed to evaluate the performance and to explain the applicability of the modified Anderson-Darling test.

Original languageEnglish
Pages (from-to)41-49
Number of pages9
JournalJournal of Hydrology
Publication statusPublished - 2013 Aug 30

Bibliographical note

Funding Information:
The authors thank to the comments and suggestions of the anonymous referee which improved this article. This study was financially supported by the Construction Technology Innovation Program (08-Tech-Inovation-F01) through the Research Center of Flood Defense Technology for Next Generation in Korea Institute of Construction & Transportation Technology Evaluation and Planning (KICTEP) of Ministry of Land, Transport and Maritime Affairs (MLTM).

All Science Journal Classification (ASJC) codes

  • Water Science and Technology


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