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http://dx.doi.org/10.3741/JKWRA.2010.43.9.813

Derivation of Modified Anderson-Darling Test Statistics and Power Test for the Gumbel Distribution  

Shin, Hong-Joon (School of Civil and Environmental Engineering, Yonsei Univ.)
Sung, Kyung-Min (School of Civil and Environmental Engineering, Yonsei Univ.)
Heo, Jun-Haeng (School of Civil and Environmental Engineering, Yonsei Univ.)
Publication Information
Journal of Korea Water Resources Association / v.43, no.9, 2010 , pp. 813-822 More about this Journal
Abstract
An important problem in frequency analysis is the estimation of the quantile for a certain return period. In frequency analysis an assumed probability distribution is fitted to the observed sample data to estimate the quantile at the upper tail corresponding to return periods which are usually much larger than the record length. In most cases, the selection of an appropriate probability distribution is based on goodness of fit tests. The goodness of fit test method can be described as a method for examining how well sample data agrees with an assumed probability distribution as its population. However it gives generally equal weight to differences between empirical and theoretical distribution functions corresponding to all the observations. In this study, the modified Anderson-Darling (AD) test statistics are provided using simulation and the power study are performed to compare the efficiency of other goodness of fit tests. The power test results indicate that the modified AD test has better rejection performances than the traditional tests. In addition, the applications to real world data are discussed and shows that the modified AD test may be a powerful test for selecting an appropriate distribution for frequency analysis when extreme cases are considered.
Keywords
goodness-of-fit test; modified Anderson-Darling test; power test;
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