The Goodness-of-fit Test for Gumbel Distribution: A Comparative Study

Abstract

Several types of Goodness-of-fit tests for Gumbel are compared. These are Anderson-Darling, Modified Anderson-Darling $(B^2),$ Cramer-von Mises, Zhang Anderson-Darling, Zhang Cramer von-Mises and Liao-Shimokawa $(L_n).$ The parameters values of Gumbel are estimated by Maximum Likelihood Estimation. The critical values are modeled by two methods. For the first method, the critical values are obtained from the average of $\sigma.$ The second method is based on polynomial relationship. In power study, several alternative distributions are selected to determine the rejection rates. The result shows that, Anderson-Darling test is the most powerful. Critical values by polynomial are more reliable for small sample size. Keywords: Gumbel distribution; Goodness-of-fit; Critical values; Power. 2010 Mathematics Subject Classification: 62N03