Hypothesis tests of goodness-of-fit for Fréchet distribution

Extreme Value Theory (EVT) is a statistical field whose main focus is to investigate extreme phenomena. In EVT, Fréchet distribution is one of the extreme value distributions and it is used to model extreme events. The degree of fit between the model and the observed values was measured by Goodness-of-fit (GOF) test. Several types of GOF tests were also compared. The tests involved were Anderson-Darling (AD), Cramer-von Mises (CVM), Zhang Anderson Darling (ZAD), Zhang Cramer von-Mises (ZCVM) and Ln. The values of parameters μ, σ and ξ were estimated by Maximum Likelihood. The critical values were developed by Monte-Carlo simulation. In power study, the reliability of critical values was determined. Besides, it is of interest to identify which GOF test is superior to the other tests for Fréchet distribution. Thus, the comparisons of rejection rates were observed at different significance levels, as well as different sample sizes, based on several alternative distributions. Overall, given by Maximum Likelihood Estimation of Fréchet distribution, the ZAD and ZCVM tests are the most powerful tests for smaller sample size (ZAD for significance levels 0.05 and 0.1, ZCVM for significance level 0.01) as compared to AD, which is more powerful for larger sample size.

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