SCIENCES & TECHNOLOGY Hypothesis Tests of Goodness-of-Fit for Fréchet Distribution

N Abidin, M Adam, H Midi
2014 Pertanika J. Sci. & Technol   unpublished
either at maximum or minimum level (Coles, 2001). For instance, the likelihood of the flood during certain period of time is predicted by observing the volume of water at maximum level. Likewise, the study on the occurrence of draught was done by taking into account the minimum volume of rainfall (Castillo et al., 2005). These maximum and minimum values were collected and modelled based on the statistical extreme models. There are several statistical extreme models in EVT that are broadly used
more » ... or the extrapolation. The EVT comprises Gumbel, ABSTRACT 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 L n. 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.