The cramer-von mises test statistic of the generalized extreme value distribution and weibull distribution

Abstract

Goodness of fit (GOF) test is a statistical technique in selection of an appropriate probability distribution for a given sample data. This study use a goodness of fit test, which is the Cramer Von Mises (CVM) test, in order to analyze the GEV distribution and Weibull distribution that best fit to model the annual rainfall data in Peninsular Malaysia. There are two objectives covered in this study, which are to develop the calculation critical values of CVM test statistic for GEV distribution and Weibull distribution by using simulation experiment, and to compare the accuracy of CVM test between both distributions in real data. The result of goodness of fit test using the CVM test statistic shows that the Weibull distribution has the greater rejection power at three different significance levels compare to the GEV distribution. It can be conclude that, the result of goodness of fit test using CVM test for this rainfall data in Peninsular Malaysia is most appropriate by using the Weibull distribution to fit the model of this rainfall data.