Parameter estimation for generalized extreme value and generalized pareto in extreme rainfall analysis

Abstract

Analyzing extreme rainfall events is important as the results found can be advantageous for civil engineers and town planners to estimate the strength of building under the most extreme conditions. The annual maximum series (AMS) data of daily rainfall in Malacca were fitted to two distributions, namely Generalized Extreme Value (GEV) and Generalized Pareto (GP) distribution, by using Method of Moments (MOM), Maximum Likelihood Estimator (MLE) and Bayesian Markov Chain Monte Carlo (MCMC) simulations. Previous studies have shown that the performance of the parameter estimations by using MOM was better than MLE. However, some researchers acknowledged that the parameter estimations of MLE can be additionally improved and developed by using Bayesian MCMC. To get posterior densities, non-informative and independent priors were used. The performance of the results were tested by several goodness of fit (GOF) tests. The results showed that GEV distribution is a better distribution than GP distribution in estimating the parameters of extreme daily rainfall amount in Malacca. MOM had maximum value return level for 10, 25, 50 and 100 years for most of stations followed by Bayesian MCMC. Conclusively, the results showed that Bayesian MCMC and MLE were equally better than MOM in estimating GEV and GP parameters.