Parameter estimations of the generalized extreme value distributions for small sample size

Abstract

The standard method of the maximum likelihood has poor performance in GEV parameter estimates for small sample data. This study aims to explore the Generalized Extreme Value (GEV) parameter estimation using several methods focusing on small sample size of an extreme event. We conducted simulation study to illustrate the performance of different methods such as the Maximum Likelihood (MLE), probability weighted moment (PWM) and the penalized likelihood method (PMLE) in estimating the GEV parameters. Based on the simulation results, we then applied the superior method in modelling the annual maximum stream flow in Sabah. The result of the simulation study shows that the PMLE gives better estimate compared to MLE and PMW as it has small bias and root mean square errors, RMSE. For an application, we can then compute the estimate of return level of river flow in Sabah.