A penalized likelihood approach to model the annual maximum flow with small sample sizes

Abstract

The aim of this study is to model the annual maximum flow of several sites in Sabah with small sample sizes using the generalized extreme value (GEV) distribution. Previous studies have shown that the standard method of maximum likelihood estimates would give a poor estimation of the GEV parameters and quantiles for small data set. This study will consider the penalized likelihood estimates as an alternative method to improve the inference over the standard method and retains the modeling flexibility. As comparisons, we will illustrate the results of both methods to model the annual maximum flow in Sabah. The results show the implementation of the penalty function had the same effect to the GEV parameter estimates as suggested by previous studies.