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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.

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The Generalized Extreme Value (GEV) distribution is often used to describe the frequency of occurrence of extreme rainfall. Modelling the extreme event using the independent Generalized Extreme Value to spatial data fails to account the behaviour of dependency data. However, the wrong statistical assumption by this marginal approach can be adjusted using sandwich estimator. In this paper, we used the conventional method of the marginal fitting of generalized extreme value distribution to the extreme rainfall then corrected the standard error to account for inter-site dependence. We also applied the penalized maximum likelihood to improve the generalized parameter estimations. A case study of annual maximum rainfall from several stations at western Sabah is studied, and the results suggest that the variances were found to be greater than the standard error in the marginal estimation as the inter-site dependence being considered. Key words: Generalized Extreme Value theory, sandwich estimator, penalized maximum likelihood, annual maximum rainfall