Semi-parametric Estimation Based on Second Order Parameter for Selecting Optimal Threshold of Extreme Rainfall Events

Abstract

Analysis of extreme rainfall events can be performed using two main approaches; fitting Generalized Extreme Value distribution to the yearly peaks of events in the observation period or the annual maximum series, and fitting Generalized Pareto distribution to the peaks of events that exceed a given threshold or the partial duration series. Even though partial duration series are able to reduce sampling uncertainty and are useful for analyzing extreme values and tail asymmetries, the series require an optimal threshold. The objective of this study is to compare and determine the best method for selecting the optimal threshold of partial duration series using hourly, 12-hour and 24-hour data of rainfall time series in Peninsular Malaysia. Nine semi-parametric second order reduced-bias estimators are applied to estimate extreme value index and six estimators are used for the external estimation of the second order parameter. A semi-parametric bootstrap is used to estimate mean square error of the estimator at each threshold and the optimal threshold is then selected based on the smallest mean square error. Based on the plots of extreme value index and mean square error, several second order reduced-bias estimators behave reasonably well compared to Hill estimator, as indicated by their stable sample paths and flatter mean square errors.