Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events
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Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events Wendy Ling Shinyie · Noriszura Ismail · Abdul Aziz Jemain
Received: 27 June 2012 / Accepted: 20 January 2013 / Published online: 28 February 2013 © Springer Science+Business Media Dordrecht 2013
Abstract The two primary approaches of extreme events analysis are annual maximum series (AMS), which fits Generalized Extreme Value (GEV) distribution to the yearly peaks of events in the observation period, and partial duration series (PDS), which fits Generalized Pareto (GP) distribution to the peaks of events that exceed a given threshold. The PDS is able to reduce sampling uncertainty and is more useful in dealing with extreme values and asymmetries in the tails, but the optimal threshold is required. The objective of this study is to compare and determine the best method for selecting the optimal threshold of PDS using the hourly, 12-h and 24-h aggregated data of rainfall time series in Peninsular Malaysia. The choice of the threshold, or the number of largest order statistics, can be estimated by the parameters of extreme events. In this study, thirteen semi-parametric estimators are considered and applied to estimate the shape parameter or extreme value index (EVI). A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. Based on the smallest MSE, the majority of stations and data durations favor the Adapted Hill estimator, followed by the QQ, Hill and Moment Ratio 1 estimators. Therefore, this study proves that the application of different estimators on real data may result in different optimal values of threshold and the choice of the best method is very much data-dependent. Keywords Semi-parametric estimators · Threshold selection · Extreme rainfall events · Semi-parametric bootstrap
W. L. Shinyie (B) · N. Ismail · A. A. Jemain School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia e-mail: [email protected] N. Ismail e-mail: [email protected] A. A. Jemain e-mail: [email protected]
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1 Introduction Over the past several decades, changes in frequency and intensity of severe rainfall events have been consistently associated with changes in weather and climate (IPCC 2007). Understanding changes in extreme climate events is therefore crucial, especially in estimating their impacts on human livelihood, society, economic and environment. The importance of analysis of extreme rainfall events in the assessment of climate change have been emphasized in several hydrological studies (Lana et al. 2006; Kouchak and Nasrollahi 2010; Shinyie and Ismail 2012; Zakaria et al. 2012; Zhao et al. 2012). Extreme Value Theory (EVT) is a powerful and robust approach for capturing extreme movements in the tail behaviour of extreme rainfall distributions and has been widely applied in water resource management and environment sciences for
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