Proceedings of the IConSSE FSM SWCU (2015), pp. MA.42–47 ISBN: 978-602-1047-21-7 SWUP MA.42 Bivariate generalized pareto distribution to predict the return level of extreme rainfall data (Case: Applied in Ajung and Ledokombo Stations) Windy Lestari * , Sutikno, Purhadi Department of Statistics, Faculty Mathematics and Natural Sciences, ITS - Surabaya, 60111, Indonesia Abstract Extreme value theory (EVT) is a method developed to study extreme events. This method focuses on the behavior of the tail distribution to determine the probability of extreme values. EVT are becoming widely used in various fields of science, such as hydrology, climatology, insurance, and finance. There are two methods to identifying extreme value, Block Maxima (BM) and Peaks Over Threshold (POT). In the case of the univariate approach each methods are follow the Generalized Extreme Value distribution (GEV) and Generalized Pareto Distribution (GPD). Fawcett and Walshaw (2008) defines multivariate extreme as extreme events of a particular variable at several nearby locations (e.g. rainfall over a network of sites). One approach used is based on threshold excess models using bivariate threshold called the Bivariate Generalized Pareto Distribution (BGPD) methods. In this study it will be used BGPD methods with parameter estimation using Maximum Likelihood Estimation, which is then used to estimate the return level of rainfall data at two stations Ajung and Ledokombo in Jember. To get the return level precisely, in this study it will be compared by the Univariate GPD methods. The results showed that the return level of BGPD give more accurate results than Univariate GPD based on RMSE criteria. Keywords extreme rainfall data, extreme value theory, generalized pareto distribution, bivariate generalized pareto distribution, bivariate threshold 1. Introduction EVT is a method that has been widely applied to rainfall data. This method focuses on the behavior of the tail of distribution to determine the probability of extreme values, and predict the extreme events in a heavy tail data. The application of extreme value method has been done by Li et al. (2005) with a data modeling extreme rainfall in the Southwest Australia with GDP. Gilleland & Katz (2006) analyzed the extremes of weather and climate of temperature data in Port Jervis, Newyork and Septless, Quebec with GEV. Generally, there are two approaches to the study of extreme value distribution, i.e., BM and POT. In the case of the univariate approach each follows the GEV and GPD (Coles, 2001). Most research is limited to univariate case. Basically in Zona Musim (ZOM) there are several locations, where some locations have the same characteristic or patterns of rainfall. If so, the one location with another one will be related. When studying the extremes of the * Corresponding author. Tel.: +62 856 4914 1515; E-mail address: windylestari.01@gmail.com