Parameter Estimation and Application of Spatial Extreme Value Modeling with Peaks over Threshold - Kumaraswamy Generalized Pareto (POT-KumGP) Method (Case Study: Extreme Rainfall in Maluku province)

Extreme weather events are one of the phenomena that cause unavoidable losses in various sectors and have a serious impact on aspects of life. These impacts can be minimized by studying the patterns and characteristics of extreme events. Extreme Value Theory (EVT) is one of the statistical techniques to detect extreme events. In order to detect extreme events in many locations (multivariate), this technique was then developed into spatial extreme value (SEV). This research applies the Peaks Over-Threshold method to excessive rainfall situations using an extreme value model based on the Kumaraswamy Generalized-Pareto Distribution. This model is performed by combining the generalized Pareto and Kumaraswamy distributions. In this study, the POT-KumGP model will be applied to monthly rainfall data from 1990–2023 in Maluku Province. Extreme values are determined based on threshold selection with visualization of the mean residual life plot. A distribution suitability test using Kolmogorov-Smirnov test statistics and a probability plot is performed to validate whether the model fits the Kum-GP distribution. If the model is suitable, parameter estimation will be carried out using maximum likelihood estimation (MLE) and continued with BFGS numerical iteration. Then a trend surface model will be formed to connect longitude and latitude variables with parameter estimates so as to further increase the robustness of the analysis. The best model is selected based on the smallest AIC value and used to calculated the return level for the next few periods. This research aims to build a POT-KumGP spatial extreme value model and get the return level estimation results for the next few periods in Maluku Province in order to inform future disaster management policies or strategies.