Comparative Methods for Estimating Parameters of the Generalized Pareto Distribution with Application to Extreme Rainfall in Bangkok

This study aims to compare the performance of various parameter estimation methods for the Generalized Pareto Distribution (GPD) in modeling and forecasting the return level of yearly maximum rainfall in Bangkok, Thailand. Four estimation methods, namely Maximum Likelihood (ML), Generalized Maximum Likelihood (GML), Bayesian, and L-Moments, were investigated through both simulation experiments and real data analyses. In the simulation study, data were generated with fixed location and scale parameters, varying shape parameters, and threshold percentiles. The results indicated that the ML method performed best for short-tailed distributions, the GML method for medium-tailed distributions, and the L-Moments method for heavy-tailed distributions. Using 360 monthly observations (January 1994–December 2023) from four rainfall stations, including QSNCC, Don Mueang, Bang Na, and Klong Toey, the GPD model was fitted to the real data. The results revealed that the L-Moments method achieved the lowest Root Mean Square Error (RMSE) across all stations, confirming its superior performance in estimating extreme rainfall. The return level analysis for return periods of 2-9 years showed an increasing trend in extreme rainfall at all stations. Overall, the study concludes that the L-Moments-based GPD model is the most effective method for fitting extreme rain in Bangkok.