Parameter Estimation For Generalized Extreme Value Distribution In Rainfall Forecasting: A Case Study Of Bangkok

Abstract

This study aims to compare efficiency methods for the estimated parameter of Generalized Extreme Value Distribution (GEVD), which consists of location, scale, and shape parameters. The parameter estimation employs the maximum likelihood (ML), generalized maximum likelihood (GML), Bayesian, and L-moments methods. The data is generated through simulation data in Gumbel, Fréchet, and Weibull distributions verified by shape parameters. The performance of these methods is evaluated using the minimum mean squared error (MSE) and mean absolute percentage error (MAPE). The results indicate that the Bayesian, ML, and GML methods consistently achieve the lowest MSE values, such as 0.0120 for location, 0.0066 for scale, and 0.005 for shape parameters when the sample size is 100 of the Gumbel distribution. In the real data application using 29 years of Bangkok rainfall data (1994-2023), the GEVD model estimated return levels for 2 to 9 years, with MAPE values ranging from 32.57% to 56.92% across different stations. The findings suggest that ML and GML methods outperform others in simulated and real-world applications. The proposed approach provides accurate and reliable forecasts of extreme rainfall, which are crucial for Bangkok’s urban planning and flood risk management.