Modeling of Multiple Statistical Distributions for Extreme Rainfall Data Using Maximum Likelihood Estimation Methods and Bayesian Methods

The city of Pekanbaru has rapidly developed into a metropolitan hub, facing challenges such as floods and haze caused by extreme rainfall events. This study proposes a novel combination of Generalized Extreme Value (GEV), Generalized Logistic (GLO), and Generalized Pareto (GP) distributions, utilizing Bayesian Markov Chain Monte Carlo (MCMC) and Maximum Likelihood Estimation (MLE) methods, to model annual extreme rainfall data for the period 2010–2024. Rainfall data were sourced from NASA/POWER. Model performance was evaluated using Relative Root Mean Square Error (RRMSE), Relative Absolute Square Error (RASE), and Probability Plot Correlation Coefficient (PPCC). The Bayesian method yielded superior performance with RRMSE = 0.3166, RASE = 0.2682, and PPCC = 0.00485 for the GEV distribution, outperforming MLE. The novelty lies in applying this methodological combination to Pekanbaru's rainfall dataset for the first time, providing valuable insights for flood mitigation, drainage planning, and urban water resource management.