Development of a Mixed Method for Estimation of Generalized Extreme Value Distribution with Application in Hydrology

Abstract

The Generalized Extreme Value (GEV) distribution is widely used for modelling extreme environmental events such as rainfall, floods, and wind speeds. This study proposes a Mixed Estimation Method (MEM) that combines Trimmed LMoments (1,1) and Maximum Likelihood Estimation for improved parameter estimation of the GEV distribution. The performance of the proposed method was evaluated using Monte Carlo simulation for different sample sizes and compared with MLE, L-Moments, and TL-Moments (1,1) using Mean Squared Error (MSE) as the criterion. Results showed that the MEM consistently produced more accurate parameter estimates with lower MSE values. The method was also applied to annual maximum rainfall data from Ogun State, Nigeria, where it outperformed the other estimation methods. Return level analysis indicated increasing rainfall magnitudes with higher return periods, suggesting potential future extreme rainfall events. The study concludes that the proposed MEM is a robust and efficient approach for GEV parameter estimation in extreme value and hydrological studies.