Application of the Bivariate Exponentiated Gumbel Distribution for Extreme Rainfall Frequency Analysis in Contrasting Climates of Mexico

This study proposes a bivariate distribution with Exponentiated Gumbel (BEG) marginals to estimate return levels of annual maximum daily rainfall in Mexico. A dataset of 181 gauging stations from two contrasting climatic regions was analyzed, and the BEG model was compared against the Generalized Extreme Value (GEV), Gumbel (EVI), and Exponentiated Gumbel (EG) distributions. Parameters were estimated using the maximum likelihood method. Goodness-of-fit assessment based on AICc and BIC indicated that 71.8% of the samples were better described by the BEG model than by the univariate alternatives. Moreover, differences in return level estimates became more pronounced at higher non-exceedance probabilities. These results suggest that the BEG distribution provides a robust and reliable tool for the frequency analysis of extreme rainfall.