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 (AMDR) in Mexico. We analyze 181 gauging stations across two contrasting climates (Coahuila, Tabasco) and compare BEG against Generalized Extreme Value (GEV), Gumbel (G), and Exponentiated Gumbel (EG). Parameters are estimated by maximum likelihood. Model selection uses AICc (primary) and BIC (tie-breaker), both computed from the same maximized log-likelihood. On a per-station basis, BEG yields the lowest AICc for 70% of samples. Differences in return levels become more pronounced at high non-exceedance probabilities. Monte Carlo reliability checks show that BEG reduces bias and mean squared error (MSE) relative to univariate fits. Using L-moments to delineate homogeneous regions and fitting all BEG pairs confirms these results. A worked example (station 5001) shows that bootstrap 95% CIs for BEG are narrower than for EG, illustrating reduced marginal-quantile uncertainty under joint estimation. Together, BEG provides a robust, dependence-aware tool for regional frequency analysis of extreme rainfall.