Mixture Probability Distributions for Low-Flow Frequency Analysis in Mexico: Implications for Environmental Impact Assessment, Drought Management, and Regional Water Policy

Reliable estimation of low-flow statistics is essential for water quality regulation, ecological protection, and drought management. This study evaluates traditional univariate and two-component Mixture Probability Distributions for modeling 7-day annual minimum flows (7Q) using records from 293 gauging stations across Mexico’s 37 hydrological planning regions, each with at least 20 years of data. Candidate models include Lognormal-3, Gamma-3, Gumbel, Weibull-3, and mixtures (Gumbel–Gumbel, Gumbel–Weibull-3, Weibull-3–Gumbel, Weibull-3–Weibull-3). Parameters are estimated by maximum likelihood, goodness-of-fit is assessed with Kolmogorov–Smirnov and Anderson–Darling tests. Sampling uncertainty is quantified via nonparametric bootstrap, providing 95% confidence intervals for design return levels, including 7Q10. Mixture models are selected as the best fit at 253 of 293 stations (86.3%), with Weibull-3–Weibull-3 dominating (45.1% of all stations) followed by Gumbel–Weibull-3 and Weibull-3–Gumbel; univariate models account for only 13.7% of cases, mainly Lognormal-3, and Gumbel alone is never preferred. Gumbel-only and symmetric G–G mixtures yield negative low-flow return levels at some sites and are therefore considered physically implausible. In contrast, mixtures containing Weibull-3 components ensure non-negative support, provide superior fit to the lower tail, and generally produce narrower bootstrap confidence intervals than the best univariate alternatives, indicating more stable and defensible 7Q10 estimates and providing an additional criterion to distinguish between models with similar goodness-of-fit statistics. These findings have direct implications for Environmental Impact Assessment, effluent permitting, ecological flow setting, drought planning, and regional water policy. The results support integrating Weibull-based mixtures—especially Weibull-3–Weibull-3 and Gumbel–Weibull-3—into Mexico’s national framework for low-flow frequency analysis and regulatory design.