Mixed-tail quantile functions for extreme value analysis

This article introduces a parametric mixed-tail quantile model which flexibly combines Gumbel, Fréchet and Weibull tail behaviours through weighted quantile functions. Unlike classical extreme value models, our approach simultaneously captures multiple tail types, enhancing finite-sample adaptability and modelling accuracy. The extension of the approach for the context of regression for extremes is here termed mixed-tail quantile regression. Parameters are estimated using a computationally efficient least squares approach based on the expected order statistics. We establish asymptotic properties and address inference challenges via bootstrap methods. Theoretical results, including tail dominance and adaptive bias–variance decomposition, guide practical quantile estimation. Simulations and an application on global ice extents demonstrate improved performance in modelling extreme quantiles.