Mixed-Tail Quantile Functions for Extreme Value Analysis

Abstract This paper introduces a parametric mixed-tail quantile model which flexibly combines Gumbel, Fr\'echet, and Weibull tail behaviors through weighted quantile functions. Unlike classical extreme value models, our approach simultaneously captures multiple tail types, enhancing finite-sample adaptability and modeling accuracy. 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 modeling extreme quantiles.