A new operational max-stable copula for asymmetric spatial dependence in extreme value analysis

Abstract

Modeling the spatial dependence of extremes presents a dual challenge: guaranteeing max-stability while capturing the asymmetries observed in the field. We introduce a simplified version of an asymmetric Schlather copula, obtained by a clever reparametrization. This formulation offers both an explicit density, facilitating estimation by maximum likelihood and three interpretable parameters controlling the range, intensity and asymmetry of the dependence. Applied to a real dataset of extreme temperatures, our model outperforms several classical copulas (including Hüsler-Reiss and Schlather) in terms of fit. We also detail the analytical properties of the model (tail distribution, max-stability, density), demonstrating its flexibility and practical relevance for the analysis of extreme climate risks.