A semi-parametric stochastic generator for bivariate extreme events

Abstract

The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate extreme events is convenient for end users who need a large number of random replications of extremes as input of a given complex system to test its sensitivity. The simulation of multivariate extremes is often based on the assumption that the dependence structure, the so-called extremal dependence function, is described by a specific parametric model. We propose a simulation method for sampling bivariate extremes, under the assumption that the extremal dependence function is semiparametric. This yields a flexible tool that can be broadly applied in real-data analyses. With the aim of estimating the probability of belonging to some extreme sets, our methodology is examined via simulation and illustrated by an analysis of strong wind gusts in France.