Generalized Pareto copulas: A key to multivariate extremes.

This paper reviews generalized Pareto copulas (GPC), which are a key to multivariate extreme value theory. Any generalized Pareto copula can be represented in an easy analytical way using a particular type of norm on R d , called D -norm. The characteristic property of a generalized Pareto copula is its exceedance stability. They might help to end the following debate: What is a multivariate generalized Pareto distribution? We present an easy way to simulate data from an arbitrary generalized Pareto copula and, thus, form an arbitrary generalized Pareto distribution. As an application we derive nonparametric estimates of the probability that a random vector, which follows a generalized Pareto copula, exceeds a high threshold, together with confidence intervals. A case study on joint exceedance probabilities for air pollutants completes the paper. [ABSTRACT FROM AUTHOR]