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