We introduce two models for multivariate maxima and threshold exceedances. The asymptotic distribution function of multivariate normalized maxima is obtained by representing multivariate extreme value distributions in terms of univariate generalized extreme value distributions and extreme value copulas. We give criteria for sequences of independent and identically distributed random variables to be in the maximum domain of attraction of a multivariate extreme value distribution. Using Pickands' representation theorem, we calculate the dependence functions for the bivariate Gumbel and Galambos extreme value copulas. The coeffcient of upper-tail dependence is calculated for the bivariate Gumbel and Galambos extreme value copulas. To arrive at a model for multivariate threshold exceedances, we approximate the margins by generalized Pareto distributions and the dependence structure by an extreme value copula. In a special case, we obtain lower and upper threshold copulas by conditioning on lower and upper tail events, respectively. Upper threshold copulas can be used as dependence structure of multivariate excess distributions. Applications in R point out the models' capability, but also theoretical and practical limitations.     «

We introduce two models for multivariate maxima and threshold exceedances. The asymptotic distribution function of multivariate normalized maxima is obtained by representing multivariate extreme value distributions in terms of univariate generalized extreme value distributions and extreme value copulas. We give criteria for sequences of independent and identically distributed random variables to be in the maximum domain of attraction of a multivariate extreme value distribution. Using Pickands'...     »