Generating multivariate extreme value distributions

We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail dependence and extremal coefficients. Based on the obtained results for these coefficients, we propose a method to built multivariate extreme value distributions with prescribed tail/extremal coefficients. We illustrate the results with examples of simulation of these distributions.