  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.
