Extreme-value limit of the convolution of exponential and multivariate normal distributions: Link to the Hüsler-Reiß distribution

The multivariate Hüsler-Reiß copula is obtained as a direct extreme-value limit from the convolution of a multivariate normal random vector and an exponential random variable multiplied by a vector of constants. It is shown how the set of Hüsler-Reiß parameters can be mapped to the parameters of this convolution model. Assuming there are no singular components in the Hüsler-Reiß copula, the convolution model leads to exact and approximate simulation methods. An application of simulation is to check if the Hüsler-Reiß copula with different parsimonious dependence structures provides adequate fit to some data consisting of multivariate extremes.