Journal article

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

Pavel Krupskii, Harry Joe, David Lee, Marc G Genton



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.

University of Melbourne Researchers


Awarded by Natural Sciences and Engineering Research Council of Canada

Funding Acknowledgements

This research was supported by the King Abdullah University of Science and Technology (KAUST), Discovery Grant No. 8698 from the Natural Sciences and Engineering Research Council of Canada, a Collaborative Research Team grant for the project Copula Dependence Modeling: Theory and Applications of the Canadian Statistical Sciences Institute (CANSSI), and a University of British Columbia four-year doctoral fellowship. We are grateful to the two referees, the Associate Editor, and the Editor-in-Chief for their comments.