Dense classes of multivariate extreme value distributions

Anne-Laure Fougères (1) , Cécile Mercadier (2) , John P. Nolan (3)

1 PSPM - Probabilités, statistique, physique mathématique
2 ICJ - Institut Camille Jordan
3 Department of Mathematics and Statistics

In this paper, we explore tail dependence modelling in multivariate extreme value distributions. The measure of dependence chosen is the scale function, which allows combinations of distributions in a very flexible way. The correspondences between the scale function and the spectral measure or the stable tail dependence function are given. Combining scale functions by simple operations, three parametric classes of laws are (re)constructed and analyzed, and resulting nested and structured models are discussed. Finally, the denseness of each of these classes is shown.

Mots clés: models for multivariate extremes; multivariate extreme value distribution; extremal dependence; max-stable; dependence function; logistic distributions; models for multivariate extremes.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Anne-Laure Fougères, Cécile Mercadier, John P. Nolan. Dense classes of multivariate extreme value distributions. 2012. ⟨hal-00713516v1⟩