Modelling multivariate extreme value distributions. (English) Zbl 0716.62051

Tawn, Jonathan A.

Biometrika 77, No. 2, 245-253 (1990).

Summary: Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for the dependence between the margins. This paper extends to more than two variables the models and results for the bivariate case obtained by the author [ibid. 75, No.3, 397-415 (1988; Zbl 0653.62045)]. Two new families of physically motivated parametric models for the dependence structure are presented and are illustrated with an application to trivariate extreme sea level data.

MSC:

62H05	Characterization and structure theory for multivariate probability distributions; copulas
62H10	Multivariate distribution of statistics

Keywords:

generalized Pareto distribution; multivariate exponential distribution; nonregular estimation; Multivariate extreme value distributions; limiting joint distribution of normalized componentwise maxima/minima; dependence structure; trivariate extreme sea level data