New characterizations of multivariate Max-domain of attraction and D-Norms

Abstract

In this paper we derive new results on multivariate extremes and D-norms. In particular we establish new characterizations of the multivariate max-domain of attraction property. The limit distribution of certain multivariate exceedances above high thresholds is derived, and the distribution of that generator of a D-norm on ${\mathbb R}^{d}$ ℝ d , whose components sum up to d, is obtained. Finally we introduce exchangeable D-norms and show that the set of exchangeable D-norms is a simplex.

Exceedance Counts and GOD’s Order Statistics

“…. , d. The following result is, therefore, an immediate consequence of Theorem 3.5 in Falk and Fuller (2021).…”

“…Recent results on D-norms (Falk (2019), Falk and Fuller (2021)) enable in the present paper the representation of the distribution of N x in terms of order statistics corresponding to the generator of a D-norm, introduced below.…”