MPS-RR 2000-27
July 2000

Multivariate Type $\mathcal{G}$ Distributions

Ole E. Barndorff-Nielsen

Victor Pérez-Abreu

Abstract

The class of multivariate distributions all of whose one-dimensional projections are of type $G$ is discussed and examples of such distributions presented. In the course of this, we introduce a new representation of the cumulant function of the symmetric multivariate stable laws as well as multivariate extensions of the Inverse Gaussian and the symmetric Normal Inverse Gaussian laws. A concept of weak infinite divisibility of random matrices is introduced and this leads to further examples.

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