%0 Journal Article
%T Riesz measures and Wishart laws associated to quadratic maps
%A Piotr Graczyk
%A Ishi Hideyuki
%J Statistics
%D 2011
%I arXiv
%X We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the Wishart laws. Moreover, if the quadratic map has an equivariance property under the action of a linear group acting on the cone $\Omega$ transitively, then the associated Riesz measure and Wishart law are described explicitly by making use of theory of relatively invariant distributions on homogeneous cones.
%U http://arxiv.org/abs/1107.0147v1