Natural exponential families invariant by a subgroup of the general affine group and a characterization of the Riesz measure on homogeneous cones

Hideyuki Ishi, Bartosz Kołodziejek

Published 2016-05-12Version 1

In the paper we present a systematic study of natural exponential families invariant by a subgroup of general affine group of finite dimensional linear space. We give a characterization theorem of a generating measure of such family. As an application of our main theorem, we prove a characterization of the Riesz measure on homogeneous cones through the invariance property of natural exponential family under the action of the triangular group.