WISHART LAWS AND VARIANCE FUNCTION ON HOMOGENEOUS
Abstract: We present a systematic study of Riesz measures and their natural exponential families
of Wishart laws on a homogeneous cone. We compute explicitly the inverse of the mean map
and the variance function of a Wishart exponential family.
2000 AMS Mathematics Subject Classification: Primary: 15B48; Secondary:
Keywords and phrases: Natural exponential families, variance function, Wishart laws,
Riesz measure, homogeneous cones, graphical cones.