Riesz exponential families on homogeneous cones

Details Riesz exponential families on homogeneous cones Riesz exponential families on homogeneous cones

2009-06-10

arxiv.org/abs/0906.1892v1

Mathematics

Probability

Scientific paper

In this paper, we introduce, for a multiplier $\chi$, a notion of generalized power function $x\mapsto \Delta_{\chi}(x),$ defined on the homogeneous cone ${\mathcal{P}}$ of a Vinberg algebra ${\mathcal{A}}$. We then extend to ${\mathcal{A}}$ the famous Gindikin result, that is we determine the set of multipliers $\chi$ such that the map $\theta \mapsto \Delta_{\chi}(\theta ^{-1})$, defined on ${\mathcal{P}}^{\ast}$, is the Laplace transform of a positive measure $R_{\chi}$. We also determine the set of $\chi $ such that $R_{\chi}$ generates an exponential family, and we calculate the variance function of this family

Affiliated with

Also associated with

No associations

Rating

Riesz exponential families on homogeneous cones does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Riesz exponential families on homogeneous cones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riesz exponential families on homogeneous cones will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-206757