Riesz Exponential Families on Symmetric Cones

A. Hassairi () and S. Lajmi
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A. Hassairi: Sfax University
S. Lajmi: Sfax University

Journal of Theoretical Probability, 2001, vol. 14, issue 4, 927-948

Abstract: Abstract Let E be a simple Euclidean Jordan algebra of rank r and let Ω be its symmetric cone. Given a Jordan frame on E, the generalized power Δ s (−θ −1) defined on −Ω is the Laplace transform of some positive measure R s on E if and only if s is in a given subset Ξ of R r . The aim of this paper is to study the natural exponential families (NEFs) F(R s ) associated to the measures R s . We give a condition on s so that R s generates a NEF, we calculate the variance function of F(R s ) and we show that a NEF F on E is invariant by the triangular group if and only if there exists s in Ξ such that either F=F(R s ) or F is the image of F(R s ) under the map x↦−x.

Keywords: Jordan algebra; symmetric cone; triangular group; exponential family; variance function (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/A:1012592618872

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