Classification of Riesz Exponential Families on a Symmetric Cone by Invariance Properties

A. Hassairi () and S. Lajmi
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A. Hassairi: Faculté des Sciences de Sfax
S. Lajmi: Faculté des Sciences de Sfax

Journal of Theoretical Probability, 2004, vol. 17, issue 3, 521-539

Abstract: Abstract Letac(5) has characterized the Wishart natural exponential families (NEFs) on the symmetric cone Ω of a Jordan algebra E by invariance under a group G of automorphisms of E preserving Ω. Hassairi and Lajmi(4) have introduced the so called Riesz NEF's as an extension of the Wishart NEF's and they have characterized them by invariance under the triangular group T. Pursuing these classifications, we construct a class of subgroups of G containing the triangular group T and we use them to classify the Riesz NEFs on Ω and therefore to characterize each class by an invariance property.

Keywords: Symmetric cone; generalized power; exponential family; variance function (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTP.0000040287.87081.ba

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