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Comptes Rendus Mathématique
Volume 341, n° 1
pages 43-48 (juillet 2005)
Doi : 10.1016/j.crma.2005.05.022
Received : 5 April 2005 ;  accepted : 24 May 2005
Characterization of the Wishart distributions on homogeneous cones
Caractérisation des lois de Wishart sur les cônes homogènes
 

Imen Boutouria
Laboratoire de probabilités et statistique, faculté des sciences de Sfax, B.P. 802, Sfax, Tunisia 

Abstract

The aim of this Note is to give an extension to the Wishart distribution on homogeneous cones of the characterization of the ordinary Wishart on symmetric matrices, as given by Bobecka and Wesołowski [Studia Math. 152 (2002) 147-160]. Our method of proof is parallel to theirs. We also define the beta distribution on homogeneous cones, which appears in the course of this characterization. To cite this article: I. Boutouria, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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Résumé

Le résultat principal de cette Note est la caractérisation de la loi de Wishart sur le cône homogène dʼune algèbre de Vinberg. Ce résultat est obtenu par une méthode parallèle à celle utilisé par Bobecka et Wesołowski [Studia Math. 152 (2002) 147-160] et représente une extention de leur résultat concernant les lois de Wishart ordinaires sur les matrices symétriques. Nous définissons aussi la loi bêta sur les cones homogènes qui apparait dans cette caracterisation. Pour citer cet article : I. Boutouria, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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