Characterization of the Wishart distributions on homogeneous cones. (English. Abridged French version) Zbl 1065.62095
Summary: 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 K. Bobecka and J. Wesolowski [Studia Math. 152, 147–160 (2002; Zbl 0993.62043)]. 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.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 60E05 | Probability distributions: general theory |
Citations:
Zbl 0993.62043References:
| [1] | Andersson, S.; Wojnar, G., The Wishart distribution on homogeneous cones, J. Theoret. Probab., 17, 781-818 (2004) · Zbl 1058.62044 |
| [2] | Bobecka, K.; Wesołowski, J., The Lukacs-Olkin-Rubin theorem without invariance of the “quotient”, Studia Math., 152, 147-160 (2002) · Zbl 0993.62043 |
| [3] | Massam, H.; Neher, E., On transformations and determinants of Wishart variables on symmetric cones, J. Theoret. Probab., 10, 867-902 (1997) · Zbl 0890.60016 |
| [4] | Vinberg, E. B., The theory of convex homogeneous cones, Trans. Moscow Math. Soc., 12, 340-403 (1963) · Zbl 0138.43301 |
| [5] | Vinberg, E. B., The structure of the group of automorphisms of a homogeneous convex cone, Trans. Moscow Math. Soc., 13, 63-93 (1965) · Zbl 0311.17008 |
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