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Wishart distributions on homogeneous cones. (English) Zbl 1058.62044
Summary: The classical family of Wishart distributions on a cone of positive definite matrices and its fundamental features are extended to a family of generalized Wishart distributions on a homogeneous cone using the theory of exponential families. The generalized Wishart distributions include all known families of Wishart distributions as special cases. The relationships to graphical models and Bayesian statistics are indicated.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62F15 Bayesian inference
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