The Wishart distributions on homogeneous cones

  • Steen A. Andersson Indiana University
  • G. Gerard Wojnar Frostburg State University
Keywords: Wishart distributions, homogeneous cones, Vinberg algebras, exponential families, posets, matrices with zeroes, normal graphical models


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 relations to graphical models and Bayesian statistics are indicated.


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Author Biographies

Steen A. Andersson, Indiana University

Department of Mathematics

G. Gerard Wojnar, Frostburg State University

Department of Mathematics