Summary
Shanbhag’s clever method for finding the Jorgensen set of the family of Wishart distributions on symmetric matrices is extended here to Wishart distributions on symmetric cones, such as Hermitian matrices on complex numbers or quaternions. The idea is also extended to various other multivariate distributions, including the natural exponential family associated with the set of normal distributions onR with unknown mean and variance.
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Casalis, M., Letac, G. Characterization of the Jorgensen set in generalized linear models. Test 3, 145–162 (1994). https://doi.org/10.1007/BF02562678
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DOI: https://doi.org/10.1007/BF02562678