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Mixture of the Riesz distribution with respect to the generalized multivariate gamma distribution. (English) Zbl 1294.62139

Summary: Wishart natural exponential families (NEFs) characterized by G. Letac [J. Theor. Probab. 2, No. 1, 71–86 (1989; Zbl 0672.62061)] are extended to the Riesz NEFs on symmetric matrices. These families are characterized by their variance functions defined in [A. Hassairi and S. Lajmi, J. Theor. Probab. 14, No. 4, 927–948 (2001; Zbl 0984.60022)]. This work uses a particular basis of these NEFs to describe the class of the generalized multivariate gamma distributions and then to study the statistical model obtained by the mixture of this distribution with the Riesz one on the space of symmetric matrices.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
60B20 Random matrices (probabilistic aspects)
44A10 Laplace transform
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