Louati, Mahdi Mixture of the Riesz distribution with respect to the generalized multivariate gamma distribution. (English) Zbl 1294.62139 J. Korean Stat. Soc. 42, No. 1, 83-93 (2013). 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. Cited in 8 Documents 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 Keywords:Laplace transform; natural exponential family; variance function; Riesz distribution; generalized multivariate gamma distribution Citations:Zbl 0672.62061; Zbl 0984.60022 PDFBibTeX XMLCite \textit{M. Louati}, J. Korean Stat. Soc. 42, No. 1, 83--93 (2013; Zbl 1294.62139) Full Text: DOI