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Mathai, A. M.; Pederzoli, Giorgio

Hypergeometric functions of many matrix variables and distributions of generalized quadratic forms. (English) Zbl 0855.62037

Am. J. Math. Manage. Sci. 15, No. 3-4, 343-354 (1995).
Linear functions of matrix-variate gamma random variables, in the real case, and their distributions are discussed. Properties of Lauricella functions of matrix arguments are used in deriving different representations of the moment generating functions thereby evaluating the density without going through standard methods. Distributions of determinants and generalized quadratic forms are also considered. The results are given in terms of special functions of several matrix arguments as well as in \(G\)-functions of scalar variables.
Reviewer: A.M.Mathai

Cited in 1 Review

MSC:

62H10 Multivariate distribution of statistics
33C65 Appell, Horn and Lauricella functions
33C70 Other hypergeometric functions and integrals in several variables
15A63 Quadratic and bilinear forms, inner products
62H05 Characterization and structure theory for multivariate probability distributions; copulas

Keywords:

linear functions of matrix-variate gamma random variables; \(G\)-functions of scalar variables; Lauricella functions of matrix arguments; moment generating functions; determinants; generalized quadratic forms; special functions of several matrix arguments
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References:

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