A Note on the Existence of the Multivariate Gamma Distribution

Abstract

The p-variate gamma distribution in the sense of Krishnamoorthy and Parthasarathy exists for all positive integer degrees of freedom d and at least for all real values d > p-2, p > 1. For special structures of the "associated" covariance matrix it also exists for all positive d. In this paper a relation between central and non-central multivariate gamma distributions is shown, which implies the existence of the p-variate gamma distribution at least for all non-integer d greater than the integer part of (p-1)/2 without any additional assumptions for the associated covariance matrix.

5 pages

References in corpus (1)

• A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions

Cited by in corpus (2)

• Stein characterizations for linear combinations of gamma random variables
• Some improved Gaussian correlation inequalities for symmetrical n-rectangles extended to some multivariate gamma distributions and some further probability inequalities