  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.
