Products and ratios of generalized gamma variates

This article gives the exact distribution of Y=(X 1 X 2 ... X m /X m+1 ... X k ) where X 1 ..., X k are independently distributed as generalized Gamma variates. The case when (X 1, ..., X k ) is a simple random sample of size k from a generalized Gamma distribution, is discussed in detail and the other cases are mentioned briefly. The techniques of inverse Mellin transform and Calculus of residues are used in deriving the results. Different representations of the density of Y are also given and a particular case is verified.