(Received August 31, 1992; revised September 9, 1993)
Abstract. Any correlation matrix R can be mapped to a graph with edges corresponding to the non-vanishing correlations. In particular R is said to be of a ``tree type'' if the corresponding graph is a spanning tree. The tridiagonal correlation matrices belong to this class. If the accompanying correlation matrix R or its inverse is of a tree type, then some representations of the multivariate gamma distribution are obtained with a much simpler structure than the integral or series representations for the general case.
Key words and phrases: Multivariate gamma distribution, multivariate chi-square distribution, multivariate Rayleigh distribution.