ON SOME MULTIVARIATE GAMMA-DISTRIBUTIONS CONNECTED WITH SPANNING TREES

T. ROYEN

Fachhochschule Rheinland-Pfalz, Abteilung Bingen, Rochusallee 4, D-55411 Bingen, Germany

(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 chisquare distribution, multivariate Rayleigh distribution.