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ON SOME MULTIVARIATE GAMMA-DISTRIBUTIONS

CONNECTED WITH SPANNING TREES

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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 chi-square distribution, multivariate
Rayleigh distribution.

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