On some multivariate gamma-distributions connected with spanning trees

Abstract

Multivariate gamma distribution, multivariate chisquare distribution, multivariate Rayleigh distribution,

Multivariate Markovian gamma distributions for multitemporal sequences of SAR images

“…(6) is that when the shape parameter is an half integer, i.e., q = L/2, the Markovian MGD reduces to the distribution of the diagonal elements of A ∼ W(L, R 1/2 ) (i.e., the distribution of the diagonal elements of a Wishart distribution). Another interesting result is that the Markovian MGDs studied in this paper generalize the MGD models with tridiagonal inverse covariance matrix considered in [10][11][12].…”

Finite-Dimensional Distributions of a Square-Root Diffusion

“…Series solutions for the density and cumulative distribution functions of the Krishnamoorthy-Parthasarathy distribution were derived by Royen (1994) for a class of correlation matrices (see also Kotz et al (2000, Section 48.3.6)). This class includes any correlation matrix with tridiagonal inverse.…”

Multivariate Gamma Distributions—II

“…The joint distribution functions of the X j = Y j /2 from (25), (26), (27) are given by (14) with α = d/2, a 2 j = n j /(n j + n k ) for (25) and by a 2 j = −n j /(n − n j ) for (26), (27) (Royen [24]). For d k − 1 the joint density of the Y ij is (29) on the region S > 0, where w k−1 is a Wishart density with the (k − 1) × (k − 1) correlation matrix R = (r ij ), r ij = a i a j , i = j, a 2 j = n j /(n j + n k ) and…”

“…with the Bessel function J α , again an mvariate integral representation has been derived in Royen [27].…”