Other forms have been proposed by Krishnamoorthy and Parthasarathy , Gaver , Prekopa and Szantai who also allowed for non-standard univariate gamma distributions as building blocks. In this paper we use a multivariate gamma distribution in the spirit of Mathai and Moschopoulos with known lower truncation points. The only method of estimation that has been proposed in con- nection with the multivariate gamma distribution is the method of moments, which, admittedly, is quite simple. Department of Economics, Athens University of Economics and Business, 76 Patission Street, 34 Athens, Greece Received January and accepted November The paper considers the multivariate gamma distribution for which the method of moments has been considered as the only method of estimation due to the complexity of the likelihood function. The paper takes up Bayesian analysis of the multivariate gamma distribution, and shows how the posterior distribution, although complicated by the presence of integrals with respect to latent variables, is amenable to integration by Monte Carlo methods, and especially the Gibbs sampling algorithm with data augmentation. The model and methods are described in Section 3.