A Simple Scheme for Generating Multivariate Gamma Distributions with Non-Negative Covariance Matrix

Abstract

To generate the gamma distributed random vector ? (of dimension K) the scheme η = ξ(1) + Tξ(2) is considered where ξ(1) (of dimension K) and ξ(2) (of dimension N) consist of independently gamma distributed variables and T is a (K × N) incidence matrix. For certain “patterns” of T the implied restrictions on the parameter space of the desired multivariate gamma distribution are discussed; in particular the scheme does not allow negative covariances.