The multivariate Poisson-log normal distribution

The statistical analysis of multivariate counts has proved difficult because of the lack of a parametric class of distributions supporting a rich enough correlation structure. With increasing availability of powerful computing facilities an obvious candidate for consideration is now the multivariate log normal mixture of independent Poisson distributions, the multivariate Poisson-log normal distribution. The properties of this discrete multivariate distribution are studied and its uses in a variety of applications to multivariate count data are illustrated.