A Generic Multivariate Distribution for Counting Data
  Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete distribution. Based on blending the Binomial, Poisson and Negative-Binomial distributions, and using a normal multivariate copula, the required distribution is defined. This distribution tends to the Multivariate Normal for large counts and has an approximate pmf version that is quite simple to evaluate. 
Marcos Capistr\'an and J. Andr\'es Christen
stat.AP