Simulation of correlated Poisson variables

Generating correlated Poisson random variables is fundamental in many applications in the management and engineering fields, and in many others where multivariate count data arise. Multivariate Poisson data are often approximately simulated by either independent univariate Poisson or multivariate Normal data, whose implementation is provided by the most common statistical software packages such as R. However, such simulated data are often not satisfactory. Alternatively, methods for simulating multivariate Poisson data can be used, but they are adversely affected by limitations ranging from computational complexity to restrictions on the correlation matrix, which dramatically reduce their practical applicability. In this work, we propose a new method that is highly accurate and computationally efficient and can be usefully employed even by non-expert users in generating correlated Poisson data (and, more generally, any discrete variable), with assigned marginal distributions and correlation matrix.