Simulating select families of multivariate discrete variates with positive correlations

Procedures for simulating multivariate discrete distributions are often needed for modeling real-life situations. Several authors have provided algorithms to simulate data from such distributions, yet the need for algorithms that produce multivariate discrete correlated variates persists. Thus, we propose a simple algorithm to simulate values from several multivariate discrete distributions with positive correlations. The algorithm samples from the mixture distribution that arises from a suitable two-level hierarchical structure. Our algorithm is computationally efficient, straightforward to implement, and produces values with any positive correlation in (0,1). We illustrate our proposal through two trivariate examples implemented in R.