A heuristic approach for the generation of multivariate random samples with specified marginal distributions and correlation matrix

Summary  This paper presents a heuristic approach for multivariate random number generation. Our aim is to generate multivariate samples with specified marginal distributions and correlation matrix, which can be incorporated into risk analysis models to conduct simulation studies. The proposed sampling approach involves two distinct steps: first a univariate random sample from each specified probability distribution is generated; then a heuristic combinatorial optimization procedure is used to rearrange the generated univariate samples, in order to obtain the desired correlations between them. The combinatorial optimization step is performed with a simulated annealing algorithm, which changes only the positions and not the values of the numbers generated in the first step. The proposed multivariate sampling approach can be used with any type of marginal distributions: continuous or discrete, parametric or non-parametric, etc.