A matching algorithm for generation of statistically dependent random variables with arbitrary marginals

Simulation has gained acceptance in the operations research community as a viable method for analyzing complex problems. While random generation of variables with various marginal distributions has been studied at length, developing ability to preserve a given degree of statistical dependence among them has been lagging behind. This paper includes a short summary of the previous work and a description of the proposed algorithm for efficient re-arranging of generated random variables such that a desired product moment correlation matrix is induced. The proposed approach is different from similar algorithms that induce a desired rank-order correlation among random variables. The algorithm is demonstrated using three numerical examples, one of which also includes a comparison with @RISK commercial package. Its main features are simplicity, ease of implementation and the ability to handle either theoretical or empirical distribution functions.