GENERATING STATISTICALLY DEPENDENT PAIRS OF RANDOM-VARIABLES - A MARGINAL DISTRIBUTION APPROACH

A procedure is presented for generating statistically dependent pairs of random variates (X, Y) that can be used in a variety of Monte Carlo simulations. The variates follow the marginal distributions of both X and Y, while maintaining a given linear or quadratic regression relationship. A special case of the procedure can be used to achieve a given product moment correlation between X and Y. The random variables X and Y can have a wide variety of skewed or symmetric marginal probability distributions. The random variate X is sampled according to the specifications of its marginal distribution. Sample values for the random variable Y are easily obtained. They preserve the first three (or four) moments of Y's marginal distribution. The procedure is easily set up and used. It is useful in a number of straightforward situations, where other methods are not applicable or difficult to use. The setup of the procedure does not use any elaborate Operational Research techniques.