Modeling dependencies in stochastic simulation inputs

Abstract

We discuss some basic techniques for modeling dependence between the random variables that are inputs to a simulation model, with the main emphasis being continuous bivariate distributions that have flexible marginal distributions and that are readily extended to higher dimensions. First we examine the bivariate normal distribution and its advantages and drawbacks for use in simulation studies. To achieve a greater variety of distributional shapes while accurately reflecting a desired dependency structure, we discuss bivariate Johnson distributions. Although space limitations preclude inclusion in this article, the oral presentation of this tutorial will also include discussions of how to use (a) bivariate Bezier distributions as a means for achieving even greater flexibility in modeling the marginal distributions, and (b) ARTA (AutoRegressive To Anything) processes as a means for generating an entire stochastic process with specified marginals and a desired covariance structure.