Multivariate Input Models for Stochastic Simulation

Techniques are presented for modeling and randomly sampling many of the multivariate probabilistic input processes that drive discrete-event simulation experiments. Emphasis is given to bivariate and trivariate extensions of the univariate beta, Johnson, and Bézier distribution families because of the flexibility of these families to model a wide range of shapes for the marginal distributions while also representing the stochastic dependencies between the components of the target random vector. An application to simulation-based medical decision analysis illustrates the proposed technique. Also discussed is a multivariate extension of the univariate Johnson distribution family that facilitates computationally efficient fitting and randomly sampling a high-dimensional distribution with a given correlation matrix as well as given values of the mean, variance, skewness, and kurtosis for each marginal distribution. Finally methods are described for modeling and simulating time-dependent arrival processes via computationally efficient methods that yield tractable estimates of the associated rate functions.