Modeling and Generating Random Vectors with Arbitrary Marginal Distributions and Correlation Matrix

Abstract

We describe a model for representing random vectors whose component random variables have arbitrary marginal distributions and correlation matrix, and describe how to generate data based upon this model for use in a stochastic simulation. The central idea is to transform a multivariate normal random vector into the desired random vector, so we refer to these vectors as having a NORTA (NORmal To Anything) distribution. NORTA vectors are most useful when the marginal distributions of the component random variables are neither identical nor from the same family of distributions, and they are particularly valuable when the dimension of the random vector is greater than two. Several numerical examples are provided. Keywords: simulation, random vector, input modeling, correlation matrix, copulas 1 Introduction In many stochastic simulations, simple input models---idependent and identically distributed sequences from standard probability distributions---are not faithful representations of th..