Simulating Correlated Multivariate Nonnormal Distributions: Extending the Fleishman Power Method

Abstract

A procedure for generating multivariate nonnormal distributions is proposed. Our procedure gener-ates average values of intercorrelations much closer to population parameters thancompeting procedures for skewed and/or heavy tailed distributions and for small sample sizes. Also, it eliminates the necessity of conducting a factorization procedure on the population correlation matrix that underlies the random devi-ates, and it is simpler to code in a programming language (e.g,, FORTRAN). Numerical examples demon-strating the procedures are given. Monte Carlo results indicate our procedure yields excellent agreement between population parameters and average values of intercorrelation, skew, andkurtosis.