A simple simulation technique for nonnormal data with prespecified skewness, kurtosis, and covariance matrix

Abstract

We present and investigate a simple way to generate non-normal data using linear combinations of independent generator (IG) variables. The simulated data have prespecified univariate skewness and kurtosis, and a given covariance matrix. In contrast to the widely used Vale-Maurelli (VM) transform, the obtained data is shown to have a non-Gaussian copula. Analytically, we obtain asymptotic robustness conditions for the IG distribution. Empirically, we show that popular test statistics in covariance analysis tend to reject true models more often under the IG transform than under the VM transform. This implies that overly optimistic evaluations of stimators and fit statistics in covariance sstructure analysis may be tempered by including the IG transform for non-normal data generation. We provide an implementation of the IG transform in the R environment.