A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness, Kurtosis, and Covariance Matrix

We present and investigate a simple way to generate nonnormal 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 are shown to have a non-Gaussian copula. We analytically obtain asymptotic robustness conditions for the IG distribution. We show empirically 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 estimators and fit statistics in covariance structure analysis may be tempered by including the IG transform for nonnormal data generation. We provide an implementation of the IG transform in the R environment.