Generating univariate and multivariate nonnormal data

Because the assumption of normality is common in statistics, the robustness of statistical procedures to the violation of the normality assumption is often of interest. When one examines the impact of the violation of the normality assumption, it is important to simulate data from a nonnormal distribution with varying degrees of skewness and kurtosis. Fleishman (1978, Psychometrika 43: 521-532) developed a method to simulate data from a univariate distribution with specific values for the skewness and kurtosis. Vale and Maurelli (1983, Psychometrika 48: 465-471) extended Fleishman’s method to simulate data from a multivariate nonnormal distribution. In this article, I briefly introduce these two methods and present two new commands, rnonnormal and rmvnonnormal, for simulating data from the univariate and multivariate nonnormal distributions.