Generating nonnormal distributions via Gaussian mixture models

The purpose of this paper is to (1) present a method of generating nonnormal univariate and/or uncorrelated multivariate distributions using mixture models, and (2) compare the accuracy of generating nonnormal distributions using the mixture-based method against power transformation method and generalized lambda method. Monte Carlo methods were used to generate data with each of the three nonnormal generation techniques to manipulate levels of skewness and kurtosis. Generally, all three methods produced relatively accurate levels of skewness, but the mixture-based method was most accurate in the vast majority of conditions. With respect to kurtosis, only the mixture model-based method produces distributions with kurtosis with trivial levels of bias, on average. The mixture-based method was the most stable also. An R function is also provided to allow users to generate distributions with specified mean, variance, skewness, and kurtosis.