Comparison of the procedures of Fleishman and Ramberg et al. for generating non normal data in simulation studies

Abstract

Simulation techniques must be able to generate the types of distributions most commonly encountered in real data, for example, non-normal distributions. Two recognized procedures for generating non-normal data are Fleishman's linear transformation method and the method proposed by Ramberg et al. that is based on generalization of the Tukey lambda distribution. This study compares these procedures in terms of the extent to which the distributions they generate fit their respective theoretical models, and it also examines the number of simulations needed to achieve this fit. To this end, the paper considers, in addition to the normal distribution, a series of non-normal distributions that are commonly found in real data, and then analyses fit according to the extent to which normality is violated and the number of simulations performed. The results show that the two data generation procedures behave similarly. As the degree of contamination of the theoretical distribution increases, so does the number of simulations required to ensure a good fit to the generated data. The two procedures generate more accurate normal and non-normal distributions when at least 7000 simulations are performed, although when the degree of contamination is severe (with values of skewness and kurtosis of 2 and 6, respectively) it is advisable to perform 15000 simulations.