A Comparison Study of Finding Efficient Methods for Generating Normal Random Numbers

Abstract

Normal distribution is one of the most commonly used non-uniform distributions in applications involving simulations. Advanced computing facilities make the simulation tasks simple but the challenge is to meet the increasingly stringent requirements on the statistical quality of the generated samples. In this paper, we examine performances of different existing methods available to generate random samples from normal distribution based on statistical quality of the generated samples (randomness and normality) and computational complexities. From the simulation study, it is observed that CDF approximation based method and acceptance-rejection method devised by Rao et al.12 and Sigman14 are the fastest and the slowest respectively among all algorithms considered in this paper while generated samples produced by all methods satisfy randomness and normality properties. An application involving simulation from normal distribution is shown by considering a Monte Carlo integration problem.