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

A. Sajib, Syeda Fateha Akter
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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 al12 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. Dhaka Univ. J. Sci. 67(2): 91-98, 2019 (July)
寻找生成正态随机数的有效方法的比较研究
正态分布是模拟应用中最常用的非均匀分布之一。先进的计算设施使模拟任务变得简单,但挑战在于如何满足对生成样本的统计质量日益严格的要求。在本文中,我们根据生成样本的统计质量(随机性和正态性)和计算复杂性,研究了不同现有方法的性能,这些方法可用于从正态分布中生成随机样本。从仿真研究中可以看出,基于CDF近似的方法和由Rao et al12和Sigman14设计的接受-拒绝方法在本文所考虑的所有算法中分别是最快和最慢的,并且所有方法产生的生成样本都满足随机性和正态性。通过考虑蒙特卡罗积分问题,给出了一个涉及正态分布模拟的应用。达卡大学学报(自然科学版),67(2):91- 98,2019 (7)
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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