Non-Uniform Random Number Generation: A Survey And Tutorial

J. Ahrens
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Abstract

The basic pseudo-random number generators on computers return deviates which are uniformly distributed in the interval between 0 and 1. For simulations and other applications other random variables are needed which follow given statistical distributions, for instance normal deviates. The survey will concentrate on the most important distributions arising in simulation applications. The considered non-uniform distributions fall into two categories: continuous and discrete. In either class very efficient methods for sampling from general distributions are presented. Specific cases considered include the exponential, normal, gamma, beta and Cauchy distributions in the continuous, and Poisson, binomial and hypergeometric generators in the discrete category. In selecting suitable specific algorithms for each distribution we rejected the 'easiest' methods which are not fast enough. On the other hand, some of the most efficient generators are rather difficult to implement. The selected algorithms are almost as fast as these, but not too complex. Their Fortran versions are portable except for the employed basic (0, 1)-uniform generators for which, however, the user may substitute his or her own favorite. A number of the proposed methods are the author's recent developments. Some well-known alternatives will also be mentioned.
非均匀随机数生成:调查和教程
计算机上的基本伪随机数生成器返回的偏差在0到1的区间内均匀分布。对于模拟和其他应用,需要遵循给定统计分布的其他随机变量,例如正态偏差。调查将集中在模拟应用中出现的最重要的分布。所考虑的非均匀分布分为两类:连续分布和离散分布。在这两类中,都给出了从一般分布中进行抽样的非常有效的方法。考虑的具体情况包括指数分布、正态分布、伽玛分布、β分布和连续分布中的柯西分布,以及离散类别中的泊松分布、二项式分布和超几何生成。在为每个分布选择合适的特定算法时,我们拒绝了速度不够快的“最简单”方法。另一方面,一些最有效的生成器很难实现。所选择的算法几乎和这些一样快,但不太复杂。它们的Fortran版本是可移植的,除了所使用的基本(0,1)-统一生成器,但是,用户可以替换他或她自己喜欢的。许多提出的方法是作者最近的发展。还将提到一些众所周知的替代方案。
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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