Sim L H, Nitschke K N
Department of Physical Sciences, Princess Alexandra Hospital, Brisbane.
Australas Phys Eng Sci Med. 1993 Mar;16(1):22-32.
Central to any system for modelling radiation transport phenomena using Monte Carlo techniques is the method by which pseudo random numbers are generated. This method is commonly referred to as the Random Number Generator (RNG). It is usually a computer implemented mathematical algorithm which produces a series of numbers uniformly distributed on the interval [0,1). If this series satisfies certain statistical tests for randomness, then for practical purposes the pseudo random numbers in the series can be considered to be random. Tests of this nature are important not only for new RNGs but also to test the implementation of known RNG algorithms in different computer environments. Six RNGs have been tested using six statistical tests and one visual test. The statistical tests are the moments, frequency (digit and number), serial, gap, and poker tests. The visual test is a simple two dimensional ordered pair display. In addition the RNGs have been tested in a specific Monte Carlo application. This type of test is often overlooked, however it is important that in addition to satisfactory performance in statistical tests, the RNG be able to perform effectively in the applications of interest. The RNGs tested here are based on a variety of algorithms, including multiplicative and linear congruential, lagged Fibonacci, and combination arithmetic and lagged Fibonacci. The effect of the Bays-Durham shuffling algorithm on the output of a known "bad" RNG has also been investigated.
使用蒙特卡罗技术对辐射传输现象进行建模的任何系统的核心，都是生成伪随机数的方法。这种方法通常被称为随机数生成器（RNG）。它通常是一种计算机实现的数学算法，生成一系列在区间[0,1)上均匀分布的数字。如果这个序列满足某些随机性统计测试，那么从实际目的出发，该序列中的伪随机数就可以被认为是随机的。这种性质的测试不仅对新的随机数生成器很重要，而且对于在不同计算机环境中测试已知随机数生成算法的实现也很重要。已经使用六种统计测试和一种可视化测试对六种随机数生成器进行了测试。统计测试包括矩、频率（数字和数值）、序列、间隔和扑克测试。可视化测试是一种简单的二维有序对显示。此外，这些随机数生成器还在一个特定的蒙特卡罗应用中进行了测试。这类测试常常被忽视，然而，除了在统计测试中表现令人满意之外，随机数生成器在感兴趣的应用中能够有效运行也很重要。这里测试的随机数生成器基于多种算法，包括乘同余和线性同余、滞后斐波那契以及算术与滞后斐波那契的组合。还研究了贝叶斯 - 达勒姆洗牌算法对一个已知“劣质”随机数生成器输出的影响。
