On Using the Box‐Müller Transformation with Multiplicative Congruential Pseudo‐Random Number Generators
On Using the Box‐Müller Transformation with Multiplicative Congruential Pseudo‐Random Number Generators
复制标题
关于使用 Box-Müller 变换与乘法同余伪随机数生成器
DOI：
10.2307/2346308
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发表时间：
1973
影响因子：
1.6
通讯作者：
H. Neave
中科院分区：
文献类型：
--
作者：
H. Neave
在最近的蒙特卡罗研究中，当采用所谓的标准技术来模拟标准正态分布的简单随机样本时，得到了最不令人满意的抽样分布。表 1 给出了大小为 1,000,000 的样本分布尾部的观察频率和预期频率（后者四舍五入到最接近的整数）的选择。几乎不需要卡方检验来表明观察频率不遵循预期模式！请特别注意，所有 1,000,000 个观测值都限制在范围 (–3·3 : 3·6) 内，并且采样分布大约在点 –3·3、30 和 3·6 处标记了局部最大值。本文对此类现象进行了研究。
In a recent Monte Carlo study, a most unsatisfactory sampling distribution was obtained when supposedly standard techniques were employed to simulate a simple random sample from the standard normal distribution. A selection of observed and expected frequencies (the latter rounded to the nearest integer) in the tails of the distribution for a sample of size 1,000,000 is given in Table 1. It hardly needs a chi‐square test to indicate that the observed frequencies are not following the expected pattern! Note particularly that all the 1,000,000 observations are restricted to the range (–3·3 : 3·6), and that the sampling distribution has marked local maxima approximately at the points –3·3, 30 and 3·6. This paper investigates such phenomena.