一种快速计算随机变量函数均值与标准差的新方法  

A Fast Method to Calculate the Mean and the Standard Deviation of the Function of Random Variables

作　　者：崔维成[1] 徐向东[1] 邱强[1] 

机构地区：[1]中国船舶科学研究中心

出　　处：《船舶力学》1998年第6期50-60,共11页Journal of Ship Mechanics

摘　　要：由于在工程实际问题中对于许多物理量的认识存在着大量的不确定性，因此，必须用概率论和数理统计的方法去处理这些问题。在应用概率论解决工程实际问题时，我们经常会碰到在已知基本随机变量X1，X2，…，Xn的均值和标准差时，需要求这些变量的某个函数Y＝C（X1，X2，…，Xn）的均值和标准差的问题。本文对现有的计算随机变量函数均值与标准差的四类方法进行了详细的介绍和讨论。在此基础上，我们吸收了Rosenbluthe法计算简单的优点，改进了原方法中存在的计算精度不稳定和有时数值计算奇异两个缺点，提出了一种改进的Rosen-bluthe法。本文从数学和大量实例上证明了改进Rosenbluthe法的计算精度至少与二阶Taylr级数相当，在许多情况下，比二阶Taylor级数的精度还要高。而从本文所给出的大量例子中可以看出，原来的Rosenbluthe法，在许多场合，误差都是很大的。因此，我们相信，本文给出的改进Rosenbluthe法会具有较高的实用价值。In many engineering problems there exists a lot of uncertainties, so the theory of probability and statistics must be used in handling these problems.When applying the theories of probability to solve these practical problems, one is often required to calculate the mean and the standard deviation of the function of random variables. In this paper, four types of existing methods which can be used for this purpose are discussed in detail. It was found that the Rosenbluthe method is the simplest hut the original one has two deficiencies: (1) It does not have a stable accuracy; (2) It is singUlar for some problems. An improved Rosenbluthe method is proposed which can overcome these two deficiencies. From mathematics it can be proved that the improved Rosenbluthe method is at least of the accuracy of the second-older Taylor series. Many examples have also been used to prove this conclusion.It is believed that the improved Rosenbluthe method will be a valuable tool in solving engineering problems.

关 键 词：随机变量函数 均值 标准差 概率论 

分 类 号：O211.5[理学—概率论与数理统计]