一种计算随机变量函数均值和标准差的方法

在工程实践中常常需要对随机变量函数的均值和标准差进行计算。对于这种问题，通常采用的是Monte Carlo方法、Taylor级数展开法、Taguchi法及其改进方法、Rosenbluthe法及其改进方法等。其中最有效的是Monte Carlo方法，但其计算效率低。为此，提出利用数论方法产生分布均匀的数论网格点，以此伪随机数代表由Monte Carlo方法产生的随机数计算随机变量函数的均值及标准差。计算实例表明，这种利用伪随机数的方法不但克服了Rosenbluthe改进方法在处理高阶函数时计算结果偏离实际值的缺点，而且与Monte Carlo方法相比，提高了计算效率。

METHOD TO CALCULATE THE MEAN AND THE STANDARD DEVIATION OF THE FUNCTION OF RANDOM VARIABLES

It is usually required to calculate the mean and the standard deviation of the function of random variables in many engineering problems. Five methods for example, Monte Carlo method, Taylor series, Taguchi and improved method, Rosenbluthe and improved method, can be used to deal with this kind of question. Monte Carlo method is the most popular all of these methods, but its efficiency is low. For solving this question, pseudo random numbers based on Number theoretic Methods is used in Monte Carlo method. Some examples indicated the efficiency of this method is higher than that of Monte Carlo method. Furthermore, it overcomes the defection that improved Rosenbluthe and improved method deviates actual value for high order function.