连续随机变量非线性函数的期望和方差的近似求法

APPROXIMATE COMPUTATION OF EXPECTATION AND VARIANCE OF NONLINEAR FUNCTION OF CONTINUOUS RANDOM VARIABLE

为了研究近似法对求连续随机变量高阶非线性函数的期望和方差的影响,用典型算例分析了非线性函数的曲率强度对结果的影响。计算结果表明,由近似法求得的期望和方差,与非线性模型的固有非线性度和参数效应非线性度有关,当固有非线性度和参数效应非线性度都较弱时,可以采用近似法;随着函数的非线性强度的增大,随机变量函数的期望和方差的近似计算引起的偏差尤其是对方差的偏差也不断增大。

In order to analyze the effect of the nonlinearity of the function on calculating the expectation and variance of nonlinear function of continuous random variable, a set of examples are designed. The calculated results show that the approximate method is suitable to nonlinear functions with weak nonlinearity, and the stronger the nonlinearity of the function, the more the bias of the approximate estimations, especially for the approximate estimation of variance.