(1.湘潭工学院 土木工程系， 湘潭 411201；
2.中南工业大学 测量与国土信息研究所， 长沙 410083)
摘 要: 以MonteCarlo方法为基础研究了强非线性函数的方差估计问题。 对直接观测量的方差进行了随机扰动， 将由线性同余法产生的一组伪随机数用BoxMuller变换法转换为服从 N (0， 1)分布的正态伪随机数， 并对伪随机数作了多项统计检验。在此基础上应用Bessel公式统计出强非线性函数的模拟方差。 算例表明： MonteCarlo方法估计出的非线性函数的方差比经典方法估计出的方差更优。
关键字: MonteCarlo方法； 强非线性函数； 方差估计
（1. Department of Civil Engineering，Xiangtan Polytechnic University, Xiangtan 411201, P.R.China;
2. College of Resources, Environment and Civil Engineering,Central South University of Technology, Changsha 410083, P.R.China）
Abstract: Based on the way of MonteCarlo, the problems of varianceestimation of intensive nonlinear function has been studied. By random disturbance of the standard deviation of directly observed values, a group offalse random values of nonlinear function which submit to the regular distribution were produced, then they were transfered into false random value which submit to the N (0, 1) distribution by the way of BoxMuller, and some statistical tests had been done on them. On the basis of these statistics, the visual varianceof intensive nonlinear function was counted by Bessel formula. Example shows that the variance estimation of intensive nonlinear function counted by the way of MonteCarlo varianceestimation has some advantages over that counted by the way of classical varianceestimation.
Key words: MonteCarlo method; variance estimation; intensive nonlinear functions
