(1.湘潭工學(xué)院 土木工程系， 湘潭 411201；
2.中南工業(yè)大學(xué) 測量與國土信息研究所， 長沙 410083)
摘 要: 以MonteCarlo方法為基礎(chǔ)研究了強(qiáng)非線性函數(shù)的方差估計(jì)問題。 對直接觀測量的方差進(jìn)行了隨機(jī)擾動(dòng)， 將由線性同余法產(chǎn)生的一組偽隨機(jī)數(shù)用BoxMuller變換法轉(zhuǎn)換為服從 N (0， 1)分布的正態(tài)偽隨機(jī)數(shù)， 并對偽隨機(jī)數(shù)作了多項(xiàng)統(tǒng)計(jì)檢驗(yàn)。在此基礎(chǔ)上應(yīng)用Bessel公式統(tǒng)計(jì)出強(qiáng)非線性函數(shù)的模擬方差。 算例表明： MonteCarlo方法估計(jì)出的非線性函數(shù)的方差比經(jīng)典方法估計(jì)出的方差更優(yōu)。
關(guān)鍵字: MonteCarlo方法； 強(qiáng)非線性函數(shù)； 方差估計(jì)
（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
