| 重积分计算的分层抽样原理 |
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| 引用本文： | 陈家鑫. 重积分计算的分层抽样原理[J]. 汕头大学学报(自然科学版), 1995, 10(1): 10-16,27 |
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| 作者姓名： | 陈家鑫 |
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| 作者单位： | 汕头大学数学系 |
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| 摘 要： | Ｋ重积分的计算中，我们对联合概率密度函数ｆ（ｘ１，ｘ２，…，ｘｋ）实施有限加权展开然后，按照各联合概率密度ｆｉ（ｘ１，ｘ２，…，ｘｋ）摸拟抽样值｛ｇ（ξ（ｉ，ｔ）），ｔ＝１，２，…，Ｎｉ，ｉ＝１，２，…，Ｌ｝，由下式建立Ｊ的估计量证明了这种分层抽样方法降低方差，同时给出最小方差的一般原理．
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| 关 键 词： | 重积分；剖分；加权和；抽样；统计模拟；估计量；方差；最大最小原理 |
The principle of stratified sampling for evaluation on the multiple integrals |
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| Chen Jiaxin. The principle of stratified sampling for evaluation on the multiple integrals[J]. Journal of Shantou University(Natural Science Edition), 1995, 10(1): 10-16,27 |
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| Authors: | Chen Jiaxin |
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| Abstract: | In the evaluation of multiple integrals the multidimensional probability density function f(x1,x2,…,xk) was expanded in terms of finite weighted sum as follow:Accordingly we simulated the sample values {g(ξ(i,t)),t =1, 2, …,Ni,i = 1, 2, …,L },and set up the estimator J. for J:It has been proved that the variance can be reduced by means of this method of stratified sampling. Also, the general principle of minimum variance is presented. |
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| Keywords: | multple integrals partition weighted sum sampling statistical simulation estimator variance maximum-minimum principle |
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