摘 要:通过数学推导建立了取样方差估计值的精度与样本数目之间的定量关系。实验也证明,取样方差估计值的标准偏差与样本数目的平方根之积可近似为一常数。应用蒙特卡罗技术模拟随机取样,对该关系式进行了验证,并探讨了取样方差估计值的分布规律,表明其规律对于组分含量服从正态分布,均匀随机分布及多项分布总体是相似的。
关键词:随机取样,取样精密度,蒙特卡罗模拟
分类号:O65 文献标识码:A
Relationship Between the Precision of Estimated Sampling Variances and the Number of Samples
Gao Zhi(Department of Chemistry,Nankai University, Tianjin 300071)
Li Yijun(Department of Chemistry,Nankai University, Tianjin 300071)
He Xiwen(Department of Chemistry,Nankai University, Tianjin 300071)
Zhu Shoutian(Department of Chemistry,Nankai University, Tianjin 300071)
Abstract:The relationship between the precision of the estimated sampling variances and the number of samples was quantitatively established. It revealed that the product of the standard deviation of the estimated sampling variance and square root of the number of samples was a constant. Monte Carlo simulation technique was employed to verify the equation. Populations with Gaussian,unifohn random and multi-nomial(taking silicon carbide material as an example) distributions were studied with satisfactory results.
Keywords:Random sampling,sampling precision,Monte Carlo simulation
作者单位:高志(南开大学化学系天津,300071)
李一峻(南开大学化学系天津,300071)
何锡文(南开大学化学系天津,300071)
朱守田(南开大学化学系天津,300071)
参考文献:
[1]Kratochvil B, Wallace D, Taylor J K. Anal. Chem., 1984, 56(5):113R
[2]He Xiwen(何锡文),Guo Wei(郭薇).Chinese J. Anal. Chem.(分析化学),1995,23:1456
[3]Ramsey M H, Argyraki A, Thompson M. Analyst, 1995, 120:1353
[4]Kaiser H. Anal. Chem., 1970, 42(2):24A
[5]Meyer S L Translated by Zhou Liuyuan (周流元),Gu Zhaoliang(顾兆良).Data Analysis for Scientist and Engineers(科学和工程数据分析).Beijing(北京).Atomic Energy Publishing House(原子能出版社),1983:251
[6]Howarth R J, Thompson M. Analyst, 1976, 101:699
[7]Latinen H A, Harris W E. Chemical Analysis. 2nd ed., McGraw-Hill, U.S.,1975:539
收稿日期:1999年12月9日
修稿日期:2000年9月5日
出版日期:2001年2月20日
原载于《分析化学》2001 Vol.29 No.2 P.171-174
http://fxhx.periodicals.com.cn/default.html
作者:
2007-5-18