Applying computer simulation to analyze the normal approximation of binomial distribution

被引：2

作者：

Chang H.-J. ^{[1
]}

Lee M.-C. ^{[1
]}

机构：

[1] Department of Management Science, Tamkang University, Tamsui

来源：

Journal of Computers (Taiwan) | 2017年 / 28卷 / 05期

关键词：

Binomial distribution; Computer simulation; Data analyzing; Normal distribution;

D O I：

10.3966/199115992017102805011

中图分类号：

O211 [概率论（几率论、或然率论）];

学科分类号：

摘要：

Many statistical analyses were implicitly based on the normal distribution, and as a consequence, researchers would need to adopt the central limit theorem to perform the subsequent data analysis. When applying the central limit theorem, the sample size should be 30 or above in order to have the sampling distribution of sample means to be approximated to the normal distribution. Chang et al. (2006 and 2008) showed that when applying the central limit theorem, the sample size should vary depending on the probability distribution type. As a result, the present study examined if the sample size suggested by many textbooks for using the central limit theorem is appropriate. This study uses computer simulation on approximation of the binomial distribution to the normal distribution. It is to explore the minimum sample size required for a binomial distribution to approximate the normal distribution and be replaced by the normal distribution.

引用

页码：116 / 131

页数：15

共 32 条

[1]

Anderson D.R., Sweeney D.J., Williams T.A., Camm J.D., Cochran J.J., Statistics for Business & Economics, (2016)

[2]

Anderson M.K., A normality test for the mean estimator, Applied Economics Letters, 8, 9, pp. 633-634, (2001)

[3]

Atukorala R., King M.L., Sriananthakumar S., Applications of information measures to assess convergence in the central limit theorem, Model Assisted Statistics and Applications, 10, 3, pp. 265-276, (2015)

[4]

Berry D.A., Lindgren B.W., Statistics: Theory and Methods, (1996)

[5]

Chang H.J., Huang K.C., Wu C.H., Determination of sample size in using central limit theorem for weibull distribution, International Journal of Information and Management Sciences, 17, 3, pp. 31-46, (2006)

[6]

Chang H.J., Wu C.H., Ho J.F., Chen P.Y., On sample size in using central limit theorem for gamma distribution, International Journal of Information and Management Sciences, 19, 1, pp. 153-174, (2008)

[7]

Cortinhas C., Black K., Statistics for Business and Economics, (2014)

[8]

Fitrianto A., Hanafi I., Exploring central limit theorem on world population density data, Proc. AIP Conference Proceedings, (2014)

[9]

Hoeffding W., Robbins H., The central limit theorem for dependent random variables, Duke Math. J., 15, 3, pp. 773-780, (1948)

[10]

Jolliffe I.T., Sample sizes and the central limit theorem: The Poisson distribution as an illustration, The American Statistician, 49, 3, (1995)

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