On Normal Approximation of chi-square Distribution

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Title:	On Normal Approximation of chi-square Distribution
Other Titles:	英文
Authors:	Chang, Horng-Jinh;Lee, Ming-Chen
Keywords:	Computer Simulation, The Central Limit Theorem, Chj-square Distribution, Normal Distribution
Date:	2017-09-30
Issue Date:	2017-11-01 02:11:50 (UTC+8)
Publisher:	Tamkang University
Abstract:	According to the central limit theorem, if X1, X2,…Xv is a random sample drawn from chi-square distribution with degree 1, then, when v tends to infinite, the distribution of the sample mean X approximate to normal distribution N (1, 2/v). Also, the distribution function of the total X1+X2+…+Xv would asymptotically approximate to the normal distribution N(v,2 v). Many statistics textbooks or applied statistics research accept the use of a sample size of not less 30 for the approximation . Therefore, in the present study, computer simulation was adopted to test the required sample size for the normal approximation. This information is useful for the applications of the central limit theorem.
Relation:	Journal of Applied Science and Engineering, Vol. 20, No. 3, pp. 283-294
DOI:	10.6180/jase.2017.20.3.02
Appears in Collections:	[Department of Management Sciences] Journal Article

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