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.
關聯:
Journal of Applied Science and Engineering, Vol. 20, No. 3, pp. 283-294