Advances and Applications in Statistics
Volume 54, Issue 2, Pages 199 - 236
(February 2019) http://dx.doi.org/10.17654/AS054020199 |
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ON SIGMA-ESTIMATORS FROM A NORMAL UNIVERSE
Saeed Maghsoodloo
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Abstract: This article examines the Central Limit Theorem from the standpoint of skewness and kurtosis, and then investigates the relative and absolute efficiencies of all standard deviation estimators based on one simple random sample of size n from a normal population. We obtained the most precise estimator of the normal population standard deviation σ using Cramer-Rao's lower bound for the variance of an unbiased estimator; however, this last estimator suffers from large negative bias. As a result, we used Lindgren-Cramer-Rau's inequality to develop another estimator of σ that is more accurate than all others for sample sizes n ≥ 2. The case of M > 1 subgroups will be discussed in a subsequent paper, and for M > 1, slight modifications will be recommended for some Quality Control Charts. |
Keywords and phrases: the central limit theorem (CLT), Fisher’s information matrix (IM), mean square error (MSE), relative-efficiencies (REL-EFFs).
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