Document Type
Article
Publication Date
2015
Publication Title
Statistics
Abstract
Let X1, X2, …, Xn be iid N(μ, aμ2) (a>0) random variables with an unknown mean μ>0 and known coefficient of variation (CV) √a. The estimation of μ is revisited and it is shown that a modified version of an unbiased estimator of μ [cf. Khan RA. A note on estimating the mean of a normal distribution with known CV. J Am Stat Assoc. 1968;63:1039–1041] is more efficient. A certain linear minimum mean square estimator of Gleser and Healy [Estimating the mean of a normal distribution with known CV. J Am Stat Assoc. 1976;71:977–981] is also modified and improved. These improved estimators are being compared with the maximum likelihood estimator under squared-error loss function. Based on asymptotic consideration, a large sample confidence interval is also mentioned.
Repository Citation
Khan, Rasul A., "A Remark on Estimating The Mean of A Normal Distribution with Known Coefficient of Variation" (2015). Mathematics and Statistics Faculty Publications. 159.
https://engagedscholarship.csuohio.edu/scimath_facpub/159
DOI
10.1080/02331888.2013.809722
Version
Postprint
Publisher's Statement
This is an Author’s Accepted Manuscript of an article published in Statistics 2015, available online: http://www.tandfonline.com/10.1080/02331888.2013.809722
Volume
49
Issue
3
