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Relative Efficiency of Estimators of the Mean of a Normal Distribution when Coefficient of Variation is Known
Author(s) -
Sen A. R.
Publication year - 1979
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710210206
Subject(s) - mathematics , estimator , efficiency , statistics , bias of an estimator , efficient estimator , minimum variance unbiased estimator , coefficient of variation , standard deviation , constant (computer programming) , u statistic , distribution (mathematics) , consistent estimator , normal distribution , variance (accounting) , mathematical analysis , computer science , accounting , business , programming language
A biased but simple and consistent estimator of the parameter ϑ has been obtained for the normal distribution N(ϑ, a ϑ 2 ), ϑ>0 where a is a known constant. It is shown that the estimator is more efficient than the sample mean or any suitably chosen constant multiple of the sample standard deviation. It is also proved to be more efficient than the mimumum variance unbiased estimator among a typical class of unbiased estimators derived by R ASUL K HAN (1968).