A Note on Estimating the Mean of a Normal Distribution with Known Coefficient of Variation

Abstract

The purpose of the present note is to find the best possible estimator of the parameter θ in the normal distribution N ( θ , aθ 2 ) ( θ > 0) where α is a known positive constant. It is shown that neither the sample mean nor the sample standard deviation with suitably chosen constant is any longer the best unbiased estimator in the sense of minimum variance. Among a typical class of unbiased estimators, the one with minimum variance is obtained. It is also shown that the suggested estimator is B.A.N. (beat asymptotically normal).