Use of Apriori Information in Estimating Mean of a Normal Population– Second Order Relative Efficiencies

Background/Objective: Modified estimator for population mean using known coefficient of variation was proposed by1 . Such an estimator has minimum mean squared error but it is unbiased. In2 has proposed an estimator for population mean using an estimator for coefficient of variation. Motivated by the distribution of the sample root mean square s given in3 an estimator was constructed for mean of Normal population by4 and the relative efficiency of the proposed estimator over the conventional unbiased estimator was derived up to first order approximation. The present paper is focused on constructing two estimators for the mean of Normal population using known coefficient of variation. The relative efficiencies are derived upto second order and the numerical results are tabulated. Methods: Basing on Searle method two estimators are constructed for mean µ of Normal population. Former is a linear combination whereas the latter being a convex combination of X and s. Results: The Relative efficiencies of the proposed estimators over the conventional unbiased estimator X are obtained. Conclusions/Applications: It is established that the first estimator is more efficient than that of X where as the second estimator is equally efficient to that of X under first order approximation. Under the second order approximation it is observed that both first and second estimators are more efficient than X and the first estimator is more efficient than that of second estimator. Keywords: Normal Population, Squared Minimum Mean Squared Error, Unbiased Estimator