Let X be normally distributed with unknown mean μ and variance σ2. Assume that a prior estimate μ0 of μ is available. A two stage estimation procedure of estinating μ that incorporates prior estimate μ0 is proposed. This estimator is shown to have a smaller mean squared error in a region around μ0 in comparison to an existing two stage estimation procedure. Both the cases viz. known and σ2 unknown have been considered. The expressions for the bias and mean squared error of the proposed estimators are given. Numerical results are provided when the proposed estimators are testimators of level of significance α. Comparisons with the earlier known results show the usefulness of the estimators.
