Z.A. Al-Hemyari∗
Normal distribution; two-stage; shrinkage testimator; bias; relative efficiency.
The present article deals with an improved estimator of normal mean which is obtained by considering a two-stage procedure with appropriate shrinkage weight function. Indeed, two-stage shrunken testimators of Stein-type are proposed for the mean µ of normal distribution when a prior estimate µ0 of the mean µ is available. The goodness of this procedure as a means of reducing the time, using minimum cost of experimentation and maximizing the relative efficiency is explained in this paper. Computer-intensive calculations for bias, mean-squared error, relative efficiency, expected sample size, probability of avoiding the second-stage sample, and the percentage of the overall sample-saved expressions show that for different values of the first- and second-stage samples, for different values of levels of significance, and for varying the constants involved in the proposed estimator, the proposed testimator fares better than classical estimator and existing two stage testimation procedures.
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