Abstract
The problem of estimation of the parameter of a selected population arises when we encounter with several populations and would like to estimate the parameter of the best (worst) selected population. Suppose be independent random samples drawn from populations respectively, where observations from Π i have a -distribution with unequal known shape parameters In this paper, we use a selection rule to select the best (worst) population, and estimate the best (worst) scale parameter of the selected population under the Stein loss function. The uniformly minimum risk unbiased (UMRU) estimators of θS and θJ are obtained. A sufficient condition for inadmissibility of scale-invariant estimators of is obtained and it is shown that the UMRU estimator of is inadmissible. For k = 2, a sufficient condition for minimaxity of a given estimator of is obtained, and the generalized Bayes estimator of θS is shown to be minimax. Finally, the risk functions of the various competing estimators are compared numerically, and a real data is provided to compute the proposed estimates and their expected risks.
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