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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. Supposebeindependent random samples drawn from populationsrespectively, where observations from Πihave a-distribution with unequal known shape parametersIn this paper, we use a selection rule to select the best (worst) population, and estimate the best (worst) scale parameterof the selected population under the Stein loss function. The uniformly minimum risk unbiased (UMRU) estimators of  θ Sand  θ Jare obtained. A sufficient condition for inadmissibility of scale-invariant estimators ofis obtained and it is shown that the UMRU estimator ofis inadmissible. For  k  = 2, a sufficient condition for minimaxity of a given estimator ofis obtained, and the generalized Bayes estimator of  θ Sis 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.

Estimation of the scale parameter of a selected gamma population with unequal shape parameters under stein loss function