In some applied problems we need to choose a population from the given populations and estimate the parameter of the selected population. Suppose k random samples are chosen from k populations with proportional hazard rate model or proportional reversed hazard rate model. According to a specified selection rule, it is desired to estimate the parameter of the best (worst) selected population. In this paper, under the entropy loss function we obtain the  uniformly minimum risk unbiased (UMRU) estimator of  the parameters of the selected population, and derived sufficient conditions for minimaxity of a given estimator. Then we find the class of admissible and inadmissible linear estimators of the parameters of the selected population and determine the class of dominators of a given estimator. We show that the UMRU estimator is inadmissible and compare the obtained estimators by plotting their risk functions.