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This paper is concerned with admissible and minimax estimation of scale parameter θ of a gamma distribution under the entropy loss function, when it is known that θ > a for some known a > 0. An admissible minimax estimator of θ, which is the pointwise limit of a sequence of Bayes estimators, is derived. Also, the admissible estimators and the only minimax estimator of θ in the class of truncated linear estimators are obtained. Finally, the results are extended to a subclass of scale parameter exponential family and the family of transformed chi-square distributions