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Motivation to fit the Danish reinsurance claim and aircraft windshield data sets, we introduce exponentiated half logistic-power series (EHLPS) distributions, which are obtained by compounding exponentiated half-logistic distribution with power series distributions. Some mathematical properties have been studied. Maximum likelihood estimation of unknown parameters for the complete data is discussed via the EM algorithm. Simulation results to assess the performance of the estimation methods are discussed. Finally, two applied examples are given for indicating the flexibility and appropriateness of the distribution.