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In this paper, a new three-parameter lifetime distribution is introduced by combining an extended exponential distribution with a logarithmic distribution. This flexible distribution has increasing, decreasing and upside-down bathtub failure rate shapes. Various properties of the proposed distribution are discussed. The estimation of the parameters attained by EM algorithm and their asymptotic variance and covariance are obtained. In order to assess the accuracy of the approximation of variance and covariance of the maximum likelihood estimator, a simulation study is presented to illustrate the properties of distribution.