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The exponential Poisson logarithmic distribution

Abstract In this article, we proposed a new three parameter lifetime distribution motivated mainly by lifetime issues, which generalizes the Exponential Poisson distribution proposed by Cancho et al. (2011). We derive various standard mathematical properties of the proposed model including a formal proof of its probability density function and hazard rate function. The inference via the maximum likelihood approach is discussed. The performance of the maximum likelihood estimators, the likelihood ratio test and its power are studied by simulation. Finally, the proposed model is fitted to two real data sets and it is compared with several models.