Abstract
In this paper, we introduce a new lifetime distribution by compounding exponential and PoissonLindley distributions, named the exponential PoissonLindley (EPL) distribution. A practical situation where the EPL distribution is most appropriate for modelling lifetime data than exponentialgeometric, exponentialPoisson and exponentiallogarithmic distributions is presented. We obtain the density and failure rate of the EPL distribution and properties such as mean lifetime, moments, order statistics and Renyi entropy. Furthermore, estimation by maximum likelihood and inference for large samples are discussed. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.