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In this paper, we introduce a new compounding distribution, named the Lindley-Poisson distribution. We investigate its characterization and statistical properties. The maximum likelihood inference using EM algorithm is developed. Asymptotic properties of the MLEs are discussed and simulation studies are performed to assess the performance of parameter estimation. We illustrate the proposed model with two real applications and it shows that the new distribution is appropriate for lifetime analyses.

The Lindley-Poisson distribution in lifetime analysis and its properties