A new lifetime model with decreasing failure rate

Abstract

In this paper, we introduce a new lifetime distribution by compounding exponential and Poisson–Lindley distributions, named the exponential Poisson–Lindley (EPL) distribution. A practical situation where the EPL distribution is most appropriate for modelling lifetime data than exponential–geometric, exponential–Poisson and exponential–logarithmic distributions is presented. We obtain the density and failure rate of the EPL distribution and properties such as mean lifetime, moments, order statistics and Rényi 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.

Keywords:

• exponential distribution
• Poisson–Lindley distribution
• exponential Poisson–Lindley distribution
• order statistics
• maximum likelihood

Acknowledgements

We thank the two referees for their constructive comments and suggestions. The first author also gratefully acknowledges the financial support from CNPq (Brazil).

Additional information

Notes on contributors

Hassan S. Bakouch

Permanent address: Department of Mathematics, Faculty of Science, Tanta University, Egypt.