Pareto Poisson–Lindley distribution with applications

Abstract

A new lifetime distribution is introduced based on compounding Pareto and Poisson–Lindley distributions. Several statistical properties of the distribution are established, including behavior of the probability density function and the failure rate function, heavy- and long-right tailedness, moments, the Laplace transform, quantiles, order statistics, moments of residual lifetime, conditional moments, conditional moment generating function, stress–strength parameter, Rényi entropy and Song's measure. We get maximum-likelihood estimators of the distribution parameters and investigate the asymptotic distribution of the estimators via Fisher's information matrix. Applications of the distribution using three real data sets are presented and it is shown that the distribution fits better than other related distributions in practical uses.

Keywords:

• Pareto type II distribution
• Poisson–Lindley distribution
• Pareto Poisson–Lindley distribution
• order statistics
• maximum-likelihood estimation

Acknowledgements

This paper was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (130-130-D1432). The authors, therefore, acknowledge with thanks the DSR technical and financial support. The authors also thank the editor and referees for their suggestions which lead to improvement of the paper.

Additional information

Notes on contributors

L. Esmaeili

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