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.

Keywords:

• Logarithmic distribution
• Poisson distribution
• Exponential distribution
• Latent causes
• Maximum likelihood estimation

MATHEMATICS SUBJECT CLASSIFICATION:

• 97K60

Acknowledgments

The authors thank the editor and two anonymous referees for their valuable comments.

Funding

The work of the first and second authors were funded by CAPES - Brazil.