A New Generalized Exponential Geometric Distribution

Abstract

In this article, another version of the generalized exponential geometric distribution different to that of Silva et al. (2010) is proposed. This new three-parameter lifetime distribution with decreasing, increasing, and bathtub failure rate function is created by compounding the generalized exponential distribution of Gupta and Kundu (1999) with a geometric distribution. Some basic distributional properties, moment-generating function, rth moment, and Rényi entropy of the new distribution are studied. The model parameters are estimated by the maximum likelihood method and the asymptotic distribution of estimators is discussed. Finally, an application of the new distribution is illustrated using the two real data sets.

Keywords:

• Bathtub failure rate
• Compound distribution
• Extended exponential-geometric distribution
• Goodness of fit
• Maximum likelihood estimation

Mathematics Subject Classification:

• 60E05
• 60E10

Acknowledgments

The authors would like to sincerely thank the Editor-in-Chief, referees, and also the Research Council and Graduate Office of Shiraz University for their support.