A new four-parameter discrete distribution with bathtub and unimodal failure rate

Abstract

In this paper, a discrete counterpart of the general class of continuous beta-G distributions is introduced. A discrete analog of the beta generalized exponential distribution of Barreto-Souza et al. [2], as an important special case of the proposed class, is studied. This new distribution contains some previously known discrete distributions as well as two new models. The hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Some distributional and moment properties of the new distribution as well as its order statistics are discussed. Estimation of the parameters is illustrated using the maximum likelihood method and, finally, the model with a real data set is examined.

Keywords:

• beta-G distributions
• beta generalized exponential distribution
• discrete generalized exponential distribution
• estimation
• hazard rate function
• order statistics
• stress–strength parameter

Acknowledgements

The authors sincerely thank three anonymous referees for their valuable comments that led to improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.