A new family of lifetime models

Abstract

We introduce a new family of distributions by adding a parameter to the Marshall–Olkin family of distributions. Some properties of the new family of distributions are derived. A particular case of the family, a three-parameter generalization of the exponential distribution, is given special attention. The shape properties, moments, distributions of the order statistics, entropies and estimation procedures are derived. An application to a real data set is discussed.

Keywords:

• exponential distribution
• Marshall–Olkin family of distributions
• truncated negative binomial distribution

Acknowledgements

The authors would like to thank the Editor-in-Chief, the Associate Editor, and the referee for their careful reading and comments which greatly improved the paper. The third author acknowledges the grant of MNTR 174013 for carrying out this research.