On an Extension of the Exponentiated Weibull Distribution

Abstract

In this article, the exponentiated Weibull distribution is extended by the Marshall-Olkin family. Our new four-parameter family has a hazard rate function with various desired shapes depending on the choice of its parameters and, thus, it is very flexible in data modeling. It also contains two mixed distributions with applications to series and parallel systems in reliability and also contains several previously known lifetime distributions. We shall study some basic distributional properties of the new distribution. Some closed forms are derived for its moment generating function and moments as well as moments of its order statistics. The model parameters are estimated by the maximum likelihood method. The stress–strength parameter and its estimation are also investigated. Finally, an application of the new model is illustrated using two real datasets.

Keywords:

• Beta-generalized (exponentiated) Weibull distribution
• Compounding
• Marshall–Olkin family
• Maximum likelihood estimation
• Mixing
• Stress–strength parameter

Mathematics Subject Classification:

• 60E05
• 62E10

Acknowledgments

The authors sincerely thank the associate editor and the two anonymous referees for carefully reading the article and whose useful suggestions led to the improvement of the article.