The Marshall–Olkin extended generalized Lindley distribution: Properties and applications

ABSTRACT

In this article, we define and study a new three-parameter model called the Marshall–Olkin extended generalized Lindley distribution. We derive various structural properties of the proposed model including expansions for the density function, ordinary moments, moment generating function, quantile function, mean deviations, Bonferroni and Lorenz curves, order statistics and their moments, Rényi entropy and reliability. We estimate the model parameters using the maximum likelihood technique of estimation. We assess the performance of the maximum likelihood estimators in a simulation study. Finally, by means of two real datasets, we illustrate the usefulness of the new model.

KEYWORDS:

• Generalized Lindley distribution
• Marshall–Olkin distribution
• Maximum likelihood estimation
• Moments
• Observed information matrix

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60E05, 62E15, 62F10
• Secondary 33B15, 33F05, 41A58

Acknowledgments

The author would like to thank the two anonymous reviewers for their valuable comments and suggestions that helped to improve this article.