The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data

ABSTRACT

In this article, a two-parameter generalized inverse Lindley distribution capable of modeling a upside-down bathtub-shaped hazard rate function is introduced. Some statistical properties of proposed distribution are explicitly derived here. The method of maximum likelihood, least square, and maximum product spacings are used for estimating the unknown model parameters and also compared through the simulation study. The approximate confidence intervals, based on a normal and a log-normal approximation, are also computed. Two algorithms are proposed for generating a random sample from the proposed distribution. A real data set is modeled to illustrate its applicability, and it is shown that our distribution fits much better than some other existing inverse distributions.

Keywords:

• Entropy
• Generalized inverse Lindley distribution
• Moments
• Parameter estimation
• Quantile function
• Stochastic ordering
• Stress-strength reliability.

Mathematics Subject Classification:

• 60E05
• 62F10

Acknowledgment

The authors would like to thank the editor-in-chief Professor N. Balakrishnan and two anonymous referees for their constructive suggestions that greatly improved the last version of this manuscript.