Reliability Studies of the Log-Exponential Inverse Gaussian Distribution

Abstract

In this article, we investigate the monotonicity of the density, failure rate, and mean residual life functions of the log-exponential inverse Gaussian distribution. It turns out that, in this case, the monotonicity of the density, failure rate, and mean residual life functions take different forms depending on the range of the parameters. Maximum likelihood estimators of the critical points of the density, failure rate, and mean residual life functions of the model are evaluated using Monte Carlo simulations. An example of a published data set is used to illustrate the estimation of the critical points.

Keywords:

• Bathtub shaped
• Critical points
• Failure rate
• Log-EIG distribution
• Mean residual life
• Monotonicity
• Upside-down bathtub shaped

Mathematics Subject Classification:

• Primary 62N05
• Secondary 62N02

Acknowledgments

The authors are grateful to the Editor-in-Chief and the referee for their constructive suggestions which enhanced the presentation of the article.