Characterizations of distributions using log odds rate

Abstract

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.

Keywords:

• Log odds rate
• Hazard rate
• Reversed hazard rate
• Weighted models

Acknowledgements

The authors wish to thank the referees and the editor for the very useful and constructive comments on the earlier version of this paper, which have led to a substantial improvement. The third author wishes to acknowledge University Grants Commission, India for the financial assistance for carrying out this research work.