Some Properties of Weighted Distributions in the Context of Repairable Systems

ABSTRACT

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables.

Keywords:

• Maintainability function
• Reversed hazard rate
• Weighted distributions

Mathematics Subject Classification:

• 62E10
• 62N05

Acknowledgments

The authors wish to thank the referees and the editor for the very useful and constructive comments on the earlier version of this article, which led to a substantial improvement.