Bivariate Dynamic Weighted Failure Entropy of Order α

SYNOPTIC ABSTRACT

Recently, Rohini et al. (2017) proposed a measure of uncertainty based on the distribution function called weighted failure entropy of order α. In this article, we extend the definition of weighted failure entropy of order α to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending weighted failure entropy of order α for conditionally specified models. Several properties are obtained for conditional distributions. Along with some characterization results, it is shown that the proposed measure uniquely determines the distribution function. Moreover, we also proposed an empirical estimator for the new measure.

KEY WORDS AND PHRASES:

• Life distributions
• failure entropy
• ordering
• reliability

Acknowledgment

The authors wish to thank the editor in chief and referees for their valuable and constructive comments, which improved the earlier draft of the article.