An ordered approach on cumulative extropy measures for information analysis

Abstract

The present study focus on the ordered approach of random variables in the analysis of uncertainty using cumulative extropy and its dynamic versions. Some important results regarding bounds, aging properties and orderings of cumulative extropy measures based on order statistics have been discussed. The study also presents characterizations of some probability distribution, identical distribution of random variables and symmetry of a probability distribution using cumulative extropy measures based on extreme order statistics. Further, a simple empirical estimator has been proposed to estimate dynamic failure extropy using a real life data set.

Keywords:

• Survival extropy
• failure extropy
• dynamic survival extropy
• dynamic failure extropy
• order statistics

Acknowledgements

The authors like to cordially thank the Editor, the Associate Editor and the Reviewers for their supportive comments and suggestions to improve the earlier version of the manuscript.