Dynamic cumulative residual Renyi's entropy

Abstract

Abstract Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon's entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi's entropy, and study its properties. We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models. Keywords: cumulative residual entropyRenyi's entropyweighted distributionscharacterization AMS Subject Classifications : 62N0590B25 Acknowledgements The authors 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 of the paper.