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][1932][1933][1934][1935][1936][1937][1938][1939][1940][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.

In this paper the residual Kullback-Leibler discrimination information measure is extended to conditionally specified models. The extension is used to characterize some bivariate distributions. These distributions are also characterized in terms of proportional hazard rate models and weighted distributions. Moreover, we also obtain some bounds for this dynamic discrimination function by using the likelihood ratio order and some preceding results.

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Abtsrcat Recently, Rao (2005) introduced an alternate measure of uncertainty called cumulative entropy that parallels Shannon entropy (see Asadi (2007)). Motivated by this, in the present paper, we introduce cumulative entropies for two types of conditionally specied models. Finally, an applica- tion of the cumulative entropy using the maximum entropy principle is also illustrated.

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