Some new results on the cumulative residual entropy

The residual entropy function is a relevant dynamic measure of uncertainty in reliability and survival studies. Recently, Rao et al. [2004. Cumulative residual entropy: a new measure of information. IEEE Transactions on Information Theory 50, 1220–1228] and Asadi and Zohrevand [2007. On the dynamic cumulative residual entropy. Journal of Statistical Planning and Inference 137, 1931–1941] define the cumulative residual entropy and the dynamic cumulative residual entropy, respectively, as some new measures of uncertainty. They study some properties and applications of these measures showing how the cumulative residual entropy and the dynamic cumulative residual entropy are connected with the mean residual life function. In this paper, we obtain some new results on these functions. We also define and study the dynamic cumulative past entropy function. Some results are given connecting these measures of a lifetime distribution and that of the associated weighted distribution.