Abstract
The concepts of cumulative residual entropy (CRE) and dynamic cumulative residual entropy (DCRE) were defined first in the continuous case by Rao et al. (2004), Rao (2005) and Asadi and Zohrevand (2007). In this paper, we define and study the discrete version of CRE and obtain a lower bound for it based on mean residual life (MRL) function. Also its relation with the class of new better (worse) than used in expectation and hazard rate is achieved. Furthermore the discrete version of normalised CRE (NCRE) is defined and illustrated by some examples. Also, the DCRE in the discrete case is introduced and a lower (an upper) bound is obtained. Finally, it is shown that the DCRE can characterise the distribution function and an example of real data is presented.
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