On the dynamic information measures

The fundamental tool of measuring the uncertainty in distribution function is the notion of entropy which was introduced into the information theory by Shannon (1948). Ebrahimi (1996) has introduced a dynamic measure of uncertainty. Recently, Rao et al (2004) have proposed a new measure of uncertainty, called cumulative residual entropy (CRE), in a distribution function F and obtained some properties and applications of that. In this paper, first we review some existing results on dynamic Shannon entropy. Then we concentrate on dynamic form of CRE which is recently proposed by Asadi and Zohrevand (2006). The proposed dynamic CRE measures the cumulative uncertainty in a residual lifetime random variable at time t 0. Several properties of dynamic CRE in connection with well known reliability measures such as the mean residual life time are discussed.

Keywords:

Shannon entropy , mean residual life function , reliability function , information theory , hazard rate.