On the weighted dynamic cumulative residual entropy and dynamic cumulative past entropy with applications: A survey

The main measure of the uncertainty contained in random variable X is the Shannon entropy H(X) = −E(log(f(X)). The cumulative entropy is an information measure which is alternative to the Shannon entropy and is connected with reliability theory. The cumulative residual entropy (CRE) introduced by Rao et al. (2004) is a generalized measure of uncertainty which is applied in reliability. Asadi and Zohrevand (2007) defined a dynamic version of the CRE by ε(X,t). In this paper, weighted residual entropy and weighted cumulative residual entropy are discussed. The properties of weighted entropy, cumulative residual entropy, weighted residual entropy, weighted cumulative residual entropy, weighted past entropy, weighted cumulative past entropy, dynamic cumulative residual entropy, dynamic cumulative past entropy, are also given.