ABSTRACT
The cumulative entropy was introduced as an alternative to the Shannon entropy. In Section 1 the definition and properties of cumulative entropy as a measure of uncertainty is explained. Further the modification of this measure to accommodate residual life is explained in the next section along with some characterizations. Classes of distributions with monotone cumulative entropy are given special attention. The relationship cumulative entropy has with mean residual life at designated and random times are also discussed. The concept of cumulative entropy was further extended to that of order n and their properties are derived in different contexts. A separate analysis of weighted cumulative entropy is made in Section 5. The measure for past life is considered in Section 6. The quantile-based measure leaves scope for new models and resulting ageing properties. The applications of the results in income modelling, total time of test transforms etc are of special interest to other disciplines. The Chapter ends with some methods of estimation, results on and relative mean residual life and stochastic orderings.
