ABSTRACT
The Chapter begins with an introduction to entropy and the various developments in that area and also in Section 2 some important aspects of differential entropy and its quantile form are discussed. The Shannon measure is suitably modified to write the entropy of residual life, relationships with hazard rate, mean residual life and various characterizations, are reviewed. Some new lifetime models and monotone residual entropy and classes of life distributions based on it are also part of Section 4. The quantile-based residual entropy and its characteristics are mentioned in Section 5 along with some new results and methodologies. The next two sections deal with weighted entropy and stochastic orders that enable comparison of uncertainties in two distributions. This is followed by inference procedures like estimation and testing. Quite recently the notion of extropy that can also provide a measure of uncertainty was proposed. We discuss the definition and properties of extropy including some new results in the last section.
