ABSTRACT
In this Chapter we review some of the important generalizations of the Shannon entropy and the literature connecting them. After a brief introduction to the rationale behind the extensions of Shannon entropy the Renyi’s generalized entropy is discussed in Section2. The salient features discussed with reference to this measure are, order statistics and some weighted versions, monotonicity properties, stochastic orders, and estimation techniques. The quantile-based definition enables us to get several new results. Besides these several results pertaining to past Reny entropy is given along with the concept of relative Renyi entropy and applications. Section 4.3 deals with similar results on Tsallis entropy its residual, past and quantile versions. The Varma entropy form the discussions in Section 4.4 and a brief introduction to other generalizations are made in Section 4.5. Several examples are given for various concepts and applications of the results in this chapter.
