A link of extropy to entropy for continuous random variables via the generalized ϕ –entropy

Communication in Statistics- Theory and Methods, vol. 54, pp. 2227–2245

Abstract

The concepts of entropy and divergence, along with their past, residual, and interval variants are revisited in a reliability theory context and generalized families of them that are based on ϕ-functions are discussed. Special emphasis is given in the parametric family of entropies and divergences of Cressie and Read. For non-negative and absolutely continuous random variables, the dual to Shannon entropy measure of uncertainty, the extropy, is considered and its link to a specific member of the ϕ-entropies family is shown. A number of examples demonstrate the implementation of the generalized entropies and divergences, exhibiting their utility.

Authors 2

1. Francesco Buono corresponding Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University

   Institute of Statistics, RWTH Aachen University, Aachen, Germany

2. Maria Kateri Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University

   Institute of Statistics, RWTH Aachen University, Aachen, Germany