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

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.