A link of extropy to entropy for continuous random variables via the generalized <italic>ϕ</italic>–entropy.

AbstractThe 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 <italic>ϕ</italic>-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 <italic>ϕ</italic>-entropies family is shown. A number of examples demonstrate the implementation of the generalized entropies and divergences, exhibiting their utility. [ABSTRACT FROM AUTHOR]