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

Francesco Buono and Maria Kateri

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 8, 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.

Date: 2025
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DOI: 10.1080/03610926.2024.2363869

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