$$\phi $$-Extropy in Discrete and Continuous Settings

Methodology And Computing In Applied Probability, vol. 28

Abstract

Abstract The concept of $$\phi $$ ϕ -extropy is introduced as a generalization of extropy for discrete random variables, in analogy with Khinchin’s $$\phi $$ ϕ -entropy. The $$\phi $$ ϕ -extropy framework replaces the logarithmic function in the classical (Shannon) extropy definition with a convex function, yielding a flexible family of uncertainty measures. Its practical utility is demonstrated through applications to classification problems, where it is shown in two examples that performance can improve when using a member of the $$\phi $$ ϕ -family different from the classical extropy. Motivated by a conceptual critique of existing definitions of extropy in the continuous setting, a new definition is proposed based on the maximum of the probability density function and extended to continuous $$\phi $$ ϕ -extropy.

Authors 2

1. Francesco Buono

   University of Naples Federico II

   Affiliation as printed

   Department of Mathematics, Università degli Studi di Napoli Federico II, Naples, 80100, Italy

2. Maria Kateri corresponding Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Aachen, 52056, Germany