A generalization of the Havrda-Charvat and Tsallis entropy and its axiomatic characterization

Abstract

In this communication, we characterize a measure of information of types α, β, and γ by taking certain axioms parallel to those considered earlier by Havrda and Charvat along with the recursive relation H n (p 1,., p n; α, β, γ) - H n - 1 (p 1 + p 2, p 3,., p n; α, β, γ) = (A (α, γ) / (A (α, γ) - A (β, γ))) p 1 + p 2 α / γ H 2 (p 1 / (p 1 + p 2), p 2 / (p 1 + p 2); α, γ) + (A (β, γ) / (A (β, γ) - A (α, γ))) (p 1 + p 2) (β / γ) H 2 (p 1 / (p 1 + p 2), p 2 / (p 1 + p 2); γ, β), α ≠ γ ≠ β, α, β, γ > 0. Some properties of this measure are also studied. This measure includes Shannon's information measure as a special case. © 2014 Satish Kumar and Gurdas Ram.