A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization - Satish Kumar; Gurdas Ram (Abstract and Applied Analysis)
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 Hn(p1,…,pn; α, β, γ) - Hn-1(p1+p2, p3,…,pn; α, β, γ) = (A(α,γ)/(A(α,γ)-A(β,γ)))p1+p2α/γH2(p1/(p1+p2), p2/(p1+p2); α,γ) + (A(β,γ)/(A(β,γ)-A(α,γ)))(p1+p2)(β/γ)H2(p1/(p1+p2), p2/(p1+p2); 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.