A Generalization of the Havrda‐Charvat and Tsallis Entropy and Its Axiomatic Characterization

Satish Kumar and Gurdas Ram

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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 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.

Date: 2014
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https://doi.org/10.1155/2014/505184

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:505184

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