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2014 A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization
Satish Kumar, Gurdas Ram
Abstr. Appl. Anal. 2014: 1-8 (2014). DOI: 10.1155/2014/505184

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), αγβ, α, β, γ>0. Some properties of this measure are also studied. This measure includes Shannon’s information measure as a special case.

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Satish Kumar. Gurdas Ram. "A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/505184

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022505
MathSciNet: MR3173278
Digital Object Identifier: 10.1155/2014/505184

Rights: Copyright © 2014 Hindawi

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