A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization. (19th February 2014)

• Record Type: Journal Article
• Authors: Kumar, Satish; Ram, Gurdas
• Other Names: Zhang Chengjian Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-02-19
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/505184
• Languages: English
• ISSNs: 1085-3375

Abstract

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.