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

Abstract EN

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.