Abstract
Abstract In this communication, we characterize a measure of information of type (α, β, γ) by taking certain axioms parallel to those considered earlier by Harvda and Charvat along with the recursive relation (1.7). Some properties of this measure are also studied. This measure includes Shannon information measure as a special case
Highlights
Shannon’s measure of entropy for a discrete probability distribution nP = (p1, ...., pn), pi ≥ 0, pi = 1, i=1 given by nH(P ) = − pi log pi i=1 has been characterized in several ways
1, we introduce the following axioms: (1) Hn(p1, ..., pn; α, β, γ) is continuous in the region pi ≥ 0, n i=1 pi
The Shannon measure included in the (α, β, γ) information measure for the limiting case α = γ = 1 and β → 1 or β = γ = 1 and α → 1
Summary
For the above distribution P, as the basic postulate, and (ii) Chaundy and McLeod [3], who studied the functional equation nm n m f (piqj) = f (pi) + f (qj) i=1 j=1 i=1 j=1 f or pi ≥ 0, qj ≥ 0 Both the above mentioned approaches have been extensively exploited and generalized. Later on Tsallis[8] gave the applications of (1.5) in Physics In this communication, we characterized the measure (1.4) by taking certain axioms parallel to those considered earlier by Harvda and Charvat[6] along with the recursive relation (1.7). We characterized the measure (1.4) by taking certain axioms parallel to those considered earlier by Harvda and Charvat[6] along with the recursive relation (1.7) Some properties of this measure are studied.
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