Elements of Generalized Tsallis Relative Entropy in Classical Information Theory

08/05/2019

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by   Supriyo Dutta, et al.

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In this article, we propose a modification in generalised Tsallis entropy which makes it efficient to be utilized in classical information theory. This modification offers the product rule (xy)^r + k_{k,r}(xy) = x^r + k_{k,r}(x) + y^r + k_{k,r}(y) + 2k x^r + k y^r + k_{k,r}(x)_{k,r}(y), for the two-parameter deformed logarithm _{k,r}(x) = x^r x^k - x^-k/2k. It assists us to derive a number of properties of the generalised Tsallis entropy, and related entropy for instance the sub-additive property, joint convexity, and information monotonicity. This article is an exposit investigation on the information-theoretic, and information-geometric characteristics of generalised Tsallis entropy.