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arXiv · 1201.4285

On Shore and Johnson properties for a Special Case of Csiszár f-divergences

Jithin Vachery·Ambedkar Dukkipati
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Abstract

The importance of power-law distributions is attributed to the fact that most of the naturally occurring phenomenon exhibit this distribution. While exponential distributions can be derived by minimizing KL-divergence w.r.t some moment constraints, some power law distributions can be derived by minimizing some generalizations of KL-divergence (more specifically some special cases of Csiszár f-divergences). Divergence minimization is very well studied in information theoretical approaches to statistics. In this work we study properties of minimization of Tsallis divergence, which is a special case of Csiszár f-divergence. In line with the work by Shore and Johnson (IEEE Trans. IT, 1981), we examine the properties exhibited by these minimization methods including the Pythagorean property.

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Jithin Vachery, Ambedkar Dukkipati. 2012-07-16. On Shore and Johnson properties for a Special Case of Csiszár f-divergences. https://arxiv.org/abs/1201.4285

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