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Information 2013, 4(2), 198-239; doi:10.3390/info4020198
Article

Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures

Department of Mathematics, Federal University of Santa Catarina, Florianópolis, SC 88040-900, Brazil Retired. Current Address: R. Desembargador Vitor Lima, 354, Apt. 402, Bl. A, Carvoeira, Florian
Received: 4 January 2013 / Revised: 17 February 2013 / Accepted: 28 March 2013 / Published: 24 April 2013
(This article belongs to the Section Information Applications)
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Abstract

Jensen-Shannon, J-divergence and Arithmetic-Geometric mean divergences are three classical divergence measures known in the information theory and statistics literature. These three divergence measures bear interesting inequality among the three non-logarithmic measures known as triangular discrimination, Hellingar’s divergence and symmetric chi-square divergence. However, in 2003, Eve studied seven means from a geometrical point of view, which are Harmonic, Geometric, Arithmetic, Heronian, Contra-harmonic, Root-mean square and Centroidal. In this paper, we have obtained new inequalities among non-negative differences arising from these seven means. Correlations with generalized triangular discrimination and some new generating measures with their exponential representations are also presented.
Keywords: arithmetic mean; geometric mean; Heronian mean; Hellinger’s distance; triangular discrimination; information inequalities arithmetic mean; geometric mean; Heronian mean; Hellinger’s distance; triangular discrimination; information inequalities
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Taneja, I.J. Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures. Information 2013, 4, 198-239.

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