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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; in revised form: 17 February 2013 / Accepted: 28 March 2013 / Published: 24 April 2013
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
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MDPI and ACS Style
Taneja, I.J. Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures. Information 2013, 4, 198-239.
Taneja IJ. Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures. Information. 2013; 4(2):198-239.
Taneja, Inder J. 2013. "Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures." Information 4, no. 2: 198-239.