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

Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures

Received: 4 January 2013; in revised form: 17 February 2013 / Accepted: 28 March 2013 / Published: 24 April 2013
(This article belongs to the Section Information Applications)
View Full-Text   |   Download PDF [267 KB, uploaded 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 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |
EndNote


MDPI and ACS Style

Taneja, I.J. Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures. Information 2013, 4, 198-239.

AMA Style

Taneja IJ. Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures. Information. 2013; 4(2):198-239.

Chicago/Turabian Style

Taneja, Inder J. 2013. "Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures." Information 4, no. 2: 198-239.

Information EISSN 2078-2489 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert