Seven Means, Generalized Triangular Discrimination, and Generating Divergence Measures

Information

关键词: arithmetic mean;    geometric mean;    Heronian mean;    Hellinger’s distance;    triangular discrimination;    information inequalities;   

DOI  :  10.3390/info4020198

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.