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.
Highlights
Let nInformation 2013, 4 be the set of all complete finite discrete probability distributions
The above three measures are classical divergence measures in the literature on information theory and statistics known as Jensen-Shannon divergence, J-divergence and Arithmetic-Geometric mean divergence respectively
Connections Eve’s seven means with the non-logarithmic measures are given. We performed this through inequalities, where some new generalized means are presented
Summary
Information 2013, 4 be the set of all complete finite discrete probability distributions. The above three measures are classical divergence measures in the literature on information theory and statistics known as Jensen-Shannon divergence, J-divergence and Arithmetic-Geometric mean divergence respectively. These three measures bear the following two relations:. The above three measures ( P || Q ) , h( P || Q) and ( P || Q) are respectively known as triangular discrimination, Hellingar’s divergence and symmetric chi-square divergence These measures allow the following inequalities among the measures. The measure s ( P || Q) known as generalized arithmetic and geometric mean divergence Connections Eve’s seven means with the non-logarithmic measures are given We performed this through inequalities, where some new generalized means are presented
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