A Sequence of Inequalities among Difference of Symmetric Divergence Measures

Inder Jeet Taneja

Abstract


In this paper we have considered two one parametric generalizations. These two generalizations have in particular the well known measures such as: J-divergence, Jensen-Shannon divergence and arithmetic-geometric mean divergence. These three measures are with logarithmic expressions. Also, we have particular cases the measures such as: Hellinger discrimination, symmetric $\chi ^2$-divergence, and triangular discrimination. These three measures are also well-known in the literature of statistics, and are without logarithmic expressions. Still, we have one more non logarithmic measure as particular case calling it d-divergence. These seven measures bear an interesting inequality. Based on this inequality, we have considered different difference of divergence measures and established a sequence of inequalities among themselves.

Keywords


J-divergence; Jensen-Shannon divergence; Arithmetic-Geometric divergence; Triangular discrimination; Symmetric chi-square divergence; Hellinger's discrimination, d-divergence; Csiszar's f-divergence; Information inequalities

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DOI: http://dx.doi.org/10.26713%2Fjims.v3i1.42

eISSN 0975-5748; pISSN 0974-875X