A Sequence of Inequalities among Difference of Symmetric Divergence Measures

Authors

  • Inder Jeet Taneja Departamento de Matematica, Universidade Federal de Santa Catarina, 88.040-900 Florianopolis, SC, Brazil

DOI:

https://doi.org/10.26713/jims.v3i1.42

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

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.

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CITATION

How to Cite

Taneja, I. J. (2011). A Sequence of Inequalities among Difference of Symmetric Divergence Measures. Journal of Informatics and Mathematical Sciences, 3(1), 55–78. https://doi.org/10.26713/jims.v3i1.42

Issue

Vol. 3 No. 1 (2011)

Section

Research Articles

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