Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 820375, 9 pages
http://dx.doi.org/10.1155/2014/820375
Research Article

Bounds on Nonsymmetric Divergence Measure in terms of Other Symmetric and Nonsymmetric Divergence Measures

1Department of Mathematics, Malaviya National Institute of Technology, Jaipur, Rajasthan 302017, India
2B-1, Staff Colony, MNIT, Jaipur, Rajasthan 302017, India

Received 5 June 2014; Accepted 5 September 2014; Published 29 October 2014

Academic Editor: Angelo De Santis

Copyright © 2014 K. C. Jain and Praphull Chhabra. 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.

Abstract

Vajda (1972) studied a generalized divergence measure of Csiszar’s class, so called “Chi- divergence measure.” Variational distance and Chi-square divergence are the special cases of this generalized divergence measure at and , respectively. In this work, nonparametric nonsymmetric measure of divergence, a particular part of Vajda generalized divergence at , is taken and characterized. Its bounds are studied in terms of some well-known symmetric and nonsymmetric divergence measures of Csiszar’s class by using well-known information inequalities. Comparison of this divergence with others is done. Numerical illustrations (verification) regarding bounds of this divergence are presented as well.