On Unified Generalizations of Relative Jensen--Shannon and Arithmetic--Geometric Divergence Measures, and Their Properties

2005/01/19 by Pranesh Kumar, Inder J. Taneja, Kumar, Pranesh +1
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #FOS: Mathematics #Mathematical Inequalities and Applications #Statistical Mechanics and Entropy #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0501299

openalex publication_date 2005/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we shall consider one parametric generalization of some non-symmetric divergence measures. The non-symmetric divergence measures are such as: Kullback-Leibler relative information, χ²-divergence, relative J -- divergence, relative Jensen -- Shannon divergence and relative Arithmetic -- Geometric divergence. All the generalizations considered can be written as particular cases of Csiszár's f-divergence. By putting some conditions on the probability distribution, the aim here is to develop bounds on these measures and their parametric generalizations.

Citations

• Inequalities Among Symmetric Divergence Measures and Their Refinement
• On Information and Sufficiency
• Divergence measures based on the Shannon entropy

Related

• Generalized Non-Symmetric Divergence Measures and Inequalities
• Bounds on Non-Symmetric Divergence Measures in Terms of Symmetric Divergence Measures
• Relative Divergence Measures and Information Inequalities
• Generalized Symmetric Divergence Measures and Inequalities
• Inequalities Among Symmetric Divergence Measures and Their Refinement