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Majorization, Csiszár divergence and Zipf-Mandelbrot law
Naveed Latif1, Ðilda Pečarić2, Josip Pečarić3
1Department of Social Studies, Jubail Industrial College, Jubail, 31961 Kingdom of Saudi Arabia.
Journal of Inequalities and Applications
|September 15, 2017
Summary
This study links Shannon entropy and majorization theory, revealing stronger disorder criteria in majorization. Generalized majorization inequalities using Csiszár f-divergence offer new insights into entropy and divergence measures.
Area of Science:
- Information Theory
- Mathematical Physics
Background:
- Shannon entropy and majorization theory both quantify system disorder.
- Majorization theory often provides more stringent criteria than entropic inequalities.
Purpose of the Study:
- To explore the connection between Shannon entropy and majorization theory.
- To generalize majorization inequalities using Csiszár f-divergence.
- To apply these generalized inequalities to Shannon entropy and Kullback-Leibler divergence.
Main Methods:
- Utilizing Csiszár f-divergence with specific convex functions.
- Deriving generalized majorization inequalities.
- Investigating applications using the Zipf-Mandelbrot law.
Main Results:
- Established a link between Shannon entropy and majorization theory.
- Developed generalized majorization inequalities via Csiszár f-divergence.
- Demonstrated that Csiszár f-divergence can reduce majorization inequalities to Shannon entropy and Kullback-Leibler divergence forms.
Conclusions:
- The study provides a unified framework for understanding disorder measures.
- Generalized inequalities offer enhanced analytical power for information-theoretic systems.
- Applications of the Zipf-Mandelbrot law highlight the practical relevance of the findings.
Keywords:
Csiszár f-divergenceKullback-Leibler divergenceShannon entropyZipf-Mandelbrot lawmajorization inequalityMore Related Videos
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