Majorization, Csiszár divergence and Zipf-Mandelbrot law

DOI10.1186/s13660-017-1472-2zbMath1369.94404OpenAlexW2749979261WikidataQ41515806 ScholiaQ41515806MaRDI QIDQ2400774

Đilda Pečarić, Naveed Latif, Josip E. Pečarić

Publication date: 30 August 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-017-1472-2

zbMATH Keywords

Kullback-Leibler divergenceShannon entropyZipf-Mandelbrot lawmajorization inequalityCsiszár \( f\)-divergence

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Measures of information, entropy (94A17) Convexity of real functions in one variable, generalizations (26A51) Information theory (general) (94A15)

Related Items (9)

Difference equations related to majorization theorems via Montgomery identity and Green's functions with application to the Shannon entropy ⋮ On Zipf-Mandelbrot entropy ⋮ New estimates for Csiszár divergence and Zipf-Mandelbrot entropy via Jensen-Mercer's inequality ⋮ Majorization, ``useful Csiszár divergence and ``useful Zipf-Mandelbrot law ⋮ Hermite-Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions ⋮ Impure systems and ecological models. II: Components and thermodynamics ⋮ Majorizatiuon and Zipf-Mandelbrot law ⋮ Shannon type inequalities via time scales theory ⋮ On Shannon and Zipf-Mandelbrot entropies and related results

Uses Software

• trueskill
• TrueSkill

Cites Work

• A Mathematical Theory of Communication
• Convex functions, partial orderings, and statistical applications
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• Bounds for Shannon and Zipf-Mandelbrot entropies
• Improvements of some bounds on entropy measures in information theory
• On Information and Sufficiency
• Inequalities: theory of majorization and its applications
• On an inequality for the entropy of a probability distribution
• Convex functions and their applications. A contemporary approach
• Beyond the Zipf-Mandelbrot law in quantitative linguistics
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