On Zipf-Mandelbrot entropy

DOI10.1016/j.cam.2018.07.002zbMath1452.26021OpenAlexW2884400151MaRDI QIDQ1624634

Muhammad Adil Khan, Đilda Pečarić, Josip E. Pečarić

Publication date: 16 November 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.07.002

zbMATH Keywords

convex functionsJensen inequalityCsiszar divergenceSlater inequalityZipf-Mandelbrot entropy

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Measures of information, entropy (94A17) Information theory (general) (94A15)

Related Items (17)

New converses of Jensen inequality via Green functions with applications ⋮ Refinements of Jensen's inequality via majorization results with applications in the information theory ⋮ Some inequalities for Csiszár divergence via theory of time scales ⋮ Generalizations of cyclic refinements of Jensen's inequality by Lidstone's polynomial with applications in information theory ⋮ New estimates for Csiszár divergence and Zipf-Mandelbrot entropy via Jensen-Mercer's inequality ⋮ New improvements of Jensen's type inequalities via 4-convex functions with applications ⋮ A new refinement of the Jensen inequality with applications in information theory ⋮ Unnamed Item ⋮ New bounds for Shannon, relative and Mandelbrot entropies via Abel-Gontscharoff interpolating polynomial ⋮ On Shannon and Zipf-Mandelbrot entropies and related results ⋮ Generalized Steffensen's inequality by Montgomery identity ⋮ Several new cyclic Jensen type inequalities and their applications ⋮ New refinement of the Jensen inequality associated to certain functions with applications ⋮ Estimation of f-divergence and Shannon entropy by using Levinson type inequalities for higher order convex functions via Hermite interpolating polynomial ⋮ Estimation of divergence measures via Weighted Jensen inequality on time scales ⋮ Unnamed Item ⋮ Generalized cyclic Jensen and information inequalities

Cites Work

• A companion to Jensen-Steffensen's inequality
• A counterpart of Jensen's discrete inequality for differentiable convex mappings and applications in information theory
• Majorization, Csiszár divergence and Zipf-Mandelbrot law
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• A formal derivation of Heaps' law
• Bounds for Shannon and Zipf-Mandelbrot entropies
• Some companion inequalities to Jensen's inequality
• Refinements of some majorization type inequalities
• Improvement of Jensen's Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications
• Beyond the Zipf-Mandelbrot law in quantitative linguistics
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