Zipf-Mandelbrot law, \(f\)-divergences and the Jensen-type interpolating inequalities

DOI10.1186/s13660-018-1625-yzbMath1412.94137OpenAlexW2787931981WikidataQ49885413 ScholiaQ49885413MaRDI QIDQ681513

Đilda Pečarić, Neda Lovričević, Josip E. Pečarić

Publication date: 12 February 2018

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

Full work available at URL: https://doi.org/10.1186/s13660-018-1625-y

zbMATH Keywords

Kullback-Leibler divergenceJensen inequality\(f\)-divergencesCsiszár divergence functionalZipf and Zipf-Mandelbrot law

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 (13)

Refinement of Jensen's inequality and estimation of \(f\)- and Rényi divergence via Montgomery identity ⋮ Unnamed Item ⋮ New converses of Jensen inequality via Green functions with applications ⋮ A new approach for the derivation of bounds for the Jensen difference ⋮ Estimation of different entropies via Lidstone polynomial using Jensen-type functionals ⋮ Hermite-Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions ⋮ Estimation of different entropies via Hermite interpolating polynomial using Jensen-type functionals ⋮ Monotonicity of the Jensen functional for f-divergences with applications to the Zipf-Mandelbrot law ⋮ About the sharpness of the Jensen inequality ⋮ RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory ⋮ Generalization of the Levinson inequality with applications to information theory ⋮ Estimation of different entropies via Abel–Gontscharoff Green functions and Fink’s identity using Jensen type functionals ⋮ A new bound for the Jensen gap pertaining twice differentiable functions with applications

Cites Work

• A Mathematical Theory of Communication
• Superadditivity of the Levinson functional and applications
• Properties of some functionals related to Jensen's inequality
• On the properties of McShane's functional and their applications
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• Rényi Divergence and Kullback-Leibler Divergence
• On Information and Sufficiency
• Beyond the Zipf-Mandelbrot law in quantitative linguistics
• Computational linguistics and intelligent text processing. 2nd international conference, CICLing 2001, Mexico City, Mexico, February 18--24, 2001. Proceedings
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