New Estimations for Shannon and Zipf–Mandelbrot Entropies

Entropy. 2018;20(8):608 DOI 10.3390/e20080608

 

Journal Homepage

Journal Title: Entropy

ISSN: 1099-4300 (Online)

Publisher: MDPI AG

LCC Subject Category: Science: Astronomy: Astrophysics | Science: Physics

Country of publisher: Switzerland

Language of fulltext: English

Full-text formats available: PDF, HTML, XML

 

AUTHORS

Muhammad Adil Khan (College of Science, Hunan City University, Yiyang 413000, China)
Zaid Mohammad Al-sahwi (Department of Mathematics, University of Sa’adah, Sa’adah 1872, Yemen)
Yu-Ming Chu (Department of Mathematics, Huzhou University, Huzhou 313000, China)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 11 weeks

 

Abstract | Full Text

The main purpose of this paper is to find new estimations for the Shannon and Zipf–Mandelbrot entropies. We apply some refinements of the Jensen inequality to obtain different bounds for these entropies. Initially, we use a precise convex function in the refinement of the Jensen inequality and then tamper the weight and domain of the function to obtain general bounds for the Shannon entropy (SE). As particular cases of these general bounds, we derive some bounds for the Shannon entropy (SE) which are, in fact, the applications of some other well-known refinements of the Jensen inequality. Finally, we derive different estimations for the Zipf–Mandelbrot entropy (ZME) by using the new bounds of the Shannon entropy for the Zipf–Mandelbrot law (ZML). We also discuss particular cases and the bounds related to two different parametrics of the Zipf–Mandelbrot entropy. At the end of the paper we give some applications in linguistics.