Superquadratic Functions in Information Theory

Using Jensen’s inequality and the converse Jensen’s inequality for superquadratic functions we obtain new estimates for Shannon’s entropy of the random variable X and derive new lower and upper bounds for the Shannon entropy in the terms of the Zipf and Zipf- Mandelbrot’s law. © 2020. All Rights Reserved.

Authors
Bari´C J. 1 , Peˇcari´C Đ. 2 , Peˇcari´C J. 3
Journal
Journal of Mathematical Inequalities
Publisher
Element D.O.O.
Issue number
4
Language
English
Pages
1321-1331
State
Published
Link
External link
DOI
10.7153/JMI-2020-14-85
Volume
14
Year
2020
Organizations
  • 1 University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Rud-era Bosˇkovic´a 32, Split, 21 000, Croatia
  • 2 Catholic University of Croatia, Ilica 242, Zagreb, 10000, Croatia
  • 3 RUDN University, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
Keywords
Jensen’s inequality; Shannon entropy; Superquadratic function; Zipf- Mandelbrot’s law
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