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Bounds for Shannon and Zipf-Mandelbrot entropies
- Source :
- Mathematical Methods in the Applied Sciences. 40:7316-7322
- Publication Year :
- 2017
- Publisher :
- Wiley, 2017.
-
Abstract
- Shannon and Zipf-Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well-know Jensen inequality and obtain different bounds for Shannon and Zipf-Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf-Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf-Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf-Mandelbrot entropy.
- Subjects :
- convex function
Jensen inequality
Shannon entropy
Zipf-Mandelbrot entropy
Discrete mathematics
Mathematics::Dynamical Systems
Shannon's source coding theorem
General Mathematics
010102 general mathematics
General Engineering
Maximum entropy thermodynamics
Min entropy
Entropy in thermodynamics and information theory
01 natural sciences
010101 applied mathematics
Rényi entropy
Entropy power inequality
Combinatorics
0101 mathematics
Entropic uncertainty
Limiting density of discrete points
Mathematics
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi.dedup.....4e056ae9cc394e288e6e6ff68374ed94