New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality
Source abstract
Abstract
Zipf–Mandelbrot and Shannon entropies are some basic and useful tools to quantify information about certain phenomena in various fields of science and technology, for example statistics, ecology, biology, and information theory. In this paper, we obtain some new bounds for generalized Shannon and Zipf–Mandelbrot entropies by using some specific refinements of Jensen’s inequality. Then, as a consequence of these bounds, we deduce some new bounds for Zipf–Mandelbrot and Shannon entropies. Finally, we demonstrate the sharpness of the proposed bounds through numerical experiments.
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Research context
OpenAlex topics: Mathematical Inequalities and Applications · Statistical Mechanics and Entropy · Multi-Criteria Decision Making
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Affiliations
Department of Statistics, Islamia College Peshawar 1 , Peshawar 25000, Pakistan
Department of Mathematics, University of Peshawar 2 , Peshawar 25000, Pakistan
Department of Mathematics, Huzhou University 3 , Huzhou 313000, China
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology 4 , Changsha 410114, China
Funding
Foundation for Innovative Research Groups of the National Natural Science Foundation of China
References (24)
Show source-provided references
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