New estimates for generalized Shannon and Zipf-Mandelbrot entropies via convexity results

被引：13

作者：

Ahmad, Khurshid ^{[1
]}

Khan, Muhammad Adil ^{[2
]}

Khan, Shahid ^{[2
]}

Ali, Amjad ^{[1
]}

Chu, Yu-Ming ^{[3
,4
]}

机构：

[1] Islamia Coll Peshawar, Dept Stat, Peshawar 25000, Pakistan

[2] Univ Peshawar, Dept Math, Peshawar 25000, Pakistan

[3] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China

[4] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China

来源：

RESULTS IN PHYSICS | 2020年 / 18卷

关键词：

Jensen inequality; Convex function; Shannon entropy; Zipf-Mandelbrot entropy;

D O I：

10.1016/j.rinp.2020.103305

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Shannon and Zipf-Mandelbrot entropies have several applications in various fields such as ecology, statistics, physics and information theory etc. The aim of this article is to utilize some results of Jensen's inequality for convex functions and to present several new estimates for generalized Zipf-Mandelbrot and Shannon entropies. In particular, we deduce estimates for Shannon and Zipf-Mandelbrot entropies which are different from the estimates obtained earlier using the same results of Jensen's inequality. This way of obtaining the results for these entropies may open a new door to obtain several other estimates by using results for convex functions.

引用

页数：7

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