New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality

New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality

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 Zi...

Full description

Bibliographic Details
Main Authors: Khurshid Ahmad, Muhammad Adil Khan, Shahid Khan, Amjad Ali, Yu-Ming Chu
Format: Article
Language:English
Published: AIP Publishing LLC 2021-01-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/5.0039672
id doaj-36fb7dd02a6c4de9a3d0231373759c3b
record_format Article
spelling doaj-36fb7dd02a6c4de9a3d0231373759c3b2021-02-02T21:32:44ZengAIP Publishing LLCAIP Advances2158-32262021-01-01111015147015147-910.1063/5.0039672New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequalityKhurshid Ahmad0Muhammad Adil Khan1Shahid Khan2Amjad Ali3Yu-Ming Chu4Department of Statistics, Islamia College Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Statistics, Islamia College Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaZipf–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.http://dx.doi.org/10.1063/5.0039672
collection DOAJ
language English
format Article
sources DOAJ
author Khurshid Ahmad
Muhammad Adil Khan
Shahid Khan
Amjad Ali
Yu-Ming Chu
spellingShingle Khurshid Ahmad
Muhammad Adil Khan
Shahid Khan
Amjad Ali
Yu-Ming Chu
New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality
AIP Advances
author_facet Khurshid Ahmad
Muhammad Adil Khan
Shahid Khan
Amjad Ali
Yu-Ming Chu
author_sort Khurshid Ahmad
title New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality
title_short New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality
title_full New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality
title_fullStr New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality
title_full_unstemmed New estimation of Zipf–Mandelbrot and Shannon entropies via refinements of Jensen’s inequality
title_sort new estimation of zipf–mandelbrot and shannon entropies via refinements of jensen’s inequality
publisher AIP Publishing LLC
series AIP Advances
issn 2158-3226
publishDate 2021-01-01
description 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.
url http://dx.doi.org/10.1063/5.0039672
work_keys_str_mv AT khurshidahmad newestimationofzipfmandelbrotandshannonentropiesviarefinementsofjensensinequality
AT muhammadadilkhan newestimationofzipfmandelbrotandshannonentropiesviarefinementsofjensensinequality
AT shahidkhan newestimationofzipfmandelbrotandshannonentropiesviarefinementsofjensensinequality
AT amjadali newestimationofzipfmandelbrotandshannonentropiesviarefinementsofjensensinequality
AT yumingchu newestimationofzipfmandelbrotandshannonentropiesviarefinementsofjensensinequality
_version_ 1724291368258371584

Similar Items