Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior

Finkelshtein, Dmitri; Malyarenko, Anatoliy; Mishura, Yuliya; Ralchenko, Kostiantyn

doi:10.1007/s11009-025-10171-9

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Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior

Dmitri Finkelshtein

, Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko

Methodology and Computing in Applied Probability, Volume: 27, Issue: 2

Swansea University Author: Dmitri Finkelshtein

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DOI (Published version): 10.1007/s11009-025-10171-9

Abstract

The paper extends the analysis of the entropies of the Poisson distribution with parameter λ.It demonstrates that the Tsallis and Sharma–Mittal entropies exhibit monotonic behavior with respect to λ, whereas two generalized forms of the Rényi entropy may exhibit “anomalous” (non-monotonic) behavior....

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Published in:	Methodology and Computing in Applied Probability
ISSN:	1387-5841 1573-7713
Published:	Springer Science and Business Media LLC 2025
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa69393

first_indexed	2025-05-01T10:08:33Z
last_indexed	2025-06-03T04:46:55Z
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spelling	2025-06-02T14:15:13.4895967 v2 69393 2025-05-01 Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2025-05-01 MACS The paper extends the analysis of the entropies of the Poisson distribution with parameter λ.It demonstrates that the Tsallis and Sharma–Mittal entropies exhibit monotonic behavior with respect to λ, whereas two generalized forms of the Rényi entropy may exhibit “anomalous” (non-monotonic) behavior. Additionally, we examine the asymptotic behavior of the entropies as λ →∞and provide both lower and upper bounds for them. Journal Article Methodology and Computing in Applied Probability 27 2 Springer Science and Business Media LLC 1387-5841 1573-7713 Shannon entropy; Rényi entropy; Tsallis entropy; Sharma–Mittal entropy; Poisson distribution 22 5 2025 2025-05-22 10.1007/s11009-025-10171-9 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) Stiftelsen för Strategisk Forskning (UKR24-0004); Japan Science and Technology Agency (JPMJCR2115); Norges Forskningsråd (274410, 274410); Research Council of Finland (359815) 2025-06-02T14:15:13.4895967 2025-05-01T11:01:40.2979018 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Anatoliy Malyarenko 2 Yuliya Mishura 3 Kostiantyn Ralchenko 4 69393__34380__5af9ae732dd6427c81663317f08b8f3c.pdf 69393.VoR.pdf 2025-06-02T14:13:36.8338790 Output 3026829 application/pdf Version of Record true © The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License. true eng http://creativecommons.org/licenses/by/4.0/
title	Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior
spellingShingle	Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior Dmitri Finkelshtein
title_short	Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior
title_full	Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior
title_fullStr	Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior
title_full_unstemmed	Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior
title_sort	Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior
author_id_str_mv	4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv	4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author	Dmitri Finkelshtein
author2	Dmitri Finkelshtein Anatoliy Malyarenko Yuliya Mishura Kostiantyn Ralchenko
format	Journal article
container_title	Methodology and Computing in Applied Probability
container_volume	27
container_issue	2
publishDate	2025
institution	Swansea University
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doi_str_mv	10.1007/s11009-025-10171-9
publisher	Springer Science and Business Media LLC
college_str	Faculty of Science and Engineering
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department_str	School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
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description	The paper extends the analysis of the entropies of the Poisson distribution with parameter λ.It demonstrates that the Tsallis and Sharma–Mittal entropies exhibit monotonic behavior with respect to λ, whereas two generalized forms of the Rényi entropy may exhibit “anomalous” (non-monotonic) behavior. Additionally, we examine the asymptotic behavior of the entropies as λ →∞and provide both lower and upper bounds for them.
published_date	2025-05-22T05:23:49Z
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Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior

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