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

Dmitri Finkelshtein (), Anatoliy Malyarenko (), Yuliya Mishura () and Kostiantyn Ralchenko ()
Additional contact information
Dmitri Finkelshtein: Swansea University
Anatoliy Malyarenko: Mälardalen University
Yuliya Mishura: Taras Shevchenko National University of Kyiv
Kostiantyn Ralchenko: Taras Shevchenko National University of Kyiv

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 2, 1-32

Abstract: Abstract The paper extends the analysis of the entropies of the Poisson distribution with parameter $$\lambda $$ λ . It demonstrates that the Tsallis and Sharma–Mittal entropies exhibit monotonic behavior with respect to $$\lambda $$ 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 $$\lambda \rightarrow \infty $$ λ → ∞ and provide both lower and upper bounds for them.

Keywords: Shannon entropy; Rényi entropy; Tsallis entropy; Sharma–Mittal entropy; Poisson distribution; 94A17; 60E05 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-025-10171-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10171-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-025-10171-9

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().