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Entropies of the Poisson Distribution as Functions of Intensity: “Normal” and “Anomalous” Behavior
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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....
| Published in: | Methodology and Computing in Applied Probability |
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| ISSN: | 1387-5841 1573-7713 |
| Published: |
Springer Science and Business Media LLC
2025
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa69393 |
| 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. Additionally, we examine the asymptotic behavior of the entropies as λ →∞and provide both lower and upper bounds for them. |
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| Keywords: |
Shannon entropy; Rényi entropy; Tsallis entropy; Sharma–Mittal entropy; Poisson distribution |
| College: |
Faculty of Science and Engineering |
| Funders: |
Stiftelsen för Strategisk Forskning (UKR24-0004); Japan Science and Technology Agency (JPMJCR2115); Norges Forskningsråd (274410, 274410); Research Council of Finland (359815) |
| Issue: |
2 |