Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910714239647744 |
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| author | Finkelshtein, Dmitri Malyarenko, Anatoliy Mishura, Yuliya Ralchenko, Kostiantyn |
| author_facet | Finkelshtein, Dmitri Malyarenko, Anatoliy Mishura, Yuliya Ralchenko, Kostiantyn |
| contents | 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 $λ\to \infty$ and provide both lower and upper bounds for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior Finkelshtein, Dmitri Malyarenko, Anatoliy Mishura, Yuliya Ralchenko, Kostiantyn Probability Information Theory 94A17 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 $λ\to \infty$ and provide both lower and upper bounds for them. |
| title | Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior |
| topic | Probability Information Theory 94A17 |
| url | https://arxiv.org/abs/2411.16913 |