Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior

Dmitri Finkelshtein; Anatoliy Malyarenko; Yuliya Mishura; Kostiantyn Ralchenko

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arXiv · 2411.16913

Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior

Dmitri Finkelshtein·Anatoliy Malyarenko·Yuliya Mishura·Kostiantyn Ralchenko

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Abstract

The paper extends the analysis of the entropies of the Poisson distribution with parameter $\lambda$. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to $\lambda$, whereas two generalized forms of the R\'enyi entropy may exhibit "anomalous" (non-monotonic) behavior. Additionally, we examine the asymptotic behavior of the entropies as $\lambda \to \infty$ and provide both lower and upper bounds for them.

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Dmitri Finkelshtein, Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko. 2024-11-25. Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior. https://arxiv.org/abs/2411.16913

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