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.

翻译：本文拓展了对参数为$\lambda$的泊松分布熵的分析。研究表明，Tsallis熵与Sharma-Mittal熵关于$\lambda$呈现单调特性，而两种广义Rényi熵形式则可能表现出"异常"（非单调）行为。此外，我们考察了当$\lambda \to \infty$时各熵的渐近行为，并给出了它们的上下界估计。