{
  "id": "2411.16913",
  "version": "v1",
  "published": "2024-11-25T20:32:12.000Z",
  "updated": "2024-11-25T20:32:12.000Z",
  "title": "Entropies of the Poisson distribution as functions of intensity: \"normal\" and \"anomalous\" behavior",
  "authors": [
    "Dmitri Finkelshtein",
    "Anatoliy Malyarenko",
    "Yuliya Mishura",
    "Kostiantyn Ralchenko"
  ],
  "categories": [
    "math.PR",
    "cs.IT",
    "math.IT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-25T20:32:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94A17"
    ],
    "keywords": [
      "poisson distribution",
      "paper extends",
      "asymptotic behavior",
      "sharma-mittal entropies",
      "renyi entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}