{
  "id": "2311.15184",
  "version": "v1",
  "published": "2023-11-26T04:22:10.000Z",
  "updated": "2023-11-26T04:22:10.000Z",
  "title": "Factorial moments of the Poisson distribution of order $k$",
  "authors": [
    "S. R. Mane"
  ],
  "comment": "6 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "The factorial moments of the standard Poisson distribution are well known. The present note presents an explicit combinatorial sum for the factorial moments of the Poisson distribution of order $k$. Unlike the standard Poisson distribution (the case $k=1$), for $k>1$ the structure of the factorial moments is much more complicated. Some properties of the factorial moments of the Poisson distribution of order $k$ are elucidated in this note.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-26T04:22:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "39B05",
      "11B37",
      "05-08"
    ],
    "keywords": [
      "factorial moments",
      "standard poisson distribution",
      "explicit combinatorial sum",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}