{
  "id": "2310.08615",
  "version": "v1",
  "published": "2023-10-12T12:34:05.000Z",
  "updated": "2023-10-12T12:34:05.000Z",
  "title": "Alternative combinatorial sum for the probability mass function of the Poisson distribution of order $k$",
  "authors": [
    "S. R. Mane"
  ],
  "comment": "6 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Kostadinova and Minkova published an expression for the probability mass function (pmf) of the Poisson distribution of order $k$, as a combinatorial sum ($\\mathit{Pliska~Stud.~Math.~Bulgar.}\\ {\\bf 22},\\ 117-128\\ (2013)$). Inspired by their elegant solution, this note presents an alternative combinatorial sum for the pmf of the Poisson distribution of order $k$. The terms are partitioned into blocks of length $k$ (as opposed to $k+1$ by Kostadinova and Minkova). The new sum offers an advantage in the following sense. For $n\\in[rk+1,(r+1)k]$, the lowest power of $\\lambda$ in the pmf is $\\lambda^{r+1}$. Hence the lower limit of summation can be increased, to avoid needlessly calculating terms which cancel to identically zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-12T12:34:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "39B05",
      "11B37",
      "05-08"
    ],
    "keywords": [
      "probability mass function",
      "alternative combinatorial sum",
      "poisson distribution",
      "elegant solution",
      "kostadinova"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}