{
  "id": "1312.7139",
  "version": "v1",
  "published": "2013-12-26T18:58:47.000Z",
  "updated": "2013-12-26T18:58:47.000Z",
  "title": "A Note on the Modes of the Poisson Distribution of Order k",
  "authors": [
    "Andreas N. Philippou"
  ],
  "comment": "3 pages",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "It is shown that for any positive integer k and positive parameter lambda less than 2/k(k+1), the Poisson distribution of order k with parameter lambda has a unique mode, 0. In addition, the Poisson distribution of order 2 has a unique mode, 0, if lambda is less than -1 plus the square root of 3. It has two modes, 0 and 2, if lambda is equal to -1 plus the square root of 3, and it has a unique mode, 2, if lambda is greater than -1 plus the square root of 3 and less than 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-26T18:58:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "11B37",
      "39B05"
    ],
    "keywords": [
      "poisson distribution",
      "square root",
      "unique mode",
      "positive parameter lambda",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.7139P"
    }
  }
}