{
  "id": "2302.14356",
  "version": "v1",
  "published": "2023-02-28T07:19:52.000Z",
  "updated": "2023-02-28T07:19:52.000Z",
  "title": "A unified approach to explicit formulae for the distributions of runs",
  "authors": [
    "Hayato Takahashi"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Fu et.al (1994) studied five statistics of runs and showed explicit formulae for their distributions by Markov imbedding method. We show new simple explicit formulae for distributions of these statistics for independent and identically distributed binary random variables by a unified manner.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-28T07:19:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "62E15"
    ],
    "keywords": [
      "unified approach",
      "distributions",
      "simple explicit formulae",
      "identically distributed binary random variables",
      "showed explicit formulae"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}