{
  "id": "1707.08367",
  "version": "v1",
  "published": "2017-07-26T10:47:12.000Z",
  "updated": "2017-07-26T10:47:12.000Z",
  "title": "On Generalizations of ($k_1,k_2$)-runs",
  "authors": [
    "A. N. Kumar",
    "N. S. Upadhye"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper deals with three generalized dependent setups arising from an independent sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these setups and their waiting time. Also, explicit forms of probability generating function and probability mass function are obtained. Finally, an application to demonstrate the relevance of the results is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-26T10:47:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "62E15",
      "60C05",
      "60E10"
    ],
    "keywords": [
      "probability mass function",
      "probability generating function",
      "generalizations",
      "independent sequence",
      "bernoulli trials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}