{
  "id": "1507.02935",
  "version": "v1",
  "published": "2015-07-10T15:16:25.000Z",
  "updated": "2015-07-10T15:16:25.000Z",
  "title": "Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials",
  "authors": [
    "Takis Konstantopoulos",
    "Zhenxia Liu",
    "Xiangfeng Yang"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The longest stretch $L(n)$ of consecutive heads in $n$ i.i.d. coin tosses is seen from the prism of large deviations. We first establish precise asymptotics for the moment generating function of $L(n)$ and then show that there are precisely two large deviation principles, one concerning the behavior of the distribution of $L(n)$ near its nominal value $\\log_{1/p} n$ and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of $L(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-10T15:16:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation principles",
      "laplace transform asymptotics",
      "longest success runs",
      "bernoulli trials",
      "first establish precise asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150702935K"
    }
  }
}