{
  "id": "1206.2501",
  "version": "v5",
  "published": "2012-06-12T11:57:27.000Z",
  "updated": "2013-08-04T13:30:40.000Z",
  "title": "Sharp large deviation probabilities for sums of independent bounded random variables",
  "authors": [
    "Xiequan Fan",
    "Ion Grama",
    "Quansheng Liu"
  ],
  "comment": "19 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain some optimal inequalities on tail probabilities for sums of independent bounded random variables. Our main result completes an upper bound on tail probabilities due to Talagrand by giving a one-term asymptotic expansion for large deviations. This result can also be regarded as sharp large deviations of types of Cram\\'er and Bahadur-Ranga Rao.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-08-04T13:30:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60E15",
      "60G50",
      "62E20"
    ],
    "keywords": [
      "independent bounded random variables",
      "sharp large deviation probabilities",
      "tail probabilities",
      "one-term asymptotic expansion",
      "main result completes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2501F"
    }
  }
}