{
  "id": "1507.07576",
  "version": "v1",
  "published": "2015-07-27T20:19:38.000Z",
  "updated": "2015-07-27T20:19:38.000Z",
  "title": "Grand Lebesgue norm estimation for binary random variables, with applications",
  "authors": [
    "Eugene Ostrovsky",
    "Leonid Sirota"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable. This norm is optimal for the centered and bounded random variables (r.v.). Using this result we derive a very simple bilateral sharp exponential tail estimates for sums of these variables, not necessary to be identical distributed, under non-standard norming, and give some examples to show the exactness of our estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-27T20:19:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grand lebesgue norm estimation",
      "binary random variables",
      "sharp exponential tail estimates",
      "bilateral sharp exponential tail",
      "rademachers grand lebesgue space norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150707576O"
    }
  }
}