{
  "id": "0710.3456",
  "version": "v1",
  "published": "2007-10-18T08:29:09.000Z",
  "updated": "2007-10-18T08:29:09.000Z",
  "title": "On an extreme two-point distribution",
  "authors": [
    "V. I. Chebotarev",
    "A. S. Kondrik",
    "K. V. Mikhaylov"
  ],
  "comment": "4 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "A bound for functional $\\Delta(F)=\\sup_{x\\in\\mathbb R}|F(x)-\\Phi(x)|$ is obtained, which is uniform for all distribution functions $F$ of random variables with zero mean-value and unity variance. Moreover, a two-point distribution is found, for which this bound is reached.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-18T08:29:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15"
    ],
    "keywords": [
      "extreme two-point distribution",
      "distribution functions",
      "unity variance",
      "random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3456C"
    }
  }
}