{
  "id": "1308.5541",
  "version": "v1",
  "published": "2013-08-26T11:01:19.000Z",
  "updated": "2013-08-26T11:01:19.000Z",
  "title": "On the norming constants for normal maxima",
  "authors": [
    "Armengol Gasull",
    "Maria Jolis",
    "Frederic Utzet"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In a remarkable paper, Peter Hall [{\\it On the rate of convergence of normal extremes}, J. App. Prob, {\\bf 16} (1979) 433--439] proved that the supremum norm distance between the distribution function of the normalized maximum of $n$ independent standard normal random variables and the distribution function of the Gumbel law is bounded by $3/\\log n$. In the present paper we prove that choosing a different set of norming constants that bound can be reduced to $1/\\log n$. As a consequence, using the asymptotic expansion of a Lambert $W$ type function, we propose new explicit constants for the maxima of normal random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-26T11:01:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70",
      "60F05",
      "62G32"
    ],
    "keywords": [
      "norming constants",
      "normal maxima",
      "independent standard normal random variables",
      "distribution function",
      "supremum norm distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}