{
  "id": "1005.2781",
  "version": "v1",
  "published": "2010-05-16T22:39:23.000Z",
  "updated": "2010-05-16T22:39:23.000Z",
  "title": "Divergence of sample quantiles",
  "authors": [
    "Reza Hosseini"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We show that the left (right) sample quantile tends to the left (right) distribution quantile at p in [0,1], if the left and right quantiles are identical at p. We show that the sample quantiles diverge almost surely otherwise. The latter can be considered as a generalization of the well-known result that the sum of a random sample of a fair coin with 1 denoting heads and -1 denoting tails is 0 infinitely often. In the case that the sample quantiles do not converge we show that the limsup is the right quantile and the liminf is the left quantile.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-16T22:39:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divergence",
      "sample quantiles diverge",
      "well-known result",
      "sample quantile tends",
      "random sample"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.2781H"
    }
  }
}