{
  "id": "1209.4592",
  "version": "v1",
  "published": "2012-09-20T17:46:53.000Z",
  "updated": "2012-09-20T17:46:53.000Z",
  "title": "On the expected number of different records in a random sample",
  "authors": [
    "Marco Ferrante",
    "Nadia Frigo"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied problems, like the Heaps' Law in linguistics and the classical Coupon-collector's problem. In this note we are able to compute theoretically the expected size of such a sample and we provide an approximation strategy in the case of the Mandelbrot distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-20T17:46:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "expected number",
      "random sample drawn",
      "approximation strategy",
      "classical coupon-collectors problem",
      "discrete distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.4592F"
    }
  }
}