{
  "id": "1909.02968",
  "version": "v1",
  "published": "2019-09-06T15:25:52.000Z",
  "updated": "2019-09-06T15:25:52.000Z",
  "title": "Limit theorems for Bajraktarević and Cauchy quotient means of independent identically distributed random variables",
  "authors": [
    "Matyas Barczy",
    "Pál Burai"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "We derive strong law of large numbers and central limit theorems for Bajraktarevi\\'c, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-06T15:25:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "26E60"
    ],
    "keywords": [
      "independent identically distributed random variables",
      "limit theorems",
      "logarithmic cauchy quotient means",
      "variables behave asymptotically normal",
      "random variables behave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}