{
  "id": "2311.12634",
  "version": "v1",
  "published": "2023-11-21T14:27:51.000Z",
  "updated": "2023-11-21T14:27:51.000Z",
  "title": "On $q$-Order Statistics",
  "authors": [
    "Malvina Vamvakari"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Building on the notion of $q$-integral introduced by Thomae in 1869, we introduce $q$-order statistics (that, is $q$-analogues of the classical order statistics, for $0<q<1$) which arise from dependent and not identically distributed $q$-continuous random variables and study their distributional properties. We study the $q$-distribution functions and the $q$-density functions of the relative $q$-ordered random variables. We focus on $q$-ordered variables arising from dependent and not identically $q$-uniformly distributed random variables and we derive their $q$-distributions, including $q$-power law, $q$-beta and $q$-Dirichlet distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-21T14:27:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62E15",
      "62B05",
      "60C05",
      "60E05",
      "62G30",
      "05A30"
    ],
    "keywords": [
      "density functions",
      "classical order statistics",
      "distribution functions",
      "continuous random variables",
      "dirichlet distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}