{
  "id": "1601.02121",
  "version": "v1",
  "published": "2016-01-09T15:24:03.000Z",
  "updated": "2016-01-09T15:24:03.000Z",
  "title": "Sklar's Theorem in an Imprecise Setting",
  "authors": [
    "Ignacio Montes",
    "Enrique Miranda",
    "Renato Pelessoni",
    "Paolo Vicig"
  ],
  "comment": "A definitive version has been published in a special issue on uncertainty and imprecision modelling in decision making (EUROFUSE 2013) of Fuzzy Sets and Systems",
  "journal": "Fuzzy Sets and Systems, vol. 278, 1 November 2015, pages 48-66",
  "doi": "10.1016/j.fss.2014.10.007",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar's theorem under these conditions, and link the obtained results to stochastic ordering with imprecision.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-09T15:24:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "60E15",
      "60A05"
    ],
    "keywords": [
      "sklars theorem",
      "imprecise setting",
      "connects bidimensional distribution functions",
      "important tool",
      "ordered distribution functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}