{
  "annotation_id": "334a2d55-9011-4f32-b5aa-57c1e81d043b",
  "date_created": "2026-02-17T05:53:15.715000Z",
  "date_modified": "2026-02-17T05:53:15.715000Z",
  "file_hash": "f986ba8a922e735e58a92fa7456ec9ba273b3f74c68f94af1bf0d21d696e6f0d",
  "private": false,
  "record": {
    "abstract": "Concordance measures are used to express the degree of association between random variables. Practitioners may use several distinct concordance measures to narrow the space of possible dependence structures. Consequently, the relations between different (weak) concordance measures have been extensively studied in recent years. The goal of this paper is to study the relation between Kendall\u0027s tau, Gini\u0027s gamma and Spearman\u0027s footrule. In particular, we describe the exact region determined by these three measures, using shuffles of $M$ and ordinal sums of copulas. We also provide the formulas for five main (weak) concordance measures and Chatterjee\u0027s xi of ordinal sums of copulas.",
    "arxiv_id": "2601.07993",
    "authors": [
      "Damjana Kokol Bukov\u0161ek",
      "Petra Lazi\u0107",
      "Bla\u017e Moj\u0161kerc",
      "Nik Stopar"
    ],
    "categories": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "The exact region determined by Spearman\u0027s footrule, Gini\u0027s gamma and Kendall\u0027s tau",
    "url": "https://arxiv.org/abs/2601.07993",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e846fb65-93fe-494f-85da-7fbaea8ebc68",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}