{
  "abstract": "The tail dependence function $Λ$ of a bivariate copula, and the tail dependence order based on it, cannot distinguish between copulas whose tail dependence coefficient vanishes; for all of them $Λ\\equiv 0$. Such copulas, among them the Gaussian copulas with correlation $ρ<1$ and the lower tails of all extreme-value copulas other than the comonotonicity copula, are nevertheless ordered by the much finer information contained in their tail expansion $C(u w)\\sim u^κ\\ell(u)\\,b(w)$, where $κ$ is the tail order, $\\ell$ is slowly varying and $b$ is the tail order function of Hua and Joe. We introduce an asymptotic tail order $\\preceq$ that refines the tail dependence order and show that it is lexicographic in the three quantities $κ$, $\\ell$ and $b$. As a consequence, every real-valued measure that is monotone with respect to $\\preceq$ is constant on all but countably many tail-order classes; meaningful measures of intermediate tail dependence must therefore be defined level-wise, and we construct such measures. Finally we determine where the fine structure resides: if the joint tail is ray-regular on the exponential scale, then $b$ is determined by the tail order and the one-sided derivatives at $ω=1/2$ of the angular dependence function of Wadsworth and Tawn; it is a (possibly broken) product of powers. If the joint tail is log-concave on the exponential scale, $b$ is squeezed between two such products.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35325",
  "author_total": 1,
  "authors": [
    {
      "name": "Karl Friedrich Siburg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/erjhmvrh0qz51.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35325",
  "fulltext_url": null,
  "id": "erjhmvrh0qz51",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35325",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2003|Financial Risk and Volatility Modeling"
    ]
  ],
  "openalex": "W7223894847",
  "pdf_url": "https://arxiv.org/pdf/2610.35325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/erjhmvrh0qz51.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Comparing and measuring intermediate tail dependence",
  "title_text": "Comparing and measuring intermediate tail dependence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/erjhmvrh0qz51",
  "venue": "arXiv",
  "versions": []
}