{
  "abstract": "In this paper we propose and study arctan-skewing, a general approach to skew any symmetric distribution on the unit hypertorus. Arctan-skewing retains the main advantages of the popular sine-skewing mechanism, but improves on it by overcoming its two major limitations. These are a condition on the skewness parameter and a singular Fisher Information matrix in the vicinity of symmetry when combined with well-known symmetric models from the literature such as the circular von Mises or bivariate Cosine models. Arctan-skewing thus represents a compelling alternative to model skewed data on the circle and torus, notably from the field of protein bioinformatics. After a thorough investigation of its stochastic properties, we present a maximum likelihood estimation procedure and devise optimal tests for symmetry against our new class of skewed alternatives. Finally we show that arctan-skewed models better fit protein data compared to their sine-skewed counterparts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13310",
  "author_total": 2,
  "authors": [
    {
      "name": "Christophe Ley"
    },
    {
      "name": "Sophia Loizidou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nn9r1kef456k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13310",
  "fulltext_url": null,
  "id": "9nn9r1kef456k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13310",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7221547794",
  "pdf_url": "https://arxiv.org/pdf/2610.13310",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nn9r1kef456k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:46Z",
      "native_id": "2610.13310",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13310"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Arctan-skewing: a new skewing scheme on the hypertorus",
  "title_text": "Arctan-skewing: a new skewing scheme on the hypertorus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:46Z",
  "url": "https://research.draconitic.com/paper/9nn9r1kef456k",
  "venue": "arXiv",
  "versions": []
}