{
  "abstract": "We introduce a one-parameter family of continuous distributions on the unit interval whose cumulative distribution functions are given by the odd-height power towers \\(x\\uparrow\\uparrow n\\) (\\(n=1,3,5,\\dots\\)). The associated densities admit a simple recursive formula obtained by logarithmic differentiation. We prove that every such density is strictly positive on \\((0,1)\\) and integrates to one, thereby establishing that the construction yields a genuine probability distribution. Numerical investigation reveals a characteristic peak--dip--rise shape: a sharp mode lying just below \\(e^{-e}\\) for all examined heights, followed by a trough and a gradual recovery toward density value~1 at the right endpoint. We then identify the limiting distribution as the height tends to infinity through odd integers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03895",
  "author_total": 1,
  "authors": [
    {
      "name": "Micah Thornton"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a6pyzd38xh5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03895",
  "fulltext_url": null,
  "id": "9a6pyzd38xh5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03895",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9a6pyzd38xh5d.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03895"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A Tetration Distribution",
  "title_text": "A Tetration Distribution",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/9a6pyzd38xh5d",
  "venue": "arXiv",
  "versions": []
}