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A Tetration Distribution — arXiv:2611.03895

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03895
License (as archived): CC0-1.0
Archived: 2026-11-04T21:56:12.536Z
SHA-256 of the archived text: e5cfa86f1b4b42173839eaf3c2e68db3f223a7dc6b29f74d2d9fbf4d1ea3ae9d
Stable URL of this page: https://metraipolis.com/documento/dc_54cd238579cd

How to cite

A Tetration Distribution — arXiv:2611.03895 — arXiv (en), https://arxiv.org/abs/2611.03895 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_54cd238579cd (Metraipolis archive dc_54cd238579cd, sha256 e5cfa86f1b4b42173839eaf3c2e68db3f223a7dc6b29f74d2d9fbf4d1ea3ae9d)

BibTeX

@misc{dc54cd238579cd,
  title = {A Tetration Distribution — arXiv:2611.03895},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03895},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_54cd238579cd; sha256 e5cfa86f1b4b42173839eaf3c2e68db3f223a7dc6b29f74d2d9fbf4d1ea3ae9d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03895. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.ST, nuovi lavori del giorno).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2611.03895 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T21:40:49.586Z dalla pagina https://arxiv.org/list/math.ST/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).