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Lehmer-Lambert Distribution — arXiv:2609.12150

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.12150
License (as archived): CC0-1.0
Archived: 2026-10-16T03:44:31.356Z
SHA-256 of the archived text: 1be3c84dcc8a98d0a8c460d531320b83918474d674ddf0a668f4b93044a315db
Stable URL of this page: https://metraipolis.com/documento/dc_4e7ccdabc233

How to cite

Lehmer-Lambert Distribution — arXiv:2609.12150 — arXiv (en), https://arxiv.org/abs/2609.12150 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4e7ccdabc233 (Metraipolis archive dc_4e7ccdabc233, sha256 1be3c84dcc8a98d0a8c460d531320b83918474d674ddf0a668f4b93044a315db)

BibTeX

@misc{dc4e7ccdabc233,
  title = {Lehmer-Lambert Distribution — arXiv:2609.12150},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.12150},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4e7ccdabc233; sha256 1be3c84dcc8a98d0a8c460d531320b83918474d674ddf0a668f4b93044a315db},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.12150. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The Lehmer transform of a positive signal is the ratio of its power sums at consecutive orders, read as a function of the order, and it is a strictly increasing analytic curve from the smallest observation to the largest. Composing this curve with a map whose inverse is the Lambert function turns it into a probability law on the real line, the Lehmer-Lambert distribution, which we introduce and study. Its distribution, density and quantile functions are closed-form, its random variates are exact, and the law is invariant under changes of gain and of power-law calibration of the signal. Its modes lie at orders at which the signal changes scale, and for a sample its tails are exponential with rates equal to the two extreme logarithmic gaps of the sample. We derive moments, generating functions and limit theorems, and we investigate applications of the Lehmer-Lambert distribution in the analysis of electroencephalograms of patients with major depressive disorder.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-14 in math.ST).
Categorie arXiv: Probability (math.PR) ; Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2609.12150 — 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 2026-10-16T03:15:53.806Z dalla pagina https://arxiv.org/catchup/math.ST/2026-09-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).