{
  "abstract": "Lepto-regression is defined as the machine learning process of constructing a Regression Tree of a target feature on itself. It is a novel, model-free method potentially revealing information on important sample structure properties. But it is yet not clear what the informational content of lepto-variance is and how it is related to other well-known statistics of a sample. One significant finding is that 58% of the historical US stock return variability is 1-bit lepto-variance that can not be explained by any financial factor. The central question investigated in this paper is to use small normal N(0, 1) drawn samples to explore how the 1-bit sample lepto-variance and lepto-ratio relate to sample variance, skewness and excess kurtosis. Using a large sample simulation, the lepto ratio of a normal is found to converge to 36.3%. For smaller normally distributed simulated N(0, 1) samples, while lepto-variance itself is highly correlated to sample variance, lepto-variance as a fraction of total variance is highly correlated to excess kurtosis. Both lepto-variance and lepto-ratio are orthogonal to sample skew. Another finding is that while lepto-ratio is strongly correlated to lepto-variance it remains orthogonal to sample variance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25144",
  "author_total": 1,
  "authors": [
    {
      "name": "Vassilis Polimenis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1wdp0vwvj7b1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25144",
  "fulltext_url": null,
  "id": "d1wdp0vwvj7b1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25144",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "q-fin.RM"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25144",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1wdp0vwvj7b1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:49Z",
      "native_id": "2609.25144",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25144"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "The Informational Content in Lepto-Variance and Its Relation to Higher Moments",
  "title_text": "The Informational Content in Lepto-Variance and Its Relation to Higher Moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:49Z",
  "url": "https://research.draconitic.com/paper/d1wdp0vwvj7b1",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.4236/ib.2025.173013",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}