{
  "abstract": "Methods based on Box-Cox models have recently been developed for inference on clinically interpretable treatment effects in clinical trials. These methods model marginal outcome distributions using the power-normal distribution (PND), but the range of real-world data distributions that it can adequately approximate remains unclear. We evaluated PND approximations using two parameterizations of the four-parameter generalized $F$/generalized beta of the second kind family and 165 laboratory variables from the National Health and Nutrition Examination Survey. Overall distributional agreement was assessed using the overlap coefficient and Jensen-Shannon divergence, and location and spread on the original scale were evaluated using relative biases in the median and interquartile range. The PND closely approximated a broad range of smooth unimodal positive distributions in both the theoretical and empirical evaluations. Reduced agreement was associated with pronounced lower-bound accumulation, heaping or discretization, and multicomponent or peak-tail features. These features may be recognizable before fitting and provide practical guidance for assessing the suitability of the PND. We also developed the R package powerNormal for distributional calculations, parameter estimation, reparameterization, and random-number generation for the PND.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38454",
  "author_total": 5,
  "authors": [
    {
      "name": "Kazushi Maruo"
    },
    {
      "name": "Yusuke Yamaguchi"
    },
    {
      "name": "Ryota Ishii"
    },
    {
      "name": "Toshio Shimokawwa"
    },
    {
      "name": "Masahiko Gosho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fccndg741x0k8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38454",
  "fulltext_url": null,
  "id": "fccndg741x0k8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38454",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38454",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fccndg741x0k8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2610.38454",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38454"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Distributional Flexibility under Box-Cox Normality: A Theoretical and Empirical Evaluation of the Power-Normal Distribution",
  "title_text": "Distributional Flexibility under Box-Cox Normality: A Theoretical and Empirical Evaluation of the Power-Normal Distribution",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/fccndg741x0k8",
  "venue": "arXiv",
  "versions": []
}