{
  "abstract": "Intervals with the same probability content can have different endpoint placements and widths. This matters for tolerance inference, where a reported interval must also satisfy a repeated-sampling content-confidence statement. We develop mean-tilted intervals (MTIs), a fixed-content family indexed by retained-mean balance. The zero-tilt member is the mean-preserving interval (MPI) induced by the residual-product criterion of Pouplin et al.; nonzero tilts move through admissible contiguous windows, including distribution-specific central and shortest intervals. For tolerance inference, we introduce TCSP, a tolerance-calibrated shortest-path action. TCSP chooses the retained order-statistic count by distribution-free scan calibration and reports the shortest closed window at that count. This keeps the certified interval action separate from generalized-posterior endpoint summaries. We also study a calibrated MTI-ECM comparator that profiles fitted content and tilt over a prespecified grid and applies an independent Dirichlet-process content-probability check. In iid simulations at tolerance confidence 0.95, we compare TCSP, MTI-ECM, Young-Mathew interpolation, and Wilks intervals across feasible content-sample-size cells and eight continuous distributions. The study emphasizes skewed distributions, where placement matters most, and excludes cells where the sample range cannot support the requested two-sided distribution-free statement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.26098",
  "author_total": 3,
  "authors": [
    {
      "name": "Antonio De Leon"
    },
    {
      "name": "Raquel Prado"
    },
    {
      "name": "Bruno Sansó"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exnkbqs70yxrc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.26098",
  "fulltext_url": null,
  "id": "exnkbqs70yxrc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.26098",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7171853816",
  "pdf_url": "https://arxiv.org/pdf/2607.26098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exnkbqs70yxrc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "2607.26098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.26098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Mean-Tilted Intervals: Short Tolerance Intervals",
  "title_text": "Mean-Tilted Intervals: Short Tolerance Intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/exnkbqs70yxrc",
  "venue": "arXiv",
  "versions": []
}