Mean-Tilted Intervals: A Generalized-Bayes Approach to Fixed-Content and Tolerance Intervals

[2607.26098] Mean-Tilted Intervals: Short Tolerance Intervals Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2607.26098 (stat) [Submitted on 28 Jul 2026 ( v1 ), last revised 28 Aug 2026 (this version, v3)] Title: Mean-Tilted Intervals: Short Tolerance Intervals Authors: Antonio De Leon , Raquel Prado , Bruno Sansó View a PDF of the paper titled Mean-Tilted Intervals: Short Tolerance Intervals, by Antonio De Leon and 1 other authors View PDF HTML (experimental) 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. Comments: 22 pages, 5 figures Subjects: Methodology (stat.ME) MSC classes: 62G15, 62G30, 62F15 Cite as: arXiv:2607.26098 [stat.ME] (or arXiv:2607.26098v3 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2607.26098 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jose Antonio Aguirre Perez De Leon [ view email ] [v1] Tue, 28 Jul 2026 05:16:35 UTC (351 KB) [v2] Sat, 15 Aug 2026 04:24:34 UTC (527 KB) [v3] Fri, 28 Aug 2026 07:15:35 UTC (966 KB) Full-text links: Access Paper: View a PDF of the paper titled Mean-Tilted Intervals: Short Tolerance Intervals, by Antonio De Leon and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2026-07 Change to browse by: stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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