{
  "abstract": "Whether a mortality model needs a Makeham term, the constant representing background mortality, is commonly decided with a likelihood-ratio test. The constant cannot be negative, so testing its absence places it on a boundary, where the usual chi-squared calibration fails. Assuming independent Poisson death counts and standard regularity conditions, we show that when the constant is the only parameter on a boundary the statistic converges to an equal mixture of a point mass at zero and a chi-squared distribution with one degree of freedom: at the 5% level the critical value is 2.71, not 3.84. We state conditions under which the correction holds for Makeham models, verify them for Gompertz--Makeham and gamma-Gompertz--Makeham, and quantify the information about the constant, which fixes the local power, the smallest detectable term, and the loss of detectability as the age window narrows. When a gamma-frailty variance is estimated at a true value of zero, the limit is no longer a chi-squared mixture and the correction rejects too often. Monte Carlo experiments show the conventional cutoff rejecting at half the nominal level, a correctly calibrated test missing a term at its detection threshold in most samples, and excess rejections persisting as exposure grows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03685",
  "author_total": 1,
  "authors": [
    {
      "name": "Silvio C. Patricio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejs4eqr9s45ts.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03685",
  "fulltext_url": null,
  "id": "ejs4eqr9s45ts",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03685",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "q-bio.PE"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7220449652",
  "pdf_url": "https://arxiv.org/pdf/2610.03685",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejs4eqr9s45ts.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.03685",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03685"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.PE",
      "subfield": "evolutionary-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Boundary inference for the Makeham term in mortality models",
  "title_text": "Boundary inference for the Makeham term in mortality models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/ejs4eqr9s45ts",
  "venue": "arXiv",
  "versions": []
}