{
  "abstract": "The generalized extreme value (GEV) distribution is used to model block maxima and extrapolate beyond the observed range, making adequate tail fit essential. We propose a bounded, tunable goodness-of-fit statistic for the GEV distribution with unknown parameters, based on the probability integral transform and a symmetric weight whose amplitude and concentration are controlled separately. We establish location–scale invariance, an exact relationship with the Cramér–von Mises statistic, a known-parameter limit distribution with closed-form moments, consistency against fixed alternatives, and a composite-null limit conditional on explicit regularity assumptions. Critical values are obtained by a parametric bootstrap that refits the GEV model in every resample; the same calibration is applied to the Kolmogorov–Smirnov, Anderson–Darling, Cramér–von Mises, and upper-tail modified Anderson–Darling tests. Simulations over shape parameters from −0.4 to 0.4 and sample sizes from 15 to 100 show no evidence of over-rejection, and the proposed tests are competitive with Anderson–Darling under maximum-likelihood and probability-weighted-moment estimation. All six tests have limited power against subtle upper-tail-only departures. The return-level study shows that rejection can identify samples with greater extrapolation error, whereas non-rejection does not guarantee accurate remote-quantile estimates. Applications to environmental and actuarial block maxima illustrate sensitivity to temporal trend and block length.",
  "abstract_shown": true,
  "affiliations": [
    "Department of New Media, Faculty of Informatics, Mahasarakham University, Maha Sarakham 44150, Thailand",
    "Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Preut Thanarat",
      "orcid": "0009-0004-7172-0811"
    },
    {
      "affs": [
        1
      ],
      "name": "Nipada Papukdee",
      "orcid": "0000-0002-5103-6201"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9h4s32k0tbmyq.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213914",
  "fulltext_url": null,
  "id": "9h4s32k0tbmyq",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3914",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7210273324",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/9h4s32k0tbmyq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14213914",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3914"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Distribution Estimation and Applications",
      "subfield": "statistics"
    }
  ],
  "title": "A Tail-Weighted Goodness-of-Fit Test for the Generalized Extreme Value Distribution Based on the Probability Integral Transform",
  "title_text": "A Tail-Weighted Goodness-of-Fit Test for the Generalized Extreme Value Distribution Based on the Probability Integral Transform",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/9h4s32k0tbmyq",
  "venue": "Mathematics",
  "versions": []
}