{
  "abstract": "Classical skewness and kurtosis require finite third and fourth moments and are therefore undefined for Pareto-type and extreme-value models with small tail index. We study shape measures based on the mean absolute deviation (MAD), which require only a finite mean, and ask how they compare with L-moment ratios in interpretation, computation, and parameter estimation. For the Pareto I–IV, Fréchet, Gumbel, and Weibull families, we derive closed-form expressions, verified by numerical quadrature, for the MAD about any quantile, for MAD skewness and kurtosis, and for the corresponding L-moment ratios, using incomplete beta and gamma functions. The MAD measures are bounded and have a simple interpretation in terms of sub-means. We then propose MAD-Q, which matches theoretical and empirical MAD at the quartiles, gives its Jacobian in closed form, and characterizes identifiability: with known scale, the estimating equations have a unique solution, whereas with unknown scale, the MAD ratio is not monotone and a quartile-consistency step is required. In Monte Carlo experiments with known scale, MAD-Q is the most accurate non-likelihood method for most families and remains usable under lower-tail contamination that breaks the Pareto I likelihood; with unknown scale, its advantage is confined to infinite-variance tails. Financial loss and wind-speed applications illustrate both the strengths and limitations of the approach.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Computer Science, Metropolitan College, Boston University, 1010 Commonwealth Avenue, Boston, MA 02215, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Eugene Pinsky",
      "orcid": "0000-0002-3836-1851"
    },
    {
      "affs": [
        0
      ],
      "name": "Triparna Kundu",
      "orcid": "0009-0005-9517-3020"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8v609d4357emf.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203656",
  "fulltext_url": null,
  "id": "8v609d4357emf",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3656",
  "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": "W7221152189",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/8v609d4357emf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203656",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Distribution Estimation and Applications",
      "subfield": "statistics"
    }
  ],
  "title": "Skewness and Kurtosis for Heavy-Tailed Distributions: A Comparison of Mean Absolute Deviation and L-Moment Approaches for Pareto and Extreme-Value Families",
  "title_text": "Skewness and Kurtosis for Heavy-Tailed Distributions: A Comparison of Mean Absolute Deviation and L-Moment Approaches for Pareto and Extreme-Value Families",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/8v609d4357emf",
  "venue": "Mathematics",
  "versions": []
}