{
  "abstract": "In this study, we investigate a Slash Marshall–Olkin (SMO) family obtained by dividing a positive Marshall–Olkin random variable by an independent beta variable. Its four-parameter exponential member (SMOE) has a regularly varying power-law tail and belongs to the subexponential class. Integral representations are provided for all positive parameters. The original hypergeometric expansions are retained within their convergence domain, and an alternative convergent representation is derived for the remaining Marshall–Olkin parameter values. The density and hazard have finite, strictly positive limits at the origin. The density is decreasing for η≤2 and has at least one positive interior mode for η>2. We establish regular variation of the survival function with exponent −α and show that a positive-order moment exists exactly below order α. In addition, an exact generator, an observed-information representation, and precautions for likelihood optimization are provided. The simulations and two economic applications are also examined.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, St. Teresa’s College, Ernakulam 682011, Kerala, India",
    "School of Commerce and Professional Studies, Marian College Kuttikkanam, Kuttikkanam P.O, Peermade, Idukki 685531, Kerala, India",
    "Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia",
    "King Abdulaziz University, Jeddah 21589, Saudi Arabia",
    "Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jiju Gillariose",
      "orcid": "0000-0003-1329-8283"
    },
    {
      "affs": [
        1
      ],
      "name": "Joshin Joseph",
      "orcid": "0000-0001-8304-0005"
    },
    {
      "affs": [
        2
      ],
      "name": "Hanan Alahmadi"
    },
    {
      "affs": [
        2
      ],
      "name": "Mahmoud E. Bakr",
      "orcid": "0000-0003-3493-033X"
    },
    {
      "affs": [
        3
      ],
      "name": "Noha A. Tashkandi"
    },
    {
      "affs": [
        4
      ],
      "name": "Mustafa M. Hasaballah",
      "orcid": "0000-0001-7680-6762"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3egf2mdc0x9sw.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100773",
  "fulltext_url": null,
  "id": "3egf2mdc0x9sw",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/773",
  "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": "W7221969040",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/3egf2mdc0x9sw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100773",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Statistical Distribution Estimation and Applications",
      "subfield": "statistics"
    }
  ],
  "title": "A Flexible Heavy-Tailed Probability Model for Skewed Positive Data: Theory, Estimation, and Empirical Assessment",
  "title_text": "A Flexible Heavy-Tailed Probability Model for Skewed Positive Data: Theory, Estimation, and Empirical Assessment",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/3egf2mdc0x9sw",
  "venue": "Axioms",
  "versions": []
}