{
  "abstract": "Heavy-tailed time series with regime switching arise in environmental, financial, and engineering applications, yet conventional emission distributions such as Gaussian, Gamma, or Weibull fail to capture simultaneously extreme right-skewness, slowly decaying upper tails, and temporal dependence. This paper develops a fully Bayesian Hidden Markov Model with Singh-Maddala (Burr Type XII) emission distributions (HMMSM). We derive the complete Bayesian structure and design an adaptive Metropolis-within-Gibbs sampler combining Forward-Filtering Backward-Sampling, conjugate Dirichlet updates, and adaptive Metropolis steps. Simulations confirm parameter recovery with relative errors below 10% and 95% prediction coverage of 94.5%. On a simulated benchmark with heavy tails, Bayesian model selection via WAIC, DIC, and LOO correctly identifies K = 3, and HMMSM outperforms seven competing specifications by large margins. On a 26-year gridded rainfall record for Ireland (T = 312 monthly observations), HMMSM attains the lowest WAIC but is statistically indistinguishable from HMM-Gamma, reflecting the light tails of Irish rainfall. The selected two-regime model identifies a Moderate regime (mean approx. 87 mm) and a Wet regime (approx. 134 mm) that are persistent and seasonally coherent. We also document weak identifiability of the Singh-Maddala scale parameter. The framework is general-purpose, and reproducible code is provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22656",
  "author_total": 1,
  "authors": [
    {
      "name": "Safaa K. Kadhem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/93mzg40ej5hwa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22656",
  "fulltext_url": null,
  "id": "93mzg40ej5hwa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22656",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.22656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/93mzg40ej5hwa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:43Z",
      "native_id": "2610.22656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "A Bayesian Hidden Markov Model with Singh--Maddala Emission Distributions for Heavy-Tailed Regime-Switching Time Series",
  "title_text": "A Bayesian Hidden Markov Model with Singh--Maddala Emission Distributions for Heavy-Tailed Regime-Switching Time Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/93mzg40ej5hwa",
  "venue": "arXiv",
  "versions": []
}