{
  "abstract": "Phase-type (PH) distributions are versatile semi-parametric models for lifetime duration and can be used in survival and reliability analysis. In this paper we put forward methods and software for using PH distributions in a competing-risks model. The resulting multi-absorbing phase-type (MAPH) distribution records both the time until absorption and its cause. After formulating basic properties of this family, we develop an EM algorithm for parameter inference from exact event-time/cause observations and independently right-censored observations. For a censored subject, the E-step conditions on survival up to the censoring time and imputes both the latent transient path and its eventual cause of absorption; closed-form cause-resolved sufficient-statistic expectations are obtained from matrix exponentials. We illustrate applications and numerical properties and describe two accompanying Julia packages, in which both the exact-event and the censored E-step are implemented. Applied to intensive-care length-of-stay data in full, censored records included, the method attains a higher likelihood than the phase-type competing-risks fit previously published for those data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19921",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhihao Qiao"
    },
    {
      "name": "Budhi Surya"
    },
    {
      "name": "Azam Asanjarani"
    },
    {
      "name": "Yoni Nazarathy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2kde70bxkrkd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19921",
  "fulltext_url": null,
  "id": "d2kde70bxkrkd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19921",
  "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",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Distribution Estimation and Applications"
    ]
  ],
  "openalex": "W7213577667",
  "pdf_url": "https://arxiv.org/pdf/2609.19921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2kde70bxkrkd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data",
  "title_text": "Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:29Z",
  "url": "https://research.draconitic.com/paper/d2kde70bxkrkd",
  "venue": "arXiv",
  "versions": []
}