{
  "abstract": "We study coupon collection when each type is at risk of disappearing until its first observation, after which it becomes permanently safe. Sampling follows a fixed independent and identically distributed law. For uniform sampling and common fragility, the success probability is the probability-generating function of a pre-discovery exposure statistic. An independent weighted-geometric decomposition gives an exact product, a critical disappearance scale of n−2, and a central limit theorem with a Berry–Esseen bound. For common fragility 0<q<1, the deadline-success probability is strictly Schur-concave on the open probability simplex. For heterogeneous fragilities qi=ci/n2 and sampling probabilities pi=ai/n, we prove a uniform O(n−1) approximation to the actual success probability on a bounded-profile class. For positive fragility profiles uniformly bounded away from zero, this yields an O(n−1) optimality gap for square-root allocation whenever that allocation belongs to the same admissible class. We distinguish this conclusion from exact finite-size optimality and treat zero fragility separately. An independent-exponential continuous-time model provides a benchmark, with a quantified discrepancy from the discrete model.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Data Science, HIT—Holon Institute of Technology, Holon 5810201, Israel",
    "University of Haifa, Haifa 3498838, Israel"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Igor Kleiner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fpjv931vk8ygz.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203729",
  "fulltext_url": null,
  "id": "fpjv931vk8ygz",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3729",
  "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|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7221762224",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/fpjv931vk8ygz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203729",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3729"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Probability and Statistical Research",
      "subfield": "statistics"
    }
  ],
  "title": "The Fragile Coupon Collector: Random Deadlines, Critical Fragility, and Optimal Sampling",
  "title_text": "The Fragile Coupon Collector: Random Deadlines, Critical Fragility, and Optimal Sampling",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/fpjv931vk8ygz",
  "venue": "Mathematics",
  "versions": []
}