{
  "abstract": "We develop $L^1$ bounds for the difference between a test function of a random sum and a standard normal random variable, where the summands are assumed to be independent but not necessarily identically distributed. The bounds are obtained through a new version of the approximate zero bias transformation specifically developed for random sums. Although the identical distribution assumption is relaxed, the bounds are of order $1/\\sqrt{n}$, matching the order of existing bounds in the literature under the same distributional assumption on the number of summands. The main results are then applied to three real-world settings: random sums obtained from simple random sampling with outliers, total insurance claims, and generative AI response times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27143",
  "author_total": 2,
  "authors": [
    {
      "name": "Wasamon Jantai"
    },
    {
      "name": "Nathakhun Wiroonsri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m80p0cjfcjdf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27143",
  "fulltext_url": null,
  "id": "7m80p0cjfcjdf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27143",
  "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.PR"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7204592745",
  "pdf_url": "https://arxiv.org/pdf/2608.27143",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7m80p0cjfcjdf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2608.27143",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27143"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI",
  "title_text": "An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/7m80p0cjfcjdf",
  "venue": "arXiv",
  "versions": []
}