{
  "abstract": "Let $X$ be an integer-valued random variable with $\\mathbb{E}(|X|)<\\infty$ whose survival probabilities $S_j=\\mathbb{P}(X\\ge j), j\\in\\mathbb{Z}$, form a log-concave sequence. Suppose that for some integer $m$ and some $γ\\in (0, 1/2]$ it holds $\\mathbb{E}(X)\\ge m$ and $\\mathbb{P}(X=m+1)\\geγ\\cdot\\mathbb{P}(X=m)> 0$. It is shown that \\[ \\mathbb{P}(X \\ge m+1) \\,\\ge\\, \\fracγ{1+2γ} \\, , \\] with the bound being best possible. As a consequence, it is shown that if $H \\sim \\text{Hyp}(n, i, k)$ is a hypergeometric random variable for which both $ik/n$ and $(n-i)(n-k)/n$ are at least $\\log(4/3)$, then it holds $\\mathbb{P}(H >\\mathbb{E}(H)) \\ge 1/4$ when $\\mathbb{E}(H)$ is not an integer, and $\\mathbb{P}(H >\\mathbb{E}(H)) \\ge 1/6$ when $\\mathbb{E}(H)$ is an integer, both bounds being best possible.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24726",
  "author_total": 4,
  "authors": [
    {
      "name": "Jianhang Ai"
    },
    {
      "name": "Vassilis Karagiannis"
    },
    {
      "name": "Ondřej Kuželka"
    },
    {
      "name": "Christos Pelekis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dd8q70kzn2jtr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24726",
  "fulltext_url": null,
  "id": "dd8q70kzn2jtr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24726",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7223053534",
  "pdf_url": "https://arxiv.org/pdf/2610.24726",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dd8q70kzn2jtr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24726",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24726"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the probability that a discrete IFR random variable exceeds its mean",
  "title_text": "On the probability that a discrete IFR random variable exceeds its mean",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/dd8q70kzn2jtr",
  "venue": "arXiv",
  "versions": []
}