{
  "id": "2410.04143",
  "version": "v2",
  "published": "2024-10-05T12:38:23.000Z",
  "updated": "2025-05-08T11:17:46.000Z",
  "title": "A Probability Inequality for Convolutions of MTP2-Distribution Functions",
  "authors": [
    "Thomas Royen"
  ],
  "comment": "4 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "A probability inequality is proved for n-fold convolutions of a smooth cumulative distribution function on (0,infinity)x...x(0,infinity), which is multivariate totally positive of order 2 (MTP2). This inequality is better than an inequality of the same type as the Gaussian correlation inequality for distribution functions. An important example are some multivariate chi-square distributions, derived from the diagonal of a Wishart matrix.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-05-08T11:17:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15"
    ],
    "keywords": [
      "probability inequality",
      "mtp2-distribution functions",
      "smooth cumulative distribution function",
      "gaussian correlation inequality",
      "multivariate chi-square distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}