{
  "id": "2410.22038",
  "version": "v1",
  "published": "2024-10-29T13:45:11.000Z",
  "updated": "2024-10-29T13:45:11.000Z",
  "title": "A Cramér-Wold theorem for mixtures",
  "authors": [
    "Ricardo Fraiman",
    "Leonardo Moreno",
    "Thomas Ransford"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show how a Cram\\'er-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributions drawn from the same family. Using this abstract result, we establish a Cram\\'er-Wold theorem for mixtures of multivariate Gaussian distributions. According to this theorem, two such mixtures can be distinguished by projecting them onto a certain predetermined finite set of lines, the number of lines depending only on the total number Gaussian distributions involved and on the ambient dimension. A similar result is also obtained for mixtures of multivariate $t$-distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-29T13:45:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B11"
    ],
    "keywords": [
      "cramér-wold theorem",
      "total number gaussian distributions",
      "cramer-wold theorem",
      "multivariate probability distributions",
      "multivariate gaussian distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}