{
  "id": "1912.00160",
  "version": "v1",
  "published": "2019-11-30T08:48:27.000Z",
  "updated": "2019-11-30T08:48:27.000Z",
  "title": "On conditions under which a probability distribution is uniquely determined by its moments",
  "authors": [
    "Elena B. Yarovaya",
    "Jordan M. Stoyanov",
    "Konstantin K. Kostyashin"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the relationship between the well-known Carleman's condition guaranteeing that a probability distribution is uniquely determined by its moments, and a recent easily checkable condition on the rate of growth of the moments. We use asymptotic methods in theory of integrals and involve properties of the Lambert $W$-function to show that the quadratic rate of growth of the ratios of consecutive moments, as a sufficient condition for uniqueness, is more restrictive than Carleman's condition. We derive a series of statements, one of them showing that Carleman's condition does not imply Hardy's condition, although the inverse implication is true. Related topics are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-30T08:48:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability distribution",
      "well-known carlemans condition guaranteeing",
      "asymptotic methods",
      "inverse implication",
      "quadratic rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}