{
  "id": "1809.07460",
  "version": "v1",
  "published": "2018-09-20T03:26:03.000Z",
  "updated": "2018-09-20T03:26:03.000Z",
  "title": "Absolute moments in terms of characteristic functions",
  "authors": [
    "Gwo Dong Lin",
    "Chin-Yuan Hu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The absolute moments of probability distributions are more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the characteristic function and provide some new results as well. The case of nonnegative random variables is also investigated through both characteristic function and Laplace-Stieltjes transform. Besides, we prove that the distribution of a nonnegative random variable with a finite fractional moment can be completely determined by a proper subset of the translated fractional moments. This improves significantly Hall's (1983) result for distributions on the right-half line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-20T03:26:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E10",
      "42A38",
      "42B10"
    ],
    "keywords": [
      "characteristic function",
      "absolute moments",
      "finite fractional moment",
      "nonnegative random variable",
      "probability distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}