{
  "id": "1603.07365",
  "version": "v1",
  "published": "2016-03-23T21:10:36.000Z",
  "updated": "2016-03-23T21:10:36.000Z",
  "title": "Positive-part moments via the characteristic functions, and more general expressions",
  "authors": [
    "Iosif Pinelis"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "A unifying and generalizing approach to representations of the positive-part and absolute moments $\\mathsf{E} X_+^p$ and $\\mathsf{E}|X|^p$ of a random variable $X$ for real $p$ in terms of the characteristic function (c.f.) of $X$, as well as to related representations of the c.f.\\ of $X_+$, generalized moments $\\mathsf{E} X_+^p e^{iuX}$, truncated moments, and the distribution function is provided. Existing and new representations of these kinds are all shown to stem from a single basic representation. Computational aspects of these representations are addressed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-23T21:10:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E10",
      "60E07",
      "62E15",
      "60E15",
      "91B30"
    ],
    "keywords": [
      "characteristic function",
      "general expressions",
      "positive-part moments",
      "single basic representation",
      "absolute moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160307365P"
    }
  }
}