{
  "id": "1403.2361",
  "version": "v2",
  "published": "2014-03-10T19:37:49.000Z",
  "updated": "2014-04-06T07:59:59.000Z",
  "title": "On the Laplace transform of the Fréchet distribution",
  "authors": [
    "K. A. Penson",
    "K. Górska"
  ],
  "comment": "10 pages, 4 figures; one reference added",
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "We calculate exactly the Laplace transform of the Fr\\'{e}chet distribution in the form $\\gamma x^{-(1+\\gamma)} \\exp(-x^{-\\gamma})$, $\\gamma > 0$, $0 \\leq x < \\infty$, for arbitrary rational values of the shape parameter $\\gamma$, i.e. for $\\gamma = l/k$ with $l, k = 1,2, \\ldots$. The method employs the inverse Mellin transform. The closed form expressions are obtained in terms of Meijer G functions and their graphical illustrations are provided. A rescaled Fr\\'{e}chet distribution serves as a kernel of Fr\\'{e}chet integral transform. It turns out that the Fr\\'{e}chet transform of one-sided L\\'{e}vy law reproduces the Fr\\'{e}chet distribution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-06T07:59:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "laplace transform",
      "fréchet distribution",
      "inverse mellin transform",
      "arbitrary rational values",
      "closed form expressions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4893338",
      "journal": "Journal of Mathematical Physics",
      "year": 2014,
      "month": "Sep",
      "volume": 55,
      "number": 9,
      "pages": "093501"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JMP....55i3501P"
    }
  }
}