{
  "id": "0909.4669",
  "version": "v1",
  "published": "2009-09-25T11:34:06.000Z",
  "updated": "2009-09-25T11:34:06.000Z",
  "title": "The Real Powers of the Convolution of a Gamma Distribution and a Bernoulli Distribution",
  "authors": [
    "Ben Salah Nahla",
    "Masmoudi Afif"
  ],
  "comment": "Please, i would submit our paper to math arxiv",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we essentially compute the set of $x,y>0$ such that the mapping $z \\longmapsto \\Big{(}1-r+r e^z\\Big{)}^x \\Big{(}\\dis\\frac{\\lambda}{\\lambda-z}\\Big{)}^{y}$ is a Laplace transform. If $X$ and $Y$ are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by $\\mu$ the distribution of $X+Y.$ The above problem is equivalent to finding the set of $x>0$ such that $\\mu^{{\\ast}x}$ exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-25T11:34:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E07",
      "60E10"
    ],
    "keywords": [
      "gamma distribution",
      "bernoulli distribution",
      "real powers",
      "convolution",
      "independent random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4669S"
    }
  }
}