{
  "id": "math/0410151",
  "version": "v1",
  "published": "2004-10-06T11:38:59.000Z",
  "updated": "2004-10-06T11:38:59.000Z",
  "title": "Means of a Dirichlet process and multiple hypergeometric functions",
  "authors": [
    "Antonio Lijoi",
    "Eugenio Regazzini"
  ],
  "comment": "Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000270",
  "journal": "Annals of Probability 2004, Vol. 32, No. 2, 1469-1495",
  "doi": "10.1214/009117904000000270",
  "categories": [
    "math.PR"
  ],
  "abstract": "The Lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a Dirichlet process. This approach leads to several results, which are illustrated here. Among these are a new and more direct procedure for determining the exact form of the distribution of the mean, a correspondence between the distribution of the mean and the parameter of a Dirichlet process, a characterization of the family of Cauchy distributions as the set of the fixed points of this correspondence, and an extension of the Markov-Krein identity. Moreover, an expression of the characteristic function of the mean of a Dirichlet process is obtained by resorting to an integral representation of a confluent form of the fourth Lauricella function. This expression is then employed to prove that the distribution of the mean of a Dirichlet process is symmetric if and only if the parameter of the process is symmetric, and to provide a new expression of the moment generating function of the variance of a Dirichlet process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-06T11:38:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "62E10",
      "33C65"
    ],
    "keywords": [
      "dirichlet process",
      "multiple hypergeometric functions",
      "expression",
      "fourth lauricella function",
      "lauricella theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10151L"
    }
  }
}