{
  "id": "0710.3419",
  "version": "v2",
  "published": "2007-10-18T00:06:58.000Z",
  "updated": "2008-11-12T14:34:08.000Z",
  "title": "Moderate deviations for Poisson--Dirichlet distribution",
  "authors": [
    "Shui Feng",
    "Fuqing Gao"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/07-AAP501 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2008, Vol. 18, No. 5, 1794-1824",
  "doi": "10.1214/07-AAP501",
  "categories": [
    "math.PR"
  ],
  "abstract": "The Poisson--Dirichlet distribution arises in many different areas. The parameter $\\theta$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $\\theta$ approaching infinity is practically motivated and has led to new, interesting mathematical structures. Laws of large numbers, fluctuation theorems and large-deviation results have been established. In this paper, moderate-deviation principles are established for the Poisson--Dirichlet distribution, the GEM distribution, the homozygosity, and the Dirichlet process when the parameter $\\theta$ approaches infinity. These results, combined with earlier work, not only provide a relatively complete picture of the asymptotic behavior of the Poisson--Dirichlet distribution for large $\\theta$, but also lead to a better understanding of the large deviation problem associated with the scaled homozygosity. They also reveal some new structures that are not observed in existing large-deviation results.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-12T14:34:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "92D10"
    ],
    "keywords": [
      "moderate deviations",
      "large-deviation results",
      "poisson-dirichlet distribution arises",
      "gem distribution",
      "scaled mutation rate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3419F"
    }
  }
}