{
  "id": "1707.03546",
  "version": "v1",
  "published": "2017-07-12T05:32:08.000Z",
  "updated": "2017-07-12T05:32:08.000Z",
  "title": "Stein's method using approximate zero bias couplings with applications to combinatorial central limit theorems under the Ewens distribution",
  "authors": [
    "Nathakhun Wiroonsri"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We generalize the well-known zero bias distribution and the $\\lambda$-Stein pair to an approximate zero bias distribution and an approximate $\\lambda,R$-Stein pair, respectively. Berry Esseen type bounds to the normal, based on approximate zero bias couplings and approximate $\\lambda,R$-Stein pairs, are obtained using Stein's method. The bounds are then applied to combinatorial central limit theorems where the random permutation has the Ewens $\\mathcal{E}_\\theta$ distribution with $\\theta>0$ which can be specialized to the uniform distribution by letting $\\theta=1$. The family of the Ewens distributions appears in the context of population genetics in biology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-12T05:32:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60C05"
    ],
    "keywords": [
      "approximate zero bias couplings",
      "combinatorial central limit theorems",
      "steins method",
      "ewens distribution",
      "stein pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}