{
  "id": "1605.03896",
  "version": "v1",
  "published": "2016-05-12T17:13:17.000Z",
  "updated": "2016-05-12T17:13:17.000Z",
  "title": "Natural exponential families invariant by a subgroup of the general affine group and a characterization of the Riesz measure on homogeneous cones",
  "authors": [
    "Hideyuki Ishi",
    "Bartosz Kołodziejek"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "In the paper we present a systematic study of natural exponential families invariant by a subgroup of general affine group of finite dimensional linear space. We give a characterization theorem of a generating measure of such family. As an application of our main theorem, we prove a characterization of the Riesz measure on homogeneous cones through the invariance property of natural exponential family under the action of the triangular group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-12T17:13:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B11",
      "62E10"
    ],
    "keywords": [
      "natural exponential families invariant",
      "natural exponential family",
      "general affine group",
      "riesz measure",
      "homogeneous cones"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}