{
  "id": "1708.03789",
  "version": "v1",
  "published": "2017-08-12T15:49:17.000Z",
  "updated": "2017-08-12T15:49:17.000Z",
  "title": "The medians for exponential families and the normal law",
  "authors": [
    "Gerard Letac",
    "Mauro Piccioni"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $P$ a probability on the real line generating a natural exponential family $(P_t)_{t\\in \\R}$. The property that $t$ is a median of $P_t$ for all $t$ is fulfilled by the standard Gaussian law $N(0.1).$ We show that this property is stable in the sense that if $P$ has a bounded density with respect to $N(0,1)$ then $P=N(0,1).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-12T15:49:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal law",
      "standard gaussian law",
      "probability",
      "natural exponential family",
      "real line generating"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}