{
  "id": "2108.00272",
  "version": "v1",
  "published": "2021-07-31T15:52:40.000Z",
  "updated": "2021-07-31T15:52:40.000Z",
  "title": "On some generalization of the normal distribution",
  "authors": [
    "Krzysztof Zajkowski"
  ],
  "comment": "7 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we propose some new generalization of the normal distribution. We will call it the $\\alpha$- normal (Gaussian) distribution. For $\\alpha=2$ it becomes the standard normal distribution. We show expression for moments and the differential entropy. We also calculate the (exponential) Orlicz norm of the standard $\\alpha$-normal random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-31T15:52:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "46E30"
    ],
    "keywords": [
      "generalization",
      "standard normal distribution",
      "normal random variables",
      "differential entropy",
      "orlicz norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}