{
  "id": "2101.00516",
  "version": "v1",
  "published": "2021-01-02T20:48:03.000Z",
  "updated": "2021-01-02T20:48:03.000Z",
  "title": "Some properties of q-Gaussian distributions",
  "authors": [
    "Nahla Ben Salah"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a q-normal distribution itself. In this paper, two q-moments types called normalized and unormalized q-moments are introduced in details. Some properties of q-moments are given, and several relationships between them are established, and some results related to q-moments are also obtained. Moreover, we show that these new q-moments may be regarded as a generelazation of the classical case for q = 1. Firstly, we determine the q-moments of q-Gaussian distribution. Especially, we give explicitely the kurtosis parameters. Secondly, we compute the expression of the q-Laplace transform of the q-Gaussian distribution. Finally, we study the distribution of sum of q-independent Gaussian distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-02T20:48:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "q-gaussian distribution",
      "properties",
      "q-normal distribution",
      "q-independent gaussian distributions",
      "q-laplace transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}