{
  "id": "2210.02098",
  "version": "v1",
  "published": "2022-10-05T08:35:59.000Z",
  "updated": "2022-10-05T08:35:59.000Z",
  "title": "Asymptotic results for sums and extremes",
  "authors": [
    "Rita Giuliano",
    "Claudio Macci",
    "Barbara Pacchiarotti"
  ],
  "comment": "14",
  "categories": [
    "math.PR"
  ],
  "abstract": "The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant, and a weak convergence to a centered Gaussian distribution (when such random variables are properly centered and rescaled). We talk about non-central moderate deviations when the weak convergence is towards some non-Gaussian weak limit. In this paper we prove a non-central moderate deviation result for the bivariate sequence of sums and maxima of i.i.d. random variables. Moreover, we prove a moderate deviation result for sums of partial minima of i.i.d. exponential random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-05T08:35:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic results",
      "non-central moderate deviation result",
      "weak convergence",
      "large deviation principles",
      "term moderate deviations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}