{
  "id": "2405.10178",
  "version": "v1",
  "published": "2024-05-16T15:19:49.000Z",
  "updated": "2024-05-16T15:19:49.000Z",
  "title": "Infinite Divisibility of the Product of Two Correlated Normal Random Variables and Exact Distribution of the Sample Mean",
  "authors": [
    "Robert E. Gaunt",
    "Saralees Nadarajah",
    "Tibor K. Pogány"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent copies of such random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-16T15:19:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "60E07",
      "62E15",
      "33C15",
      "60E10"
    ],
    "keywords": [
      "correlated normal random variables",
      "sample mean",
      "exact distribution",
      "infinite divisibility",
      "probability density function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}