{
  "id": "2402.15228",
  "version": "v5",
  "published": "2024-02-23T09:44:02.000Z",
  "updated": "2024-04-15T07:45:18.000Z",
  "title": "Convolutions and Mixtures of Gamma, Stable and Mittag-Leffler Distributions",
  "authors": [
    "Nomvelo Karabo Sibisi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper uses convolutions of the gamma density and the one-sided stable density to construct higher level densities. The approach is applied to constructing a 4-parameter Mittag-Leffler density, whose Laplace transform is a corresponding Mittag-Leffler function, which is completely monotone (CM) by construction. Laplace transforms of mixtures of the stable densities with respect to the 4-parameter Mittag-Leffler distribution are compositions of the Mittag-Leffler functions with Bernstein functions, thereby generating a rich family of CM variants of the base CM Mittag-Leffler functions, including known instances as special cases.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2024-04-15T07:45:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mittag-leffler distribution",
      "convolutions",
      "construct higher level densities",
      "base cm mittag-leffler functions",
      "laplace transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}