{
  "id": "1109.5600",
  "version": "v1",
  "published": "2011-09-26T15:20:14.000Z",
  "updated": "2011-09-26T15:20:14.000Z",
  "title": "Some new approaches to infinite divisibility",
  "authors": [
    "Theofanis Sapatinas",
    "Damodar N. Shanbhag",
    "Arjun K. Gupta"
  ],
  "comment": "18 pages, no figures, To appear in the Electronic Journal of Probability",
  "journal": "Electronic Journal of Probability, Vol. 16, 2359-2374 (2011)",
  "categories": [
    "math.PR"
  ],
  "abstract": "Using an approach based, amongst other things, on Proposition 1 of Kaluza (1928), Goldie (1967) and, using a different approach based especially on zeros of polynomials, Steutel (1967) have proved that each nondegenerate distribution function (d.f.) $F$ (on $\\RR$, the real line), satisfying $F(0-) = 0$ and $F(x) = F(0) + (1-F(0)) G(x)$, $x > 0$, where $G$ is the d.f. corresponding to a mixture of exponential distributions, is infinitely divisible. Indeed, Proposition 1 of Kaluza (1928) implies that any nondegenerate discrete probability distribution ${p_x: x= 0,1, ...}$ that is log-convex or, in particular, completely monotone, is compound geometric, and, hence, infinitely divisible. Steutel (1970), Shanbhag & Sreehari (1977) and Steutel & van Harn (2004, Chapter VI) have given certain extensions or variations of one or more of these results. Following a modified version of the C.R. Rao et al. (2009, Section 4) approach based on the Wiener-Hopf factorization, we establish some further results of significance to the literature on infinite divisibility.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-26T15:20:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E05",
      "62E10"
    ],
    "keywords": [
      "infinite divisibility",
      "approaches",
      "nondegenerate discrete probability distribution",
      "nondegenerate distribution function",
      "real line"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.5600S"
    }
  }
}