{
  "id": "0705.4488",
  "version": "v3",
  "published": "2007-05-30T23:53:48.000Z",
  "updated": "2008-01-02T08:40:26.000Z",
  "title": "Explicit bounds for the approximation error in Benford's law",
  "authors": [
    "Lutz Duembgen",
    "Christoph Leuenberger"
  ],
  "comment": "16 pages, one figure",
  "journal": "Electronic Communications in Probability 13 (2008), 99-112",
  "categories": [
    "math.PR"
  ],
  "abstract": "Benford's law states that for many random variables X > 0 its leading digit D = D(X) satisfies approximately the equation P(D = d) = log_{10}(1 + 1/d) for d = 1,2,...,9. This phenomenon follows from another, maybe more intuitive fact, applied to Y := log_{10}(X): For many real random variables Y, the remainder U := Y - floor(Y) is approximately uniformly distributed on [0,1). The present paper provides new explicit bounds for the latter approximation in terms of the total variation of the density of Y or some derivative of it. These bounds are an interesting alternative to traditional Fourier methods which yield mostly qualitative results. As a by-product we obtain explicit bounds for the approximation error in Benford's law.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-01-02T08:40:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60F99"
    ],
    "keywords": [
      "explicit bounds",
      "approximation error",
      "benfords law states",
      "real random variables",
      "traditional fourier methods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.4488D"
    }
  }
}