Explicit bounds for the approximation error in Benford's law
| dc.creator | Duembgen, Lutz | |
| dc.creator | Leuenberger, Christoph | |
| dc.date | 2007-05-30 | |
| dc.date | 2008-01-02 | |
| dc.date.accessioned | 2026-07-07T09:46:17Z | |
| dc.date.available | 2026-07-07T09:46:17Z | |
| dc.description | 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. | |
| dc.description | 16 pages, one figure | |
| dc.identifier | https://arxiv.org/abs/0705.4488 | |
| dc.identifier | http://arxiv.org/abs/0705.4488 | |
| dc.identifier | Electronic Communications in Probability 13 (2008), 99-112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163474 | |
| dc.subject | Probability | |
| dc.subject | 60E15; 60F99 | |
| dc.title | Explicit bounds for the approximation error in Benford's law | |
| dc.type | text |