Explicit bounds for the approximation error in Benford's law
| Autor: | Duembgen, Lutz, Leuenberger, Christoph |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Electronic Communications in Probability 13 (2008), 99-112 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 16 pages, one figure |
| Databáze: | arXiv |
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