# Explicit Bounds for the Approximation Error in Benford's Law

```@article{Duembgen2007ExplicitBF,
title={Explicit Bounds for the Approximation Error in Benford's Law},
author={Lutz Duembgen and Christoph Leuenberger},
journal={Electronic Communications in Probability},
year={2007},
volume={13},
pages={99-112}
}```
• Published 30 May 2007
• Mathematics
• Electronic Communications in Probability
Benford's law states that for many random variables \$X > 0\$ its leading digit \$D = D(X)\$ satisfies approximately the equation \$\mathbb{P}(D = d) = \log_{10}(1 + 1/d)\$ for \$d = 1,2,\ldots,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 - \lfloor Y\rfloor\$ is approximately uniformly distributed on \$[0,1)\$. The present paper provides new explicit bounds for the latter approximation in terms…

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