Explicit Error Bounds via Total Variation

This chapter concerns the obtaining of explicit error estimates for convergence to Benford's law, with an analysis done through the total variation of the densities. This method yields reasonable estimates for Benford's law in many cases, and is often simpler to calculate and more elementary than Fourier methods. Here, the chapter provides the distribution of the remainder U in the case of Y having a Lebesgue density f, defines the measures of non-uniformity of this distribution, and collects some basic facts about the total variation of functions. The main results, examples, and proofs are then presented in the final three sections of this chapter.

Keywords: explicit error estimates, total variation, explicit error bounds, non-uniformity, densities, functions

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Steven J. Miller

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Explicit Error Bounds via Total Variation

Explicit Error Bounds via Total Variation

Lutz Dümbgen

Christoph Leuenberger