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Benford's LawTheory and Applications$
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Benford's Law: Theory and Applications

Steven J. Miller

Print publication date: 2015

Print ISBN-13: 9780691147611

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691147611.001.0001

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Explicit Error Bounds via Total Variation

Explicit Error Bounds via Total Variation

Chapter:
(p.119) Chapter Five Explicit Error Bounds via Total Variation
Source:
Benford's Law
Author(s):

Lutz Dümbgen

Christoph Leuenberger

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691147611.003.0005

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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