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Benford's LawTheory and Applications$
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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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Fourier Analysis and Benfordʼs Law

Fourier Analysis and Benfordʼs Law

(p.68) Chapter Three Fourier Analysis and Benfordʼs Law
Benford's Law

Steven J. Miller

Princeton University Press

This chapter continues the development of the theory of Benford's law. It uses Fourier analysis (in particular, Poisson Summation) to prove many systems either satisfy or almost satisfy the Fundamental Equivalence, and hence either obey Benford's law, or are well approximated by it. Examples range from geometric Brownian motions to random matrix theory to products and chains of random variables to special distributions. The chapter furthermore develops the notion of a Benford-good system. Unfortunately one of the conditions here concerns the cancelation in sums of translated errors related to the cumulative distribution function, and proving the required cancelation often requires techniques specific to the system of interest.

Keywords:   Fourier analysis, Poisson Summation, Fundamental Equivalence, Benford-good system, cumulative distribution, uniform distribution

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