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An Introduction to Benford's Law$
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Arno Berger and Theodore P. Hill

Print publication date: 2015

Print ISBN-13: 9780691163062

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691163062.001.0001

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The Uniform Distribution and Benford's Law

The Uniform Distribution and Benford's Law

(p.43) Chapter Four The Uniform Distribution and Benford's Law
An Introduction to Benford's Law

Arno Berger

Theodore P. Hill

Princeton University Press

The uniform distribution characterization of Benford's law is the most basic and powerful of all characterizations, largely because the mathematical theory of uniform distribution modulo one is very well developed for authoritative surveys. This chapter records and develops tools from that theory which will be used throughout this book to establish Benford behavior of sequences, functions, and random variables. Topics discussed include uniform distribution characterization of Benford's law, uniform distribution of sequences and functions, and uniform distribution of random variables.

Keywords:   Benford's law, uniform distribution, surveys, mathematical theory, sequences, functions, random variables

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