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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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A Short Introduction to the Mathematical Theory of Benfordʼs Law

A Short Introduction to the Mathematical Theory of Benfordʼs Law

Chapter:
(p.23) Chapter Two A Short Introduction to the Mathematical Theory of Benfordʼs Law
Source:
Benford's Law
Author(s):

Arno Berger

T. P. Hill

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691147611.003.0002

This chapter embarks on a brief discussion of the mathematical theory of Benford's law. This law is the observation that in many collections of numbers, be they mathematical tables, real-life data, or combinations thereof, the leading significant digits are not uniformly distributed, as might be expected, but are heavily skewed toward the smaller digits. More specifically, Benford's law states that the significant digits in many data sets follow a very particular logarithmic distribution. The chapter lays out the basic theory of Benford's law before highlighting its more specific components: the significant digits and the significand (function), as well as the Benford property and its four characterizations. Finally, the chapter presents the basic theory of Benford's law in the context of deterministic and random processes.

Keywords:   mathematical theory, significant digits, significand, Benford property, deterministic processes, random processes

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