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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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Significant Digits and the Significand

Significant Digits and the Significand

(p.11) Chapter Two Significant Digits and the Significand
An Introduction to Benford's Law

Arno Berger

Theodore P. Hill

Princeton University Press

Benford's law is a statement about the statistical distribution of significant (decimal) digits or, equivalently, about significands, namely fraction parts in floating-point arithmetic. Thus, a natural starting point for any study of Benford's law is the formal definition of significant digits and the significand function. This chapter contains formal definitions, examples, and graphs of significant digits and the significand (mantissa) function, and the probability spaces needed to formulate Benford's law precisely, including the crucial natural domain of “events,” the so-called significand σ‎-algebra.

Keywords:   Benford's law, statistical distribution, significant digits, significand functions

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