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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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Real-valued Random Processes

Real-valued Random Processes

(p.180) Chapter Eight Real-valued Random Processes
An Introduction to Benford's Law

Arno Berger

Theodore P. Hill

Princeton University Press

Benford's law arises naturally in a variety of stochastic settings, including products of independent random variables, mixtures of random samples from different distributions, and iterations of random maps. This chapter provides the concepts and tools to analyze significant digits and significands for these basic random processes. Benford's law also arises in many other important fields of stochastics, such as geometric Brownian motion, random matrices, and Bayesian models, and the chapter may serve as a preparation for specialized literature on these advanced topics. By Theorem 4.2 a random variable X is Benford if and only if log ¦X¦ is uniformly distributed modulo one.

Keywords:   Benford's law, random variables, significands, random processes, stochastic process, geometric Brownian motion, random matrices, Bayesian models

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