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Benford's Law
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Benford's Law: Theory and Applications

Steven J. Miller

Abstract

Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. This book demonstrates the many useful techniques that arise from the law, showing how truly multidisciplinary it is, and encouraging collaboration. Beginning with the general theory, the chapters explain the prevalence of the bias, highlighting explanations for when systems should and s ... More

Keywords: Benford's law, data sets, bias, accounting, economics, fraud, elections, medical tests, financial reports, tax filing

Bibliographic Information

Print publication date: 2015 Print ISBN-13: 9780691147611
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691147611.001.0001

Authors

Affiliations are at time of print publication.

Steven J. Miller, editor
Williams College

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Contents

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Part I General Theory I: Basis of Benfordʼs Law

Part II General Theory II: Distributions and Rates of Convergence

Chapter Five Explicit Error Bounds via Total Variation

Lutz Dümbgen and Christoph Leuenberger1

Part III Applications I: Accounting and Vote Fraud

Part IV Applications II: Economics

Chapter Eleven Measuring the Quality of European Statistics

Bernhard Rauch, Max Göttsche, Gernot Brähler, Stefan Engel1

Part V Applications III: Sciences

Chapter Fourteen Psychology and Benfordʼs Law

Bruce D. Burns and Jonathan Krygier1

Chapter Fifteen Managing Risk in Numbers Games

Mabel C. Chou, Qingxia Kong, Chung-Piaw Teo and Huan Zheng1

Chapter Seventeen Generalizing Benfordʼs Law

Joanne Lee, Wendy K. Tam Cho, and George Judge1

Part VI Applications IV: Images

Chapter Nineteen Application of Benfordʼs Law to Images

Fernando Pérez-González, Tu-Thach Quach, Chaouki T. Abdallah, Gregory L. Heileman and Steven J. Miller1

Part VII Exercises

End Matter