Benford's LawTheory and Applications

Benford's LawTheory and Applications

Steven J. Miller

Print publication date: 2017

ISBN: 9780691147611

Publisher: Princeton University Press

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 should not follow Benford's law and how quickly such behavior sets in. The book goes on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The book describes how Benford's law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book. Emphasizing common challenges and techniques across the disciplines, this book shows how Benford's law can serve as a productive meeting ground for researchers and practitioners in diverse fields.

Table of Contents

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