Miller S.J. (Ed.) Benford's Law: Theory and Applications

Princeton University Press, 2015. — 465 p. — ISBN 978-0-691-14761-1.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. Here, Steven Miller brings together many of the world's leading experts on Benford's law to demonstrate the many useful techniques that arise from the law, show how truly multidisciplinary it is, and encourage collaboration.Beginning with the general theory, the contributors 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. They go on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The contributors describe 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 accessible book shows how Benford's law can serve as a productive meeting ground for researchers and practitioners in diverse fields.GENERAL THEORY I: BASIS OF BENFORDʼS LAW
A Quick Introduction to Benfordʼs Law
A Short Introduction to the Mathematical Theory of Benfordʼs Law
Fourier Analysis and Benfordʼs Law
GENERAL THEORY II: DISTRIBUTIONS AND RATES OF CONVERGENCE
Benfordʼs Law Geometry
Explicit Error Bounds via Total Variation
Lévy Processes and Benfordʼs Law
APPLICATIONS I: ACCOUNTING AND VOTE FRAUD
Benfordʼs Law as a Bridge between Statistics and Accounting
Detecting Fraud and Errors Using Benfordʼs Law
Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections?
Complementing Benfordʼs Law for Small N: A Local Bootstrap
APPLICATIONS II: ECONOMICS
Measuring the Quality of European Statistics
Benfordʼs Law and Fraud in Economic Research
Testing for Strategic Manipulation of Economic and Financial Data
APPLICATIONS III: SCIENCES
Psychology and Benfordʼs Law
Managing Risk in Numbers Games: Benfordʼs Law and the Small-Number Phenomenon
Benfordʼs Law in the Natural Sciences
Generalizing Benfordʼs Law: A Reexamination of Falsified Clinical Data
APPLICATIONS IV: IMAGES
Partial Volume Modeling of Medical Imaging Systems Using the Benford Distribution
Application of Benfordʼs Law to Images
EXERCISES
Exercises