Benford's Law: Theory and Applications
Benford's Law: Theory and Applications
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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.
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Front Matter
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1Part I General Theory I: Basis of Benfordʼs Law
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Part II General Theory II: Distributions and Rates of Convergence
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Part III Applications I: Accounting and Vote Fraud
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Seven
Benfordʼs Law as a Bridge between Statistics and Accounting
Richard J. Cleary andJay C. Thibodeau
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Eight
Detecting Fraud and Errors Using Benfordʼs Law Mark Nigrini
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Nine
Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections?
Walter R. Mebane,
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Ten
Complementing Benfordʼs Law for Small N: A Local Bootstrap
Boudewijn F. Roukema
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Seven
Benfordʼs Law as a Bridge between Statistics and Accounting
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Part IV Applications II: Economics
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Part V Applications III: Sciences
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Part VI Applications IV: Images
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Part VII Exercises
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End Matter
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