Benford's Law

Theory and Applications

Buch | Hardcover

464 Seiten

2015
Princeton University Press (Verlag)
978-0-691-14761-1 (ISBN)

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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.

Steven J. Miller is associate professor of mathematics at Williams College. He is the coauthor of An Invitation to Modern Number Theory (Princeton).

*Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. xiii*Preface, pg. xvii*Notation, pg. xxiii*Chapter One. A Quick Introduction to Benford's Law, pg. 3*Chapter Two. A Short Introduction to the Mathematical Theory of Benford's Law, pg. 23*Chapter Three. Fourier Analysis and Benford's Law, pg. 68*Chapter Four. Benford's Law Geometry, pg. 109*Chapter Five. Explicit Error Bounds via Total Variation, pg. 119*Chapter Six. Levy Processes and Benford's Law, pg. 135*Chapter Seven. Benford's Law as a Bridge between Statistics and Accounting, pg. 177*Chapter Eight. Detecting Fraud and Errors Using Benford's Law, pg. 191*Chapter Nine. Can Vote Counts' Digits and Benford's Law Diagnose Elections?, pg. 212*Chapter Ten. Complementing Benford's Law for Small N: A Local Bootstrap, pg. 223*Chapter Eleven. Measuring the Quality of European Statistics, pg. 235*Chapter Twelve. Benford's Law and Fraud in Economic Research, pg. 244*Chapter Thirteen. Testing for Strategic Manipulation of Economic and Financial Data, pg. 257*Chapter Fourteen. Psychology and Benford's Law, pg. 267*Chapter Fifteen. Managing Risk in Numbers Games, pg. 276*Chapter Sixteen. Benford's Law in the Natural Sciences, pg. 290*Chapter Seventeen. Generalizing Benford's Law, pg. 304*Chapter Eighteen. PV Modeling of Medical Imaging Systems, pg. 319*Chapter Nineteen. Application of Benford's Law to Images, pg. 338*Chapter Twenty. Exercises, pg. 373*Bibliography, pg. 402*Index, pg. 433

Zusatzinfo	78 line illus.
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 235 mm
Gewicht	765 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
ISBN-10	0-691-14761-2 / 0691147612
ISBN-13	978-0-691-14761-1 / 9780691147611
Zustand	Neuware