Benford's Law : : Theory and Applications / / ed. by Steven J. Miller.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015
• MitwirkendeR: Abdallah, Chaouki T.,; Berger, Arno,; Brähler, Gernot,; Burns, Bruce D.,; Chiverton, John,; Cho, Wendy K. Tam,; Chou, Mabel C.,; Cleary, Richard J.,; Dümbgen, Lutz,; Engel, Stefan,; Göttsche, Max,; Heileman, Gregory L.,; Hill, T.P.,; Hoyle, David,; Judge, George,; Kong, Qingxia,; Krygier, Jonathan,; Lee, Joanne,; Leemis, Lawrence,; Leuenberger, Christoph,; Mebane, Walter R.,; Miller, Steven J.,; Moul, Charles C.,; Nigrini, Mark,; Nye, John V. C.,; Pérez-González, Fernando,; Quach, Tu-Thach,; Rauch, Bernhard,; Roukema, Boudewijn F.,; Schürger, Klaus,; Teo, Chung-Piaw,; Thibodeau, Jay C.,; Tödter, Karl-Heinz,; Wells, Kevin,; Zheng, Huan,
• HerausgeberIn: Miller, Steven J.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2015]; ©2015
• Year of Publication: 2015
• Edition: Course Book
• Language: English
• Physical Description: 1 online resource (464 p.) :; 78 line illus.

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.

Table of Contents

Frontmatter -- Contents -- Foreword -- Preface -- Notation -- PART I. General Theory I: Basis of Benfordʼs Law -- Chapter One. A Quick Introduction to Benfordʼs Law -- Chapter Two. A Short Introduction to the Mathematical Theory of Benfordʼs Law -- Chapter Three. Fourier Analysis and Benfordʼs Law -- PART II. General Theory II: Distributions and Rates of Convergence -- Chapter Four. Benfordʼs Law Geometry -- Chapter Five. Explicit Error Bounds via Total Variation -- Chapter Six. Lévy Processes and Benfordʼs Law -- PART III Applications I: Accounting and Vote Fraud -- Chapter Seven. Benfordʼs Law as a Bridge between Statistics and Accounting -- Chapter Eight. Detecting Fraud and Errors Using Benfordʼs Law -- Chapter Nine. Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections? -- Chapter Ten. Complementing Benfordʼs Law for Small N: A Local Bootstrap -- PART IV. Applications II: Economics -- Chapter Eleven. Measuring the Quality of European Statistics -- Chapter Twelve. Benfordʼs Law and Fraud in Economic Research -- Chapter Thirteen. Testing for Strategic Manipulation of Economic and Financial Data -- PART V. Applications III: Sciences -- Chapter Fourteen. Psychology and Benfordʼs Law -- Chapter Fifteen. Managing Risk in Numbers Games -- Chapter Sixteen. Benfordʼs Law in the Natural Sciences -- Chapter Seventeen. Generalizing Benfordʼs Law -- PART VI. Applications IV: Images -- Chapter Eighteen. PV Modeling of Medical Imaging Systems -- Chapter Nineteen. Application of Benfordʼs Law to Images -- PART VII. Exercises -- Chapter Twenty. Exercises -- Bibliography -- Index