Benford's Law : : Theory and Applications / / ed. by Steven J. Miller.
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 le...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2015] ©2015 |
| Year of Publication: | 2015 |
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| Physical Description: | 1 online resource (464 p.) :; 78 line illus. |
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Benford's Law : Theory and Applications / ed. by Steven J. Miller. Course Book Princeton, NJ : Princeton University Press, [2015] ©2015 1 online resource (464 p.) : 78 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Distribution (Probability theory). Probability measures. MATHEMATICS / Probability & Statistics / General. bisacsh 1938 paper. 2009 presidential elections. Benford analysis. Benford distribution. Benford property. Benford test. Benford's law geometry. Benford's law limit. Benford's law. Benford-good system. Eric Poehlman. European statistics. FSDs. Fourier analysis. Frank Benford. Fundamental Equivalence. Greek statistics. Iranian election. Iranian presidential elections. Lvy processes. PV effect. Partial Volume effect. Poisson Summation Formula. Poisson Summation. Simon Newcomb. Standard Condition. VAR. Value at Risk. accounting programs. accounting students. accounting. auditing. authentic data sets. behavioral approaches. bias. complaint data sets. computer systems. cumulative distribution. data sets. data-adaptive methods. decision-making research. densities. deterministic processes. digit bias. direct applications. econometric regression. economics. election fraud. elections. empirical economics research. empirical economics. error detection. explicit error bounds. explicit error estimates. exponential Lvy processes. finance. financial reports. financial statistics. first significant digits. first-digit analysis. first-digit frequency. fixed odds. forecasts. fraud detection. fraud. fraudulent data sets. functions. gambling. generic potential applications. geometry. government deficit. information-theoretic methods. local boostrap model. logarithms. lottery. macroeconomic data. managing risk. mathematical theory. meaningful numbers. medical tests. misreporting. natural data. natural sciences. non-uniformity. normalized functionals. number lottery games. numbers games. origins. parametric distributions. probability distributions. psychology. random processes. replication. scale invariance. scientific data sets. scientific misconduct. second digits. significand. significant digits. small number. social statistics. statistical relationship. statistics education. statistics. tampering. tax filing. tax fraud. total variation. uniform distribution. vote counts. voting. Abdallah, Chaouki T., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Berger, Arno, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Brähler, Gernot, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Burns, Bruce D., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Chiverton, John, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Cho, Wendy K. Tam, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Chou, Mabel C., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Cleary, Richard J., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Dümbgen, Lutz, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Engel, Stefan, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Göttsche, Max, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Heileman, Gregory L., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Hill, T.P., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Hoyle, David, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Judge, George, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Kong, Qingxia, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Krygier, Jonathan, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Lee, Joanne, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Leemis, Lawrence, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Leuenberger, Christoph, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Mebane, Walter R., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Miller, Steven J., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Miller, Steven J., editor. edt http://id.loc.gov/vocabulary/relators/edt Moul, Charles C., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Nigrini, Mark, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Nye, John V. C., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Pérez-González, Fernando, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Quach, Tu-Thach, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Rauch, Bernhard, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Roukema, Boudewijn F., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Schürger, Klaus, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Teo, Chung-Piaw, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Thibodeau, Jay C., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Tödter, Karl-Heinz, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Wells, Kevin, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Zheng, Huan, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 print 9780691147611 https://doi.org/10.1515/9781400866595?locatt=mode:legacy https://www.degruyter.com/isbn/9781400866595 Cover https://www.degruyter.com/cover/covers/9781400866595.jpg |
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Abdallah, Chaouki T., |
| title |
Benford's Law : Theory and Applications / |
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Benford's Law : Theory and Applications / 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 |
| title_sub |
Theory and Applications / |
| title_full |
Benford's Law : Theory and Applications / ed. by Steven J. Miller. |
| title_fullStr |
Benford's Law : Theory and Applications / ed. by Steven J. Miller. |
| title_full_unstemmed |
Benford's Law : Theory and Applications / ed. by Steven J. Miller. |
| title_auth |
Benford's Law : Theory and Applications / |
| title_alt |
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 |
| title_new |
Benford's Law : |
| title_sort |
benford's law : theory and applications / |
| publisher |
Princeton University Press, |
| publishDate |
2015 |
| physical |
1 online resource (464 p.) : 78 line illus. Issued also in print. |
| edition |
Course Book |
| 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 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>12770nam a22024495i 4500</leader><controlfield tag="001">9781400866595</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20210830012106.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">210830t20152015nju fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400866595</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400866595</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)459970</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)984651869</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA273.6</subfield><subfield code="b">.B46 2017</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT029000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">519.24</subfield><subfield code="2">23</subfield></datafield><datafield tag="245" ind1="0" ind2="0"><subfield code="a">Benford's Law :</subfield><subfield code="b">Theory and Applications /</subfield><subfield code="c">ed. by Steven J. Miller.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Course Book</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2015]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (464 p.) :</subfield><subfield code="b">78 line illus.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Foreword -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Notation -- </subfield><subfield code="t">PART I. General Theory I: Basis of Benfordʼs Law -- </subfield><subfield code="t">Chapter One. A Quick Introduction to Benfordʼs Law -- </subfield><subfield code="t">Chapter Two. A Short Introduction to the Mathematical Theory of Benfordʼs Law -- </subfield><subfield code="t">Chapter Three. Fourier Analysis and Benfordʼs Law -- </subfield><subfield code="t">PART II. General Theory II: Distributions and Rates of Convergence -- </subfield><subfield code="t">Chapter Four. Benfordʼs Law Geometry -- </subfield><subfield code="t">Chapter Five. Explicit Error Bounds via Total Variation -- </subfield><subfield code="t">Chapter Six. Lévy Processes and Benfordʼs Law -- </subfield><subfield code="t">PART III Applications I: Accounting and Vote Fraud -- </subfield><subfield code="t">Chapter Seven. Benfordʼs Law as a Bridge between Statistics and Accounting -- </subfield><subfield code="t">Chapter Eight. Detecting Fraud and Errors Using Benfordʼs Law -- </subfield><subfield code="t">Chapter Nine. Can Vote Countsʼ Digits and Benfordʼs Law Diagnose Elections? -- </subfield><subfield code="t">Chapter Ten. Complementing Benfordʼs Law for Small N: A Local Bootstrap -- </subfield><subfield code="t">PART IV. Applications II: Economics -- </subfield><subfield code="t">Chapter Eleven. Measuring the Quality of European Statistics -- </subfield><subfield code="t">Chapter Twelve. Benfordʼs Law and Fraud in Economic Research -- </subfield><subfield code="t">Chapter Thirteen. Testing for Strategic Manipulation of Economic and Financial Data -- </subfield><subfield code="t">PART V. Applications III: Sciences -- </subfield><subfield code="t">Chapter Fourteen. Psychology and Benfordʼs Law -- </subfield><subfield code="t">Chapter Fifteen. Managing Risk in Numbers Games -- </subfield><subfield code="t">Chapter Sixteen. Benfordʼs Law in the Natural Sciences -- </subfield><subfield code="t">Chapter Seventeen. Generalizing Benfordʼs Law -- </subfield><subfield code="t">PART VI. Applications IV: Images -- </subfield><subfield code="t">Chapter Eighteen. PV Modeling of Medical Imaging Systems -- </subfield><subfield code="t">Chapter Nineteen. Application of Benfordʼs Law to Images -- </subfield><subfield code="t">PART VII. Exercises -- </subfield><subfield code="t">Chapter Twenty. Exercises -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Distribution (Probability theory).</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Probability measures.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Probability & Statistics / General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">1938 paper.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">2009 presidential elections.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford property.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford test.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford's law geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford's law limit.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford's law.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Benford-good system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Eric Poehlman.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">European statistics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">FSDs.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fourier analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Frank Benford.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fundamental Equivalence.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Greek statistics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Iranian election.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Iranian presidential elections.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Lvy processes.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">PV effect.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Partial Volume effect.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Poisson Summation Formula.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Poisson Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simon Newcomb.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Standard Condition.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">VAR.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Value at Risk.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">accounting programs.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">accounting students.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">accounting.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">auditing.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">authentic data sets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">behavioral approaches.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">bias.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">complaint data sets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">computer systems.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">cumulative distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">data sets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">data-adaptive methods.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">decision-making research.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">densities.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">deterministic processes.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">digit bias.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">direct applications.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">econometric regression.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">economics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">election fraud.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">elections.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">empirical economics research.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">empirical economics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">error detection.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">explicit error bounds.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">explicit error estimates.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">exponential Lvy processes.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">finance.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">financial reports.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">financial statistics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">first significant digits.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">first-digit analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">first-digit frequency.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">fixed odds.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">forecasts.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">fraud detection.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">fraud.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">fraudulent data sets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">functions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">gambling.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">generic potential applications.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">government deficit.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">information-theoretic methods.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">local boostrap model.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">logarithms.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">lottery.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">macroeconomic data.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">managing risk.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">mathematical theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">meaningful numbers.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">medical tests.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">misreporting.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">natural data.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">natural sciences.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">non-uniformity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">normalized functionals.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">number lottery games.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">numbers games.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">origins.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">parametric distributions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">probability distributions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">psychology.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">random processes.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">replication.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">scale invariance.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">scientific data sets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">scientific misconduct.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">second digits.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">significand.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">significant digits.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">small number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">social statistics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">statistical relationship.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">statistics education.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">statistics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">tampering.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">tax filing.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">tax fraud.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">total variation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">uniform distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">vote counts.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">voting.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Abdallah, Chaouki T., </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Berger, Arno, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Brähler, Gernot, </subfield><subfield code="e">contributor.</subfield><subfield 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