Managing Risk in Numbers Games: Benford's Law and the Small-Number Phenomenonġ5.2 Patterns in Number Selection: The Small-Number Phenomenonġ5.3 Modeling Number Selection with Benford’s LawĬhapter 16. Testing for Strategic Manipulation of Economic and Financial Dataġ3.2 An Application to Value-at-Risk Dataġ4.4 Why Do People Approximate Benford’s Law?Ĭhapter 15. Benford's Law and Fraud in Economic Researchġ2.3 Benford’s Law in Macroeconomic Data and Forecastsġ2.4 Benford’s Law in Published Economic ResearchĬhapter 13. Measuring the Quality of European Statisticsġ1.3 Benford’s Law and Macroeconomic DataĬhapter 12. Complementing Benford's Law for Small N: A Local Bootstrapġ0.2 Applicability of Benford’s Law and the K7 Anomalyġ0.3 A Conservative Alternative to Benford’s Law: A Small N, Empirical, Local Bootstrap Modelġ0.4 Using a Suspected Anomaly to Select Subsets of the Dataġ0.5 When Local Bootstraps Complement Benford’s LawĬhapter 11. Can Vote Counts' Digits and Benford's Law Diagnose Elections?ĩ.3 An Example of Strategic Behavior by VotersĬhapter 10. Detecting Fraud and Errors Using Benford's LawĬhapter 9. Benford's Law as a Bridge between Statistics and Accountingħ.1 The Case for Accountants to Learn Statisticsħ.2 The Financial Statement Auditor’s Work Environmentħ.4 From Statistical Hypothesis to Decision MakingĬhapter 8. APPLICATIONS I: ACCOUNTING AND VOTE FRAUDĬhapter 7. Convergence of Normalized FunctionalsĦ.4 Necessary and Sufficient Conditions for (D) or (SC)Ħ.6 Appendix 1: Another Variant of Poisson SummationĦ.7 Appendix 2: An Elementary Property of Conditional Expectations Lévy Processes and Benford's LawĦ.1 Overview, Basic Definitions, and ExamplesĦ.2 Expectations of Normalized FunctionalsĦ.3 A.S. Explicit Error Bounds via Total VariationĬhapter 6. GENERAL THEORY II: DISTRIBUTIONS AND RATES OF CONVERGENCEĤ.3 Probability Distributions Satisfying Benford’s LawĬhapter 5.

Fourier Analysis and Benford's Lawģ.3 Products of Independent Random Variablesģ.5 Weibull Random Variables, Survival Distributions, and Order Statistics A Short Introduction to the Mathematical Theory of Benford's LawĢ.2 Significant Digits and the SignificandĢ.5 Benford’s Law for Deterministic ProcessesĬhapter 3. A Quick Introduction to Benford's LawĬhapter 2. GENERAL THEORY I: BASIS OF BENFORD'S LAWĬhapter 1.

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