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Foreword | |
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Preface | |
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About the Author | |
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Introduction and Mathematical Foundations | |
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Benford's Expected Digit Frequencies | |
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Defining the First and First-Two Digits | |
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Digit Patterns of U.S. Census Data | |
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Logging on to Benford's Law | |
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General Significant Digit Law | |
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Log and Behold, the Census Data | |
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Love at First Sight | |
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Mantissa Test and Census Data | |
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Number of Records and Benford's Law Tests | |
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When Should Data Conform to Benford's Law? | |
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Conclusions | |
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Theorems, Truisms, and a Little Trivia | |
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Digits of Corporate Payments Data | |
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Digits of Lake Data | |
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Scale Invariance Theorem | |
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Mean Absolute Deviation | |
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Scale Invariance and Census Data | |
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Scale Invariance and Corporate Payments | |
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Scale Invariance and Lake Data | |
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A Level Playing Field Becomes Benford | |
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Multiplication by 1/X | |
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All Distributions Lead to Benford | |
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Getting a Gripf on Benford and Zipf | |
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Conclusions | |
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More Formulas and Facts, and a Little Fibonacci | |
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Fibonacci Numbers | |
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Lucas Numbers | |
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Back to Square One | |
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3n+1 Problem | |
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Ultimate Uniform Distribution | |
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Benford Embraces Other Bases | |
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Nigrini's Second Last Theorem | |
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Conclusions | |
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Primary Benford's Law Tests | |
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Corporate Payments Data | |
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Data Profile | |
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First Come, First Served | |
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Playing Second Fiddle | |
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First-Two Digits Test | |
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Running the Digit Tests in Excel | |
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Running the Digit Tests in Access | |
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Conclusions | |
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Advanced Benford's Law Tests | |
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Summation Test | |
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Running the Summation Test in Excel | |
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Running the Summation Test in Access | |
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Second-Order Test | |
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An Analysis of Payments Data | |
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An Analysis of Journal Entry Data | |
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An Analysis of Census Data | |
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Running the Second-Order Test in Excel | |
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Excel, Thanks a Million(s) | |
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Scale Invariance and the Second-Order Test | |
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Conclusions | |
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Associated Benford's Law Tests | |
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Number Duplication Test | |
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An Analysis of Payments Data | |
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An Analysis of Census Data | |
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Running the Number Duplication Test in Excel | |
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Running the Number Duplication Test in Access | |
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Last-Two Digits Test | |
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An Analysis of Payments Data | |
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An Analysis of Census Data | |
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An Analysis of Election Results | |
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Running the Last-Two Digits Test in Excel | |
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Running the Last-Two Digits Test in Access | |
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Distortion Factor Model | |
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Distortion and the Census Data | |
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Conclusions | |
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Assessing Conformity to Benford's Law | |
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Z-Statistic | |
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Chi-Square Test | |
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Kolmogorov-Smirnoff Test | |
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Mean Absolute Deviation Test | |
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The Logarithmic Basis of Benford's Law | |
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Creating a Perfect Synthetic Benford Set | |
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Mantissa Arc Test | |
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Conclusions | |
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Examples of Fraudulent Data | |
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The Inside Story | |
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The Vendor Who Never Was | |
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Not Paying Attention | |
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Funny Money | |
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The Heart of the Matter | |
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Going the Extra Mile | |
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Laugh All the Way to the Bank | |
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Culture Shock | |
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Having a Bad Hair Day | |
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An Unclean Bill of Health | |
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Turning the Table on Tax Evasion | |
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Conclusions | |
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Fraudulent Financial Statements, Part I | |
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Number Crunching | |
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Wrong Numbers | |
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A Look at Enron's and AIG's Numbers | |
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Figuring Out the Controllers | |
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Conclusions | |
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Fraudulent Financial Statements, Part II | |
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Digital Yoga by Absaroka | |
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Can't See the Forest for the Trees | |
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Digit a Little Deeper into Papua New Guinea | |
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The Good, the Bad, and the Ugly | |
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Dig a Little Deeper | |
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There Are More Questions than Answers | |
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Conclusions | |
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Madoff and Other Ponzi Schemes | |
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The Madoff Claims | |
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Don't Bank on Kaupthing | |
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The Whole Ball of Waxenberg | |
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General Motors Demoted to Private | |
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Chrysler Unable to Dodge Bankruptcy | |
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Discussion of the Claims Results | |
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A Review of the Madoff Returns | |
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Apple, Dell, Berkshire, and Benford | |
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Discussion of the Returns Results | |
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Earth Science and Income Tax Applications | |
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Still Waters Run Deep | |
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The Lay of the Lake | |
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For a Few Dollars Less | |
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A Clean Bill of Clinton | |
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Conclusions | |
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Future Directions and Conclusions | |
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My Law | |
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Insights into Number Invention | |
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Lehman's Charitable Gifts | |
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The Bottom Line | |
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Glossary of Selected Terms | |
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References | |
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Index | |