What is included with this book?
Foreword | p. xi |
Preface | p. xiii |
About the Author | p. xix |
Introduction and Mathematical Foundations | p. 1 |
Benford's Expected Digit Frequencies | p. 5 |
Defining the First and First-Two Digits | p. 6 |
Digit Patterns of U.S. Census Data | p. 8 |
Logging on to Benford's Law | p. 10 |
General Significant Digit Law | p. 13 |
Log and Behold, the Census Data | p. 13 |
Love at First Sight | p. 15 |
Mantissa Test and Census Data | p. 19 |
Number of Records and Benford's Law Tests | p. 20 |
When Should Data Conform to Benford's Law? | p. 21 |
Conclusions | p. 23 |
Theorems, Truisms, and a Little Trivia | p. 25 |
Digits of Corporate Payments Data | p. 26 |
Digits of Lake Data | p. 28 |
Scale Invariance Theorem | p. 31 |
Mean Absolute Deviation | p. 34 |
Scale Invariance and Census Data | p. 34 |
Scale Invariance and Corporate Payments | p. -35 |
Scale Invariance and Lake Data | p. 36 |
A Level Playing Field Becomes Benford | p. 38 |
Multiplication by 1/X | p. 42 |
All Distributions Lead to Benford | p. 43 |
Getting a Gripf on Benford and Zipf | p. 46 |
Conclusions | p. 50 |
More Formulas and Facts, and a Little Fibonacci | p. 51 |
Fibonacci Numbers | p. 51 |
Lucas Numbers | p. 53 |
Back to Square One | p. 55 |
3n+1 Problem | p. 58 |
Ultimate Uniform Distribution | p. 60 |
Benford Embraces Other Bases | p. 62 |
Nigrini's Second Last Theorem | p. 65 |
Conclusions | p. 69 |
Primary Benford's Law Tests | p. 71 |
Corporate Payments Data | p. 72 |
Data Profile | p. 72 |
First Come, First Served | p. 74 |
Playing Second Fiddle | p. 7^ |
First-Two Digits Test | p. 78 |
Running the Digit Tests in Excel | p. 80 |
Running the Digit Tests in Access | p. 83 |
Conclusions | p. 87 |
Advanced Benford's Law Tests | p. 89 |
Summation Test | p. 90 |
Running the Summation Test in Excel | p. 94 |
Running the Summation Test in Access | p. 95 |
Second-Order Test | p. 97 |
An Analysis of Payments Data | p. 102 |
An Analysis of Journal Entry Data | p. 104 |
An Analysis of Census Data | p. 107 |
Running the Second-Order Test in Excel | p. 108 |
Excel, Thanks a Million(s) | p. 110 |
Scale Invariance and the Second-Order Test | p. 113 |
Conclusions | p. 114 |
Associated Benford's Law Tests | p. 117 |
Number Duplication Test | p. 117 |
An Analysis of Payments Data | p. 119 |
An Analysis of Census Data | p. 121 |
Running the Number Duplication Test in Excel | p. 122 |
Running the Number Duplication Test in Access | p. 126 |
Last-Two Digits Test | p. 129 |
An Analysis of Payments Data | p. 130 |
An Analysis of Census Data | p. 131 |
An Analysis of Election Results | p. 132 |
Running the Last-Two Digits Test in Excel | p. 135 |
Running the Last-Two Digits Test in Access | p. 136 |
Distortion Factor Model | p. 138 |
Distortion and the Census Data | p. 145 |
Conclusions | p. 146 |
Assessing Conformity to Benford's Law | p. 149 |
Z-Statistic | p. 150 |
Chi-Square Test | p. 153 |
Kolmogorov-Smirnoff Test | p. 157 |
Mean Absolute Deviation Test | p. 158 |
The Logarithmic Basis of Benford's Law | p. 160 |
Creating a Perfect Synthetic Benford Set | p. 163 |
Mantissa Arc Test | p. 165 |
Conclusions | p. 169 |
Examples of Fraudulent Data | p. 171 |
The Inside Story | p. 172 |
The Vendor Who Never Was | p. 174 |
Not Paying Attention | p. 175 |
Funny Money | p. 177 |
The Heart of the Matter | p. 181 |
Going the Extra Mile | p. 182 |
Laugh All the Way to the Bank | p. 184 |
Culture Shock | p. 187 |
Having a Bad Hair Day | p. 189 |
An Unclean Bill of Health | p. 191 |
Turning the Table on Tax Evasion | p. 193 |
Conclusions | p. 196 |
Fraudulent Financial Statements, Part I | p. 199 |
Number Crunching | p. 200 |
Wrong Numbers | p. 205 |
A Look at Enron's and AIG's Numbers | p. 207 |
Figuring Out the Controllers | p. 210 |
Conclusions | p. 213 |
Fraudulent Financial Statements, Part II | p. 215 |
Digital Yoga by Absaroka | p. 216 |
Can't See the Forest for the Trees | p. 218 |
Digit a Little Deeper into Papua New Guinea | p. 221 |
The Good, the Bad, and the Ugly | p. 227 |
Dig a Little Deeper | p. 233 |
There Are More Questions than Answers | p. 237 |
Conclusions | p. 244 |
Madoff and Other Ponzi Schemes | p. 247 |
The Madoff Claims | p. 248 |
Don't Bank on Kaupthing | p. 249 |
The Whole Ball of Waxenberg | p. 252 |
General Motors Demoted to Private | p. 253 |
Chrysler Unable to Dodge Bankruptcy | p. 255 |
Discussion of the Claims Results | p. 258 |
A Review of the Madoff Returns | p. 259 |
Apple, Dell, Berkshire, and Benford | p. 262 |
Discussion of the Returns Results | p. 265 |
Earth Science and Income Tax Applications | p. 267 |
Still Waters Run Deep | p. 268 |
The Lay of the Lake | p. 274 |
For a Few Dollars Less | p. 281 |
A Clean Bill of Clinton | p. 286 |
Conclusions | p. 290 |
Future Directions and Conclusions | p. 293 |
My Law | p. 295 |
Insights into Number Invention | p. 300 |
Lehman's Charitable Gifts | p. 306 |
The Bottom Line | p. 310 |
Glossary of Selected Terms | p. 315 |
References | p. 323 |
Index | p. 327 |
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