Benford's Law Applications for Forensic Accounting, Auditing, and Fraud Detection

by Nigrini, Mark J.; Wells, Joseph T.

• ISBN13: 9781118152850
• ISBN10: 1118152859
• Edition: 1st
• Format: Hardcover
• Copyright: 2012-04-24
• Publisher: Wiley

Summary

This book will provide an overview of the applications of Benford's Law to summarize its current uses. It will also set out a series of Benford's Law tests that can be run on any data set and show how to run these tests on any one of ten software programs. It will show Benford's Law can be used as a tool for auditors and data managers to insure integrity of large sets of data. There will be a companion site for the book with sample data sets readers can practice tests on and other interesting items.

Author Biography

MARK J. NIGRINI, PhD, is a professor at The College of New Jersey where he teaches forensic accounting courses. His research involves advanced theoretical work on Benford's Law and the legal process surrounding fraud convictions. Nigrini is also the author of Forensic Analytics (Wiley), which describes tests to detect fraud, errors, estimates, and biases in financial data. He has been published in national media including the Wall Street Journal and has published papers on Benford's Law and accounting in academic and professional journals. Nigrini regularly presents professional seminars for accountants and auditors in North America, Europe, and Asia with recent events in Singapore, Switzerland, and New Zealand.

Table of Contents

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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