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

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 4/24/2012
  • Publisher: Wiley
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Supplemental Materials

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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

Forewordp. xi
Prefacep. xiii
About the Authorp. xix
Introduction and Mathematical Foundationsp. 1
Benford's Expected Digit Frequenciesp. 5
Defining the First and First-Two Digitsp. 6
Digit Patterns of U.S. Census Datap. 8
Logging on to Benford's Lawp. 10
General Significant Digit Lawp. 13
Log and Behold, the Census Datap. 13
Love at First Sightp. 15
Mantissa Test and Census Datap. 19
Number of Records and Benford's Law Testsp. 20
When Should Data Conform to Benford's Law?p. 21
Conclusionsp. 23
Theorems, Truisms, and a Little Triviap. 25
Digits of Corporate Payments Datap. 26
Digits of Lake Datap. 28
Scale Invariance Theoremp. 31
Mean Absolute Deviationp. 34
Scale Invariance and Census Datap. 34
Scale Invariance and Corporate Paymentsp. -35
Scale Invariance and Lake Datap. 36
A Level Playing Field Becomes Benfordp. 38
Multiplication by 1/Xp. 42
All Distributions Lead to Benfordp. 43
Getting a Gripf on Benford and Zipfp. 46
Conclusionsp. 50
More Formulas and Facts, and a Little Fibonaccip. 51
Fibonacci Numbersp. 51
Lucas Numbersp. 53
Back to Square Onep. 55
3n+1 Problemp. 58
Ultimate Uniform Distributionp. 60
Benford Embraces Other Basesp. 62
Nigrini's Second Last Theoremp. 65
Conclusionsp. 69
Primary Benford's Law Testsp. 71
Corporate Payments Datap. 72
Data Profilep. 72
First Come, First Servedp. 74
Playing Second Fiddlep. 7^
First-Two Digits Testp. 78
Running the Digit Tests in Excelp. 80
Running the Digit Tests in Accessp. 83
Conclusionsp. 87
Advanced Benford's Law Testsp. 89
Summation Testp. 90
Running the Summation Test in Excelp. 94
Running the Summation Test in Accessp. 95
Second-Order Testp. 97
An Analysis of Payments Datap. 102
An Analysis of Journal Entry Datap. 104
An Analysis of Census Datap. 107
Running the Second-Order Test in Excelp. 108
Excel, Thanks a Million(s)p. 110
Scale Invariance and the Second-Order Testp. 113
Conclusionsp. 114
Associated Benford's Law Testsp. 117
Number Duplication Testp. 117
An Analysis of Payments Datap. 119
An Analysis of Census Datap. 121
Running the Number Duplication Test in Excelp. 122
Running the Number Duplication Test in Accessp. 126
Last-Two Digits Testp. 129
An Analysis of Payments Datap. 130
An Analysis of Census Datap. 131
An Analysis of Election Resultsp. 132
Running the Last-Two Digits Test in Excelp. 135
Running the Last-Two Digits Test in Accessp. 136
Distortion Factor Modelp. 138
Distortion and the Census Datap. 145
Conclusionsp. 146
Assessing Conformity to Benford's Lawp. 149
Z-Statisticp. 150
Chi-Square Testp. 153
Kolmogorov-Smirnoff Testp. 157
Mean Absolute Deviation Testp. 158
The Logarithmic Basis of Benford's Lawp. 160
Creating a Perfect Synthetic Benford Setp. 163
Mantissa Arc Testp. 165
Conclusionsp. 169
Examples of Fraudulent Datap. 171
The Inside Storyp. 172
The Vendor Who Never Wasp. 174
Not Paying Attentionp. 175
Funny Moneyp. 177
The Heart of the Matterp. 181
Going the Extra Milep. 182
Laugh All the Way to the Bankp. 184
Culture Shockp. 187
Having a Bad Hair Dayp. 189
An Unclean Bill of Healthp. 191
Turning the Table on Tax Evasionp. 193
Conclusionsp. 196
Fraudulent Financial Statements, Part Ip. 199
Number Crunchingp. 200
Wrong Numbersp. 205
A Look at Enron's and AIG's Numbersp. 207
Figuring Out the Controllersp. 210
Conclusionsp. 213
Fraudulent Financial Statements, Part IIp. 215
Digital Yoga by Absarokap. 216
Can't See the Forest for the Treesp. 218
Digit a Little Deeper into Papua New Guineap. 221
The Good, the Bad, and the Uglyp. 227
Dig a Little Deeperp. 233
There Are More Questions than Answersp. 237
Conclusionsp. 244
Madoff and Other Ponzi Schemesp. 247
The Madoff Claimsp. 248
Don't Bank on Kaupthingp. 249
The Whole Ball of Waxenbergp. 252
General Motors Demoted to Privatep. 253
Chrysler Unable to Dodge Bankruptcyp. 255
Discussion of the Claims Resultsp. 258
A Review of the Madoff Returnsp. 259
Apple, Dell, Berkshire, and Benfordp. 262
Discussion of the Returns Resultsp. 265
Earth Science and Income Tax Applicationsp. 267
Still Waters Run Deepp. 268
The Lay of the Lakep. 274
For a Few Dollars Lessp. 281
A Clean Bill of Clintonp. 286
Conclusionsp. 290
Future Directions and Conclusionsp. 293
My Lawp. 295
Insights into Number Inventionp. 300
Lehman's Charitable Giftsp. 306
The Bottom Linep. 310
Glossary of Selected Termsp. 315
Referencesp. 323
Indexp. 327
Table of Contents provided by Ingram. All Rights Reserved.

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