Produktbild: Benford's Law

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

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

24.04.2012

Verlag

Wiley

Seitenzahl

352

Maße (L/B/H)

26/18.3/2.3 cm

Gewicht

859 g

Sprache

Englisch

ISBN

978-1-118-15285-0

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

24.04.2012

Verlag

Wiley

Seitenzahl

352

Maße (L/B/H)

26/18.3/2.3 cm

Gewicht

859 g

Sprache

Englisch

ISBN

978-1-118-15285-0

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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Die Leseprobe wird geladen.
  • Produktbild: Benford's Law
  • Foreword xi

    Preface xiii

    About the Author xix

    Chapter 1: Introduction and Mathematical Foundations 1

    Benford's Expected Digit Frequencies 5

    Defining the First and First-Two Digits 6

    Digit Patterns of U.S. Census Data 8

    Logging on to Benford's Law 10

    General Significant Digit Law 13

    Log and Behold, the Census Data 13

    Love at First Sight 15

    Mantissa Test and Census Data 19

    Number of Records and Benford's Law Tests 20

    When Should Data Conform to Benford's Law? 21

    Conclusions 23

    Chapter 2: Theorems, Truisms, and a Little Trivia 25

    Digits of Corporate Payments Data 26

    Digits of Lake Data 28

    Scale Invariance Theorem 31

    Mean Absolute Deviation 34

    Scale Invariance and Census Data 34

    Scale Invariance and Corporate Payments 35

    Scale Invariance and Lake Data 36

    A Level Playing Field Becomes Benford 38

    Multiplication by 1/X 42

    All Distributions Lead to Benford 43

    Getting a Gripf on Benford and Zipf 46

    Conclusions 50

    Chapter 3: More Formulas and Facts, and a Little Fibonacci 51

    Fibonacci Numbers 51

    Lucas Numbers 53

    Back to Square One 55

    3n+1 Problem 58

    Ultimate Uniform Distribution 60

    Benford Embraces Other Bases 62

    Nigrini's Second Last Theorem 65

    Conclusions 69

    Chapter 4: Primary Benford's Law Tests 71

    Corporate Payments Data 72

    Data Profile 72

    First Come, First Served 74

    Playing Second Fiddle 75

    First-Two Digits Test 78

    Running the Digit Tests in Excel 80

    Running the Digit Tests in Access 83

    Conclusions 87

    Chapter 5: Advanced Benford's Law Tests 89

    Summation Test 90

    Running the Summation Test in Excel 94

    Running the Summation Test in Access 95

    Second-Order Test 97

    An Analysis of Payments Data 102

    An Analysis of Journal Entry Data 104

    An Analysis of Census Data 107

    Running the Second-Order Test in Excel 108

    Excel, Thanks a Million(s) 110

    Scale Invariance and the Second-Order Test 113

    Conclusions 114

    Chapter 6: Associated Benford's Law Tests 117

    Number Duplication Test 117

    An Analysis of Payments Data 119

    An Analysis of Census Data 121

    Running the Number Duplication Test in Excel 122

    Running the Number Duplication Test in Access 126

    Last-Two Digits Test 129

    An Analysis of Payments Data 130

    An Analysis of Census Data 131

    An Analysis of Election Results 132

    Running the Last-Two Digits Test in Excel 135

    Running the Last-Two Digits Test in Access 136

    Distortion Factor Model 138

    Distortion and the Census Data 145

    Conclusions 146

    Chapter 7: Assessing Conformity to Benford's Law 149

    Z-Statistic 150

    Chi-Square Test 153

    Kolmogorov-Smirnoff Test 157

    Mean Absolute Deviation Test 158

    The Logarithmic Basis of Benford's Law 160

    Creating a Perfect Synthetic Benford Set 163

    Mantissa Arc Test 165

    Conclusions 169

    Chapter 8: Examples of Fraudulent Data 171

    The Inside Story 172

    The Vendor Who Never Was 174

    Not Paying Attention 175

    Funny Money 177

    The Heart of the Matter 181

    Going the Extra Mile 182

    Laugh All the Way to the Bank 184

    Culture Shock 187

    Having a Bad Hair Day 189

    An Unclean Bill of Health 191

    Turning the Table on Tax Evasion 193

    Conclusions 196

    Chapter 9: Fraudulent Financial Statements, Part I 199

    Number Crunching 200

    Wrong Numbers 205

    A Look at Enron's and AIG's Numbers 207

    Figuring Out the Controllers 210

    Conclusions 213

    Chapter 10: Fraudulent Financial Statements, Part II 215

    Digital Yoga by Absaroka 216

    Can't See the Forest for the Trees 218

    Digit a Little Deeper into Papua New Guinea 221

    The Good, the Bad, and the Ugly 227

    Dig a Little Deeper 233

    There Are More Questions than Answers 237

    Conclusions 244

    Chapter 11: Madoff and Other Ponzi Schemes 247

    The Madoff Claims 248

    Don't Bank on Kaupthing 249

    The Whole Ball of Waxenberg 252

    General Motors Demoted to Private 253

    Chrysler Unable to Dodge Bankruptcy 255

    Discussion of the Claims Results 258

    A Review of the Madoff Returns 259

    Apple, Dell, Berkshire, and Benford 262

    Discussion of the Returns Results 265

    Chapter 12: Earth Science and Income Tax Applications 267

    Still Waters Run Deep 268

    The Lay of the Lake 274

    For a Few Dollars Less 281

    A Clean Bill of Clinton 286

    Conclusions 290

    Chapter 13: Future Directions and Conclusions 293

    My Law 295

    Insights into Number Invention 300

    Lehman's Charitable Gifts 306

    The Bottom Line 310

    Glossary of Selected Terms 315

    References 323

    Index 327