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Benford's Law

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

Name: Benford's Law
Brand: John Wiley & Sons
SKU: 9781118152850
Price: 800.00 HKD
Availability: OutOfStock
Author: Mark Nigrini
ISBN: 9781118152850

By Mark Nigrini

John Wiley & Sons April 2012

Specifications

ISBN-13: 9781118152850
Publisher: John Wiley & Sons
Publication: April 2012
Format: Hardback , 330 pages
Jurisdiction: International, U.S. ? Countri(es) for reference only

Details

A powerful new tool for all forensic accountants, or anyone who analyzes data that may have been altered

Benford's Law gives the expected patterns of the digits in the numbers in tabulated data such as town and city populations or Madoff's fictitious portfolio returns. Those digits, in unaltered data, will not occur in equal proportions; there is a large bias towards the lower digits, so much so that nearly one-half of all numbers are expected to start with the digits 1 or 2. These patterns were originally discovered by physicist Frank Benford in the early 1930s, and have since been found to apply to all tabulated data. Mark J. Nigrini has been a pioneer in applying Benford's Law to auditing and forensic accounting, even before his groundbreaking 1999 Journal of Accountancy article introducing this useful tool to the accounting world. In Benford's Law, Nigrini shows the widespread applicability of Benford's Law and its practical uses to detect fraud, errors, and other anomalies.

Explores primary, associated, and advanced tests, all described with data sets that include corporate payments data and election data
Includes ten fraud detection studies, including vendor fraud, payroll fraud, due diligence when purchasing a business, and tax evasion
Covers financial statement fraud, with data from Enron, AIG, and companies that were the target of hedge fund short sales
Looks at how to detect Ponzi schemes, including data on Madoff, Waxenberg, and more
Examines many other applications, from the Clinton tax returns and the charitable gifts of Lehman Brothers to tax evasion and number invention

Benford's Law has 250 figures and uses 50 interesting authentic and fraudulent real-world data sets to explain both theory and practice, and concludes with an agenda and directions for future research. The companion website adds additional information and resources.

Foreword

Preface

About the Author

Chapter 1 Introduction and Mathematical Foundations

Benford's Expected Digit Frequencies

Defining the First and First-Two Digits

The Digit Patterns of U.S. Census Data

Logging on to Benford's Law

The General Significant Digit Law

Log and Behold, the Census Data

Love at First Sight

The Mantissa Test and the Census Data

The Number of Records and Benford's Law Tests

When Should Data Conform to Benford's Law?

Conclusions

Chapter 2 Theorems, Truisms, and a Little Trivia

The Digits of Corporate Payments Data

The Digits of Lake Data

The Scale Invariance Theorem

The Mean Absolute Deviation (MAD)

Scale Invariance and Census Data

Scale Invariance and Corporate Payments Data

Scale Invariance and Lake Data

A Level Playing Field Becomes Benford

Multiplication by 1/X

All Distributions Lead to Benford

Getting a Gripf on Benford and Zipf

Conclusions

Chapter 3 More Formulas and Facts, and a Little Fibonacci

The Fibonacci Numbers

The Lucas Numbers

Back to Square One

The 3n+1 Problem

The Ultimate Uniform Distribution

Benford Embraces Other Bases

Nigrini's Second Last Theorem

Conclusions

Chapter 4 The Primary Benford's Law Tests

The Corporate Payments Data

The Data Profile

First Come First Served

Playing Second Fiddle

The First-Two Digits Test

Running the Digit Tests in Excel

Running the Digit Tests in Access

Conclusions

Chapter 5 The Advanced Benford's Law Tests

The Summation Test

Running the Summation Test in Excel

Running the Summation Test in Access

The Second-Order Test

An Analysis of Payments Data

An Analysis of Journal Entry Data

An Analysis of Census Data

Running the Second-Order Test in Excel

Excel, Thanks a million(s)

Scale Invariance and the Second-Order Test

Conclusions

Chapter 6 The Associated Benford's Law Tests

The Number Duplication Test

An Analysis of Payments Data

An Analysis of Census Data

Running the Number Duplication Test in Excel

Running the Number Duplication Test in Access

The Last-Two Digits Test

An Analysis of Payments Data

An Analysis of Census Data

An Analysis of Election Results

Running the Last-Two Digits Test in Excel

Running the Last-Two Digits Test in Access

The Distortion Factor Model

Distortion and the Census Data

Conclusions

Chapter 7 Assessing Conformity to Benford's Law

The Z-statistic

The Chi-Square Test

The Kolmogorov-Smirnoff Test

The Mean Absolute Deviation (MAD) Test

Tests Based on the Logarithmic Basis of Benford's Law

Creating a Perfect Synthetic Benford Set

The Mantissa Arc Test

Conclusions

Chapter 8 Examples of Fraudulent Data

The Inside Story

The Vendor Who Never Was

Not Paying Attention

Selling Yourself Short

The Heart of the Matter

Going the Extra Mile

Laugh All the Way to the Bank

Culture Shock

Having a Bad Hair Day

An Unclean Bill of Health

Turning the Table on Tax Evasion

Conclusions

Chapter 9 Fraudulent Financial Statements, Part I

Number Crunching

Wrong Numbers

A Look at Enron and AIG's Numbers

Figuring Out the Controllers

Conclusions

Chapter 10 Fraudulent Financial Statements, Part II

Digital Yoga by Absaroka

Can't see the Forest for the Trees

Digit a Little Deeper into Papua New Guinea

The Good, the Bad, and the Ugly

Going Back for Second-Order Seconds

There are More Questions Than Answers

Conclusions

Chapter 11 Madoff and Other Ponzi Schemes

The Madoff Claims

Don't Bank on Kaupthing

The Whole Ball of Waxenberg

General

About the Author

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 Journaland 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.