Benford's Law

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.

Auteur

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.

Texte du rabat
BENFORD'S LAW Applications for Forensic Accounting, Auditing, and Fraud Detection There are hidden patterns in the chaos that we know as data. In the 1930s, the physicist Frank Benford found that there were predictable patterns to the digits in the numbers in tabulated data. For many years, this little secret was known to only a few people, made up mainly of mathematicians and the Benford family. In the 1990s, the accountant Mark Nigrini first advocated the use of Benford's Law as a test for fraud and of data integrity. With 250 tables and figures dealing with 50 data sets revealed over 13 chapters, Nigrini takes us on a pioneering journey in Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection. Our adventure starts with the original 1938 paper on the topic and then moves through the leading-edge mathematical discoveries in the early days, finishing with recent examples from the GM, Chrysler, and Lehman bankruptcy filings, as well as an analysis of the numbers invented by students in an experiment designed to trick the researcher. The applications include:

• U.S. census population numbers
• The Fibonacci numbers
• Corporate payments
• Enron and AIG's financial statement numbers
• General Motors and Chrysler payments data
• Madoff's monthly returns
• Streamflow and lake data
• Taxpayer interest and dividend income
• The tax returns of Bill and Hillary Clinton
• Lehman's charitable gifts Benford's Law is written to be understood and enjoyed by auditors, forensic accountants, fraud investigators, financial analysts, and others concerned with data integrity and data authenticity. The book is both informative and entertaining, and is aimed at professionals with a basic knowledge of statistics and a love for numbers and figures. Nigrini's passion for the topic is clear, from the first page, where we are reminded that numbers play an integral part in our daily lives, to the final chapter, which includes an evaluation of where we are at the moment with respect to Benford's Law and where we need to go in the future. The inclusion of Excel, Access, and IDEA screenshots means that you can start working on your own data right away. A companion website has links to many of the data sets used in the book, together with PowerPoint slides for college instructors and conference presentations. The website includes the Nigrini Cycle Excel template and several Access databases with their Benford's Law queries. The tests in the book will focus your attention on the abnormal duplications, biases, and anomalies in your data.

Résumé
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.

Contenu

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 …