{"product_id":"benfords-law-isbn-9781118152850","title":"Benford's Law","description":"\u003cb\u003eA powerful new tool for all forensic accountants, or anyone who analyzes data that may have been altered\u003c\/b\u003e  \u003cp\u003eBenford'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.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eExplores primary, associated, and advanced tests, all described with data sets that include corporate payments data and election data\u003c\/li\u003e \u003cli\u003eIncludes ten fraud detection studies, including vendor fraud, payroll fraud, due diligence when purchasing a business, and tax evasion\u003c\/li\u003e \u003cli\u003eCovers financial statement fraud, with data from Enron, AIG, and companies that were the target of hedge fund short sales\u003c\/li\u003e \u003cli\u003eLooks at how to detect Ponzi schemes, including data on Madoff, Waxenberg, and more\u003c\/li\u003e \u003cli\u003eExamines many other applications, from the Clinton tax returns and the charitable gifts of Lehman Brothers to tax evasion and number invention\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eBenford's Law\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eForeword xi\u003c\/p\u003e \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAbout the Author xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1: Introduction and Mathematical Foundations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBenford’s Expected Digit Frequencies 5\u003c\/p\u003e \u003cp\u003eDefining the First and First-Two Digits 6\u003c\/p\u003e \u003cp\u003eDigit Patterns of U.S. Census Data 8\u003c\/p\u003e \u003cp\u003eLogging on to Benford’s Law 10\u003c\/p\u003e \u003cp\u003eGeneral Significant Digit Law 13\u003c\/p\u003e \u003cp\u003eLog and Behold, the Census Data 13\u003c\/p\u003e \u003cp\u003eLove at First Sight 15\u003c\/p\u003e \u003cp\u003eMantissa Test and Census Data 19\u003c\/p\u003e \u003cp\u003eNumber of Records and Benford’s Law Tests 20\u003c\/p\u003e \u003cp\u003eWhen Should Data Conform to Benford’s Law? 21\u003c\/p\u003e \u003cp\u003eConclusions 23\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2: Theorems, Truisms, and a Little Trivia 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDigits of Corporate Payments Data 26\u003c\/p\u003e \u003cp\u003eDigits of Lake Data 28\u003c\/p\u003e \u003cp\u003eScale Invariance Theorem 31\u003c\/p\u003e \u003cp\u003eMean Absolute Deviation 34\u003c\/p\u003e \u003cp\u003eScale Invariance and Census Data 34\u003c\/p\u003e \u003cp\u003eScale Invariance and Corporate Payments 35\u003c\/p\u003e \u003cp\u003eScale Invariance and Lake Data 36\u003c\/p\u003e \u003cp\u003eA Level Playing Field Becomes Benford 38\u003c\/p\u003e \u003cp\u003eMultiplication by 1\/X 42\u003c\/p\u003e \u003cp\u003eAll Distributions Lead to Benford 43\u003c\/p\u003e \u003cp\u003eGetting a Gripf on Benford and Zipf 46\u003c\/p\u003e \u003cp\u003eConclusions 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3: More Formulas and Facts, and a Little Fibonacci 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFibonacci Numbers 51\u003c\/p\u003e \u003cp\u003eLucas Numbers 53\u003c\/p\u003e \u003cp\u003eBack to Square One 55\u003c\/p\u003e \u003cp\u003e3n+1 Problem 58\u003c\/p\u003e \u003cp\u003eUltimate Uniform Distribution 60\u003c\/p\u003e \u003cp\u003eBenford Embraces Other Bases 62\u003c\/p\u003e \u003cp\u003eNigrini’s Second Last Theorem 65\u003c\/p\u003e \u003cp\u003eConclusions 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4: Primary Benford’s Law Tests 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eCorporate Payments Data 72\u003c\/p\u003e \u003cp\u003eData Profile 72\u003c\/p\u003e \u003cp\u003eFirst Come, First Served 74\u003c\/p\u003e \u003cp\u003ePlaying Second Fiddle 75\u003c\/p\u003e \u003cp\u003eFirst-Two Digits Test 78\u003c\/p\u003e \u003cp\u003eRunning the Digit Tests in Excel 80\u003c\/p\u003e \u003cp\u003eRunning the Digit Tests in Access 83\u003c\/p\u003e \u003cp\u003eConclusions 87\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5: Advanced Benford’s Law Tests 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSummation Test 90\u003c\/p\u003e \u003cp\u003eRunning the Summation Test in Excel 94\u003c\/p\u003e \u003cp\u003eRunning the Summation Test in Access 95\u003c\/p\u003e \u003cp\u003eSecond-Order Test 97\u003c\/p\u003e \u003cp\u003eAn Analysis of Payments Data 102\u003c\/p\u003e \u003cp\u003eAn Analysis of Journal Entry Data 104\u003c\/p\u003e \u003cp\u003eAn Analysis of Census Data 107\u003c\/p\u003e \u003cp\u003eRunning the Second-Order Test in Excel 108\u003c\/p\u003e \u003cp\u003eExcel, Thanks a Million(s) 110\u003c\/p\u003e \u003cp\u003eScale Invariance and the Second-Order Test 113\u003c\/p\u003e \u003cp\u003eConclusions 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6: Associated Benford’s Law Tests 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eNumber Duplication Test 117\u003c\/p\u003e \u003cp\u003eAn Analysis of Payments Data 119\u003c\/p\u003e \u003cp\u003eAn Analysis of Census Data 121\u003c\/p\u003e \u003cp\u003eRunning the Number Duplication Test in Excel 122\u003c\/p\u003e \u003cp\u003eRunning the Number Duplication Test in Access 126\u003c\/p\u003e \u003cp\u003eLast-Two Digits Test 129\u003c\/p\u003e \u003cp\u003eAn Analysis of Payments Data 130\u003c\/p\u003e \u003cp\u003eAn Analysis of Census Data 131\u003c\/p\u003e \u003cp\u003eAn Analysis of Election Results 132\u003c\/p\u003e \u003cp\u003eRunning the Last-Two Digits Test in Excel 135\u003c\/p\u003e \u003cp\u003eRunning the Last-Two Digits Test in Access 136\u003c\/p\u003e \u003cp\u003eDistortion Factor Model 138\u003c\/p\u003e \u003cp\u003eDistortion and the Census Data 145\u003c\/p\u003e \u003cp\u003eConclusions 146\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7: Assessing Conformity to Benford’s Law 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eZ-Statistic 150\u003c\/p\u003e \u003cp\u003eChi-Square Test 153\u003c\/p\u003e \u003cp\u003eKolmogorov-Smirnoff Test 157\u003c\/p\u003e \u003cp\u003eMean Absolute Deviation Test 158\u003c\/p\u003e \u003cp\u003eThe Logarithmic Basis of Benford’s Law 160\u003c\/p\u003e \u003cp\u003eCreating a Perfect Synthetic Benford Set 163\u003c\/p\u003e \u003cp\u003eMantissa Arc Test 165\u003c\/p\u003e \u003cp\u003eConclusions 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8: Examples of Fraudulent Data 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Inside Story 172\u003c\/p\u003e \u003cp\u003eThe Vendor Who Never Was 174\u003c\/p\u003e \u003cp\u003eNot Paying Attention 175\u003c\/p\u003e \u003cp\u003eFunny Money 177\u003c\/p\u003e \u003cp\u003eThe Heart of the Matter 181\u003c\/p\u003e \u003cp\u003eGoing the Extra Mile 182\u003c\/p\u003e \u003cp\u003eLaugh All the Way to the Bank 184\u003c\/p\u003e \u003cp\u003eCulture Shock 187\u003c\/p\u003e \u003cp\u003eHaving a Bad Hair Day 189\u003c\/p\u003e \u003cp\u003eAn Unclean Bill of Health 191\u003c\/p\u003e \u003cp\u003eTurning the Table on Tax Evasion 193\u003c\/p\u003e \u003cp\u003eConclusions 196\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9: Fraudulent Financial Statements, Part I 199\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eNumber Crunching 200\u003c\/p\u003e \u003cp\u003eWrong Numbers 205\u003c\/p\u003e \u003cp\u003eA Look at Enron’s and AIG’s Numbers 207\u003c\/p\u003e \u003cp\u003eFiguring Out the Controllers 210\u003c\/p\u003e \u003cp\u003eConclusions 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10: Fraudulent Financial Statements, Part II 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDigital Yoga by Absaroka 216\u003c\/p\u003e \u003cp\u003eCan’t See the Forest for the Trees 218\u003c\/p\u003e \u003cp\u003eDigit a Little Deeper into Papua New Guinea 221\u003c\/p\u003e \u003cp\u003eThe Good, the Bad, and the Ugly 227\u003c\/p\u003e \u003cp\u003eDig a Little Deeper 233\u003c\/p\u003e \u003cp\u003eThere Are More Questions than Answers 237\u003c\/p\u003e \u003cp\u003eConclusions 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11: Madoff and Other Ponzi Schemes 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Madoff Claims 248\u003c\/p\u003e \u003cp\u003eDon’t Bank on Kaupthing 249\u003c\/p\u003e \u003cp\u003eThe Whole Ball of Waxenberg 252\u003c\/p\u003e \u003cp\u003eGeneral Motors Demoted to Private 253\u003c\/p\u003e \u003cp\u003eChrysler Unable to Dodge Bankruptcy 255\u003c\/p\u003e \u003cp\u003eDiscussion of the Claims Results 258\u003c\/p\u003e \u003cp\u003eA Review of the Madoff Returns 259\u003c\/p\u003e \u003cp\u003eApple, Dell, Berkshire, and Benford 262\u003c\/p\u003e \u003cp\u003eDiscussion of the Returns Results 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12: Earth Science and Income Tax Applications 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eStill Waters Run Deep 268\u003c\/p\u003e \u003cp\u003eThe Lay of the Lake 274\u003c\/p\u003e \u003cp\u003eFor a Few Dollars Less 281\u003c\/p\u003e \u003cp\u003eA Clean Bill of Clinton 286\u003c\/p\u003e \u003cp\u003eConclusions 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13: Future Directions and Conclusions 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMy Law 295\u003c\/p\u003e \u003cp\u003eInsights into Number Invention 300\u003c\/p\u003e \u003cp\u003eLehman’s Charitable Gifts 306\u003c\/p\u003e \u003cp\u003eThe Bottom Line 310\u003c\/p\u003e \u003cp\u003eGlossary of Selected Terms 315\u003c\/p\u003e \u003cp\u003eReferences 323\u003c\/p\u003e \u003cp\u003eIndex 327\u003c\/p\u003e   \u003cp\u003e\u003cb\u003eMARK J. NIGRINI, P\u003csmall\u003eH\u003c\/small\u003eD,\u003c\/b\u003e 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 \u003ci\u003eForensic Analytics\u003c\/i\u003e (Wiley), which describes tests to detect fraud, errors, estimates, and biases in financial data. He has been published in national media including the \u003ci\u003eWall Street Journal\u003c\/i\u003e 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.     \u003c\/p\u003e\u003cp\u003e\u003cb\u003eBENFORD'S LAW\u003c\/b\u003e Applications for Forensic Accounting, Auditing, and Fraud Detection  \u003c\/p\u003e\u003cp\u003eThere 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.  \u003c\/p\u003e\u003cp\u003eThe applications include:  \u003c\/p\u003e\u003cul\u003e \u003cli\u003eU.S. census population numbers\u003c\/li\u003e \u003cli\u003eThe Fibonacci numbers\u003c\/li\u003e \u003cli\u003eCorporate payments\u003c\/li\u003e \u003cli\u003eEnron and AIG's financial statement numbers\u003c\/li\u003e \u003cli\u003eGeneral Motors and Chrysler payments data\u003c\/li\u003e \u003cli\u003eMadoff's monthly returns\u003c\/li\u003e \u003cli\u003eStreamflow and lake data\u003c\/li\u003e \u003cli\u003eTaxpayer interest and dividend income\u003c\/li\u003e \u003cli\u003eThe tax returns of Bill and Hillary Clinton\u003c\/li\u003e \u003cli\u003eLehman's charitable gifts\u003c\/li\u003e \u003c\/ul\u003e  \u003cp\u003e\u003ci\u003eBenford's Law\u003c\/i\u003e 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.  \u003c\/p\u003e\u003cp\u003eA 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988802650341,"sku":"NP9781118152850","price":84.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118152850.jpg?v=1761781648","url":"https:\/\/k12savings.com\/es\/products\/benfords-law-isbn-9781118152850","provider":"K12savings","version":"1.0","type":"link"}