Benford's Law

Applications for Forensic Accounting, Auditing, and Fraud Detection

Author: Mark Nigrini

Publisher: John Wiley & Sons

ISBN: 1118152859

Category: Business & Economics

Page: 330

View: 4585

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.

Fraud and Fraud Detection, + Website

A Data Analytics Approach

Author: Sunder Gee

Publisher: John Wiley & Sons

ISBN: 1118779657

Category: Business & Economics

Page: 352

View: 1467

This book takes an advanced approach to fraud management, providing step-by-step guidance on automating detection and forensics using CaseWare's IDEA software. Readers will learn to use complex data analysis techniques, including automation scripts, allowing easier and more sensitive detection of anomalies that require further review. You will learn to: understand the different areas of fraud and their specific detection methods; identify anomalies and risk areas using computerized techniques; develop a step-by-step plan for detecting fraud through data analytics; utilize IDEA software to automate detection and identification procedures. The delineation of detection techniques for each type of fraud makes this book a must-have for students and new fraud prevention professionals, and the step-by-step guidance to automation and complex analytics will prove useful for even experienced examiners. --

Journal Entry Testing im Mittelstand

Effizientes Werkzeug oder notwendiges Übel?

Author: Dominique Hoffmann

Publisher: BoD – Books on Demand

ISBN: 3844105417

Category: Business & Economics

Page: 236

View: 7572

„Big Data“ und Digitalisierung, also der Einsatz technologischer Innovationen im betrieblichen Umfeld, verändern Unternehmen und damit den Gegenstand der Abschlussprüfung. Konkret führt die Digitalisierung von Unternehmen zu Anpassungen und Veränderungen des Geschäftsmodells, der Unternehmenskultur, der Unternehmensorganisation und der Geschäftsprozesse. Trotz aller Vorteile der neuen digitalen Welt ergeben sich jedoch auch einige Problemfelder. So führen die ständig wachsenden Datenberge zu Intransparenzen in Unternehmensstrukturen, Prozessen und Abläufen, die in der Vergangenheit nicht selten Auslöser großer Bilanzskandale waren. Für den Abschlussprüfer bedeutet diese Entwicklung, dass sich mit zunehmender Digitalisierung auch die Methoden der Abschlussprüfung verändern müssen, um Verstöße zu erkennen, und die Entwicklung neuer innovativer Prüfungstechniken unumgänglich für den Berufsstand der Wirtschaftsprüfer ist. Ein Ansatzpunkt dafür kann ein effizientes und effektives Journal Entry Testing sein, für das eine konkrete Anleitung im Detail beschrieben wird. Dabei muss die Integration in den risikoorientierten Prüfungsansatz sichergestellt werden. Als innovative Weiterentwicklung wird beschrieben, wie der Einsatz von Data Mining Verfahren die Effizienz der Abschlussprüfung erhöhen und Verstöße aufdecken kann. Mit Hilfe eines Scoring-Modells wird das Ermessen des Abschlussprüfers sichtbar gemacht. Weiterhin wird dargestellt, wie Process Mining Verfahren eingesetzt werden können, um die gestiegene Intransparenz des internen Kontrollsystems durch die Digitalisierung zu vermindern und außer Kraft gesetzte oder umgangene Kontrollen aufzudecken.

An Introduction to Benford's Law

Author: Arno Berger,Theodore P. Hill

Publisher: Princeton University Press

ISBN: 1400866588

Category: Mathematics

Page: 256

View: 3688

This book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law’s colorful history, rapidly growing body of empirical evidence, and wide range of applications. An Introduction to Benford’s Law begins with basic facts about significant digits, Benford functions, sequences, and random variables, including tools from the theory of uniform distribution. After introducing the scale-, base-, and sum-invariance characterizations of the law, the book develops the significant-digit properties of both deterministic and stochastic processes, such as iterations of functions, powers of matrices, differential equations, and products, powers, and mixtures of random variables. Two concluding chapters survey the finitely additive theory and the flourishing applications of Benford’s law. Carefully selected diagrams, tables, and close to 150 examples illuminate the main concepts throughout. The text includes many open problems, in addition to dozens of new basic theorems and all the main references. A distinguishing feature is the emphasis on the surprising ubiquity and robustness of the significant-digit law. This text can serve as both a primary reference and a basis for seminars and courses.

Theorie der Gleichverteilung

Author: Edmund Hlawka

Publisher: N.A

ISBN: N.A

Category: Distribution, Uniform (Probability theory)

Page: 142

View: 362

Benford's Law

Theory, the General Law of Relative Quantities, and Forensic Fraud Detection Applications

Author: Alex Ely Kossovsky

Publisher: World Scientific Publishing Company Incorporated

ISBN: 9789814583688

Category: Mathematics

Page: 649

View: 1865

This book tells the story of a newly discovered and apparently mysterious digital phenomenon of Benford's Law. This phenomenon manifests itself by the empirical finding that not all digits are created equal, but rather that low digits such as 1, 2, 3 occur much more frequently than high digits such as 7, 8, 9, in accounting, financial, scientific, and almost all other data types. This work represents the first ever published work giving a comprehensive and in depth account of all the theoretical aspects and applications of Benford's Law. The reader is subsequently led into a fascinating intellectual journey through the interacting worlds of digits, numbers, and quantities, a journey that ends with the compelling conclusion that the entire phenomenon is truly quantitative in nature, and applicable just as well to the ancient Roman, Mayan, and Egyptian digit-less civilizations. The second section covers the applications of the law in forensic data analysis for the purpose of fraud detection. It is concise, reader-friendly, and can be understood without deep knowledge in statistical theory or difficult mathematics. This fraud detection section gathers all known methods, results, and standards in the accounting and auditing industry, from quite a wide variety of articles on this issue, summarizes and fuses them into a singular coherent whole. In addition, a newly invented (patent-pending) digital algorithm is presented, enabling the auditor to detect such fraud even when the sophisticated and well-educated cheater is aware of the law and attempts to appear as if he or she is innocently complying with the digital pattern. A large portion of the book is devoted to understanding the variety of causes explanations of the phenomenon. Seeing Benford's Law in this bird's eye view enables the reader to see the forest in all its glory and beauty instead of tiring one's self repeatedly checking individual trees.

Forensic Analytics

Methods and Techniques for Forensic Accounting Investigations

Author: Mark J. Nigrini

Publisher: John Wiley & Sons

ISBN: 9781118087633

Category: Business & Economics

Page: 480

View: 2996

Discover how to detect fraud, biases, or errors in your datausing Access or Excel With over 300 images, Forensic Analytics reviews andshows how twenty substantive and rigorous tests can be used todetect fraud, errors, estimates, or biases in your data. For eachtest, the original data is shown with the steps needed to get tothe final result. The tests range from high-level data overviews toassess the reasonableness of data, to highly focused tests thatgive small samples of highly suspicious transactions. These testsare relevant to your organization, whether small or large, forprofit, nonprofit, or government-related. Demonstrates how to use Access, Excel, and PowerPoint in aforensic setting Explores use of statistical techniques such as Benford's Law,descriptive statistics, correlation, and time-series analysis todetect fraud and errors Discusses the detection of financial statement fraud usingvarious statistical approaches Explains how to score locations, agents, customers, oremployees for fraud risk Shows you how to become the data analytics expert in yourorganization Forensic Analytics shows how you can use Microsoft Accessand Excel as your primary data interrogation tools to findexceptional, irregular, and anomalous records.

Benford's Law

Theory, the General Law of Relative Quantities, and Forensic Fraud Detection Applications

Author: Alex Ely Kossovsky

Publisher: World Scientific

ISBN: 9814583707

Category: Mathematics

Page: 672

View: 1892

Contrary to common intuition that all digits should occur randomly with equal chances in real data, empirical examinations consistently show that not all digits are created equal, but rather that low digits such as {1, 2, 3} occur much more frequently than high digits such as {7, 8, 9} in almost all data types, such as those relating to geology, chemistry, astronomy, physics, and engineering, as well as in accounting, financial, econometrics, and demographics data sets. This intriguing digital phenomenon is known as Benford's Law. This book gives a comprehensive and in-depth account of all the theoretical aspects, results, causes and explanations of Benford's Law, with a strong emphasis on the connection to real-life data and the physical manifestation of the law. In addition to such a bird's eye view of the digital phenomenon, the conceptual distinctions between digits, numbers, and quantities are explored; leading to the key finding that the phenomenon is actually quantitative in nature; originating from the fact that in extreme generality, nature creates many small quantities but very few big quantities, corroborating the motto "small is beautiful", and that therefore all this is applicable just as well to data written in the ancient Roman, Mayan, Egyptian, and other digit-less civilizations. Fraudsters are typically not aware of this digital pattern and tend to invent numbers with approximately equal digital frequencies. The digital analyst can easily check reported data for compliance with this digital law, enabling the detection of tax evasion, Ponzi schemes, and other financial scams. The forensic fraud detection section in this book is written in a very concise and reader-friendly style; gathering all known methods and standards in the accounting and auditing industry; summarizing and fusing them into a singular coherent whole; and can be understood without deep knowledge in statistical theory or advanced mathematics. In addition, a digital algorithm is presented, enabling the auditor to detect fraud even when the sophisticated cheater is aware of the law and invents numbers accordingly. The algorithm employs a subtle inner digital pattern within the Benford's pattern itself. This newly discovered pattern is deemed to be nearly universal, being even more prevalent than the Benford phenomenon, as it is found in all random data sets, Benford as well as non-Benford types. Contents:Benford's LawForensic Digital AnalysisFraud DetectionData Compliance TestsConceptual and Mathematical FoundationsBenford's Law in the Physical SciencesTopics in Benford's LawThe Law of Relative Quantities Readership: Professionals, researchers and serious students of financial and data analysis, forensic accounting, fraud investigation, auditing, mathematics and probability and statistics. Key Features:The book is a concise account of practical applications of the phenomenon of fraud detection and it corrects several errors committed in the field where mistaken applications are usedThe perceptive reader interested in knowing about the use of this digital law in fraud detection, would be able to learn about it with a minimal amount of effort and time, without searching through literally hundreds of various small articles on the topicThe book provides numerous new theoretical points-of-view of the phenomenon, new methods for testing data for compliance, and fuses many different aspects of the law into a singular explanationKeywords:Benford's Law;Digits;Quantities;Relative Quantities;Numbers;Fraud;Fraud Detection;Data;Data Analysis;Forensic Analysis;Pattern;Physics;Chemistry;Geology;Astronomy

Using Analytics to Detect Possible Fraud

Tools and Techniques

Author: Pamela S. Mantone

Publisher: John Wiley & Sons

ISBN: 1118715985

Category: Business & Economics

Page: 368

View: 2772

Detailed tools and techniques for developing efficiency andeffectiveness in forensic accounting Using Analytics to Detect Possible Fraud: Tools andTechniques is a practical overview of the first stage offorensic accounting, providing a common source of analyticaltechniques used for both efficiency and effectiveness in forensicaccounting investigations. The book is written clearly so thatthose who do not have advanced mathematical skills will be able tounderstand the analytical tests and use the tests in a forensicaccounting setting. It also includes case studies and visualtechniques providing practical application of the analytical testsdiscussed. Shows how to develop both efficiency and effectiveness inforensic accounting Provides information in such a way that non-practitioners caneasily understand Written in plain language: advanced mathematical skills are notrequired Features actual case studies using analytical tests Essential reading for every investor who wants to preventfinancial fraud, Using Analytics to Detect Possible Fraudallows practitioners to focus on areas that require furtherinvestigative techniques and to unearth deceptive financialreporting before it's too late.

GAMMA

Eulers Konstante, Primzahlstrände und die Riemannsche Vermutung

Author: Julian Havil

Publisher: Springer-Verlag

ISBN: 3540484965

Category: Mathematics

Page: 302

View: 1616

Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.

Einführung in die Wahrscheinlichkeitstheorie und Statistik

Author: Ulrich Krengel

Publisher: Springer-Verlag

ISBN: 3663098850

Category: Mathematics

Page: 258

View: 5266

Stochastik ist die Mathematik des Zufalls. Sie ist von größter Bedeutung für die Berufspraxis der Mathematiker. An vielen Schulen hat sie ihren festen Platz gefunden. Die beiden Hauptgebiete der Stochastik sind Wahrscheinlichkeitstheorie und Statistik.

Auditing

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Auditing

Page: N.A

View: 2919

Geometrie und Billard

Author: Serge Tabachnikov

Publisher: Springer-Verlag

ISBN: 3642319254

Category: Mathematics

Page: 165

View: 6685

Wie bewegt sich ein Massenpunkt in einem Gebiet, an dessen Rand er elastisch zurückprallt? Welchen Weg nimmt ein Lichtstrahl in einem Gebiet mit ideal reflektierenden Rändern? Anhand dieser und ähnlicher Fragen stellt das vorliegende Buch Zusammenhänge zwischen Billard und Differentialgeometrie, klassischer Mechanik sowie geometrischer Optik her. Dabei beschäftigt sich das Buch unter anderem mit dem Variationsprinzip beim mathematischen Billard, der symplektischen Geometrie von Lichtstrahlen, der Existenz oder Nichtexistenz von Kaustiken, periodischen Billardtrajektorien und dem Mechanismus für Chaos bei der Billarddynamik. Ergänzend wartet dieses Buch mit einer beachtlichen Anzahl von Exkursen auf, die sich verwandten Themen widmen, darunter der Vierfarbensatz, die mathematisch-physikalische Beschreibung von Regenbögen, der poincaresche Wiederkehrsatz, Hilberts viertes Problem oder der Schließungssatz von Poncelet.​