Benford's law : theory, the general law of relative quantities, and forensic fraud detection applications / Alex Ely Kossovsky.

Format:

Book

Author/Creator:

Kossovsky, Alex Ely, author.

Language:

English

Subjects (All):

Fraud investigation--Statistical methods.

Fraud investigation.

Fraud--Statistical methods.

Fraud.

Distribution (Probability theory).

Forensic statistics.

Forensic sciences--Statistical methods.

Forensic sciences.

Physical Description:

1 online resource (672 p.)

Place of Publication:

Singapore : World Scientific Publishing, 2015.

Language Note:

English

Summary:

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 represents an attempt to give a comprehensive and in

Contents:

Benford's Law; Foreword; Introduction; Acknowledgment; CONTENTS; Section 1: Benford's Law; 1. Digits versus Numbers; 2. To Find Fraud, Simply Examine Its Digits!; 3. First Leading Digits; 4. Empirical Evidence from Real-Life Data on Digit Distribution; 5. Physical Clues of the Digital Pattern; 6. Historical Background of the Two Discoverers; 7. Benford's Law; 8. The Prevalence of Benford's Law; 9. Physical Law versus Numerical Law; 10. Nature's Way of Counting Single-Issue Phenomena; 11. Case Study I: Time Between Earthquakes

12. Data on Population Counts of Cities, Towns, Regions, and Districts13. Case Study II: U.S. Census Data on Population Centers; 14. Data sets on USA Population by State and by County; 15. Four Distinct Numerical Processes Leading to Benford; 16. Random Linear Combinations and Accounting Revenue Data; 17. Aggregation of Data Sets as a Prominent Cause of Benford's Law; 18. Random Pick from a Variety of Data Sources is Logarithmic; 19. Integral Powers of Ten; 20. The Logarithmic as Repeated Multiplications; 21. Case Study III: Exponential 0.5% Growth Series for 3,233 Periods

22. Case Study IV: 140 Cumulative Dice Multiplications23. The Universality of Benford's Law - True in any Scale System; 24. A Hidden Digital Signature within Benford's Digital Signature; Section 2: Forensic Digital Analysis & Fraud Detection; 25. Historical Background of the First Applications of Benford's Law; 26. Methods in Financial and Accounting Fraud Detection; 27. The Part and Type of Data Applicable to Forensic Testing; 28. Case Study V: U.S. Market Capitalization on January 1, 2013; 29. Case Study VI: Microsoft Corporation Financial Statement

30. Case Study VII: Total Return of Athena Guaranteed Futures Fund31. Establishing Direct Connection Between Digit Anamoly & Fraud; 32. Post-Test Conclusions; 33. Detecting Fraud via Digital Development Pattern; 34. The Dilemma of FTD versus LTD for Digit-Anemic Numbers; Section 3: Data Compliance Tests; 35. Testing Data for Conformity to Benford's Law; 36. The Z Test; 37. The chi-Square Test; 38. SSD as a Measure of Distance from the Logarithmic; 39. Saville Regression Measure; 40. Value Repetition Test; 41. The Confusion and Mistaken Applications of Summation Test

42. Summation Test in the Context of Fraud Detection43. Methods in Digital Development Pattern Detection; 44. Case Study VIII: Price List of a Large Manufacturer; 45. Case Study IX: USA County Area Data; 46. Random Linear Combinations and Revenue Data Revisited; 47. Case Study X: Forensic Analysis of Revenue Data for Small Shop; Section 4: Conceptual and Mathematical Foundations; 48. Hybrid Data Sets Blending Several Data Types; 49. Second-Generation Distributions; 50. A Leading Digits Parable; 51. Simple Averaging Scheme as a Model for Typical Data; 52. More Complex Averaging Schemes

53. Digital Proportions within the Number System Itself

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781322100111

132210011X

9789814583695

9814583693