A Study of Benford's Law, With Applications to the Analysis of Corporate Financial Statements

Open Access
Author:
Chang, Juan
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 31, 2017
Committee Members:
  • Donald St. P. Richards, Thesis Advisor
  • David R. Hunter, Committee Member
  • James L. Rosenberger, Committee Member
Keywords:
  • Benford's Law
  • Pearson's chi-square test
  • discrete Kolmogorov-Smirnov test
  • goodness-of-fit test
  • finances
Abstract:
We consider in this thesis the numerical phenomenon, known as Benford's Law, which asserts numerical values for the empirical probabilities of first digits appearing in many lists of numbers. We introduce Benford's Law through motivating explanations and examples, and we explain why this numerical phenomenon can be applied to many different data sets. We also apply Benford's Law to the financial statements of three companies to test whether data derived from those statements follow Benford's Law. In the early part of the thesis, we introduce extensions of Benford's Law to calculating the empirical frequencies of specific digits and each sequence of digits. We motivate Benford's Law by compound growth processes, the scale-invariance of many randomly occurring processes, and the Central Limit Theorem. We also introduce extensions of Benford's Law beyond the first digit phenomenon to calculating the empirical frequencies of the second, third, and any given digit or sequence of digits. We apply Benford's Law to data drawn from the financial statements of three corporations: Bernard L. Madoff Investment Securities LLC, Toshiba Corporation, and Valeant Pharmaceuticals International, Inc., each of which has received widespread scrutiny in recent years. We apply Pearson's chi-square and the discrete Kolmogorov-Smirnov goodness-of-fit statistics to test the hypotheses that the data obtained from the statements of each of these three corporations follows Benford's Law. Finally, we provide in an appendix the software code, from the statistical package R, which was used to carry out the analyses of the data drawn from the corporate financial statements.