Detecting fraud in data sets using Benford's Law

An important need of governments, for tax purposes, and corporations, for internal audits, is the ability to detect fraudulently reported financial data. Benford's Law is a numerical phenomenon in which sets of data that are counting or measuring some event follow a certain distribution. A history of the origins of Benford's Law is given and the types of data sets expected to follow Benford's Law are presented. A statistical detection method developed by Nigrini to test whether or not a particular data set follows Benford's Law is discussed; the purpose of this method is to detect fraud in data sets such as tax data. An obvious alternative to Nigrini's method using a classical approach is given as well as two Bayesian approaches to this problem. A simulation study is performed to compare the different approaches.