Detecting Anomalies by Benford's Law

Abstract

Benford's law gives expected patterns of the digits in numerical data. It can be used as a tool to detect outliers for example in as a test for the authenticity and reliability of transaction level accounting data. Based on Benford's law tests for first two digits, first three digits, last digits, last digit, last two digits have been derived as an additional analytical tool. Benford's law is known as a 'first digit law', 'digit analysis' or 'Benford-Newcomb phenomenon'. The second order test is an analysis of the digit frequencies of the differences between the ordered (ranked) values in a data set. The digit frequencies of these differences approximates the frequencies of Benford's law for most distributions of the original data. From some auditor's point of view it is very important if it is possible to use Benford's law to trace siginificant changes in data in some period of time or detect some trends within them.