# Fraud detection

Benford's law frequency indicator

The Benford Law Frequency indicator (first-digit law) is based on examining the actual frequency of the digits 1 through 9 in numerical data. It is usually used as an indicator of accounting and expenses fraud in lists or tables.

Benford's law states that in lists and tables the digit 1 tends to occur as a leading digit about 30% of the time. Larger digits occur as the leading digits with lower frequency, for example the digit 2 about 17%, the digit 3 about 12% and so on. Valid, unaltered data will follow this expected frequency. A simple comparison of first-digit frequency distribution from the data you analyze with the expected distribution according to Benford's law ought to show up any anomalous results.

For example, let's assume an employee has committed fraud by creating and sending payments to a fictitious vendor. Since the amounts of these fictitious payments are made up rather than occurring naturally, the leading digit distribution of all fictitious and valid transactions (mixed together) will no longer follow Benford's law. Furthermore, assume many of these fraudulent payments have 2 as the leading digit, such as 29, 232 or 2,187. By using the Benford Law indicator to analyze such data, you should see the amounts that have the leading digit 2 occur more frequently than the usual occurrence pattern of 17%.

In the result chart of the Benford Law Frequency indicator, digits 1 through 9 are represented by bars and the height of the bar is the percentage of the first-digit frequency distribution of the analyzed data. The dots represent the expected first-digit frequency distribution according to Benford's law.

The red bar labeled as invalid means that this percentage of the analyzed data does not start with a digit. And the 0 bar represents the percentage of data that starts with 0. Both cases are not expected when analyzing columns using the Benford Law Frequency indicator and this is why they are represented in red.