Benford's Law definition
/What is Benford’s Law?
Benford’s Law states that, in a naturally occurring set of numbers, the smaller digits appear disproportionately more often as the leading digits. The leading digits have the distribution shown in the following table, where the number 1 appears slightly more than 30% of the time as the leading digit, and the number 9 appears as the leading digit less than 5% of the time (which is a difference of 6x).
1 = 30.1% frequency of occurrence
2 = 17.6% frequency of occurrence
3 = 12.5% frequency of occurrence
4 = 9.7% frequency of occurrence
5 = 7.9% frequency of occurrence
6 = 6.7% frequency of occurrence
7 = 5.8% frequency of occurrence
8 = 5.1% frequency of occurrence
9 = 4.6% frequency of occurrence
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Benford’s Law in Fraud Detection
Benford’s Law is a useful tool for the detection of fraud. For example, someone engaged in fraud might create a series of false invoices with a normal distribution of billed amounts. If all digits were to appear as the leading digit in a uniform manner, then each one would appear about 11.1% of the time. Since there is quite a disparity between the distributions stated in Benford’s Law and what a uniform distribution would indicate, this disparity can be used to locate instances of fraud. The reason for the disparity is that someone committing fraud will create randomly generated numbers, rather than following Benford’s distribution.
It is important to understand the situations to which Benford’s Law can be applied. The frequency distribution only applies to naturally occurring numbers. In a business, examples of these numbers are the grand total billed on an invoice, the compiled cost of a product, or the number of units in stock. It does not apply in situations where numbers are assigned, such as a sequentially assigned check number or invoice number.
Terms Similar to Benford’s Law
Benford’s Law is also known as the Law of First Digits.