Question

What is Benford’s Law? How Does It Work?Are there any issues or challenges with Benford’s Law?

Answer 1

Benford Law also known as the law of first digits is the observation about the frequency distribution of the first digits in real life set of numerical data. The law underlines that in many numerical sets the leading digit is likely to be small. If the digits were distributed uniformly, they would occur 11.1% of the time. The law also makes prediction about 2nd digits and so on. It is a probability distribution for the likelihood of the first digit in the number set. The formula is as follows-

P{d}=ln(1+1/d)/ln(10)

Where d is the leading digit (a number from 1 to 9)

Benford law is used by many IT Auditors. It helps in detecting fraud. In 2009, analysis using Benford law was used as evidence to detect voter fraud in Iranian election.

The challenges in Benford Law are as follows-

1. Randomly generated numbers-Benford law runs on the assumption that the numbers in large data set are randomly generated. For example, US telephone numbers have specific area code and a limited number of 3-digit prefaces to the last 4 digits . Thus, before benford's law is applied, the auditor should ensure that the numbers are randomly generated without any real or artificial restriction of occurrence.

2. Large data sets- It can be only applied on large data sets. Some experts suggest that the data set be of 100 records. Using fewer records can lead to false positives.

Benford law helps in recognizing the highly likely or unlikely frequencies of number in data set.