Benford’s Law

Kevin Feasel


Data, R

Tomaz Kastrun is starting a series on fraud analysis and starts with Benford’s Law:

One of the samples Microsoft provided with release of new SQL Server 2016 was using simple logic of Benford’s law. This law works great with naturally occurring numbers and can be applied across any kind of problem. By naturally occurring, it is meant a number that is not generated generically such as a page number in a book, incremented number in your SQL Table, sequence number of any kind, but numbers that are occurring irrespective from each other, in nature (length or width of trees, mountains, rivers), length of the roads in the cities, addresses in your home town, city/country populations, etc. The law calculates the log distribution of numbers from 1 to 9 and stipulates that number one will occur 30% of times, number two will occur 17% of time, number three will occur 12% of the time and so on. Randomly generated numbers will most certainly generate distribution for each number from 1 to 9 with probability of 1/9. It might also not work with restrictions; for example height expressed in inches will surely not produce Benford function. My height is 188 which is 74 inches or 6ft2. All three numbers will not generate correct distribution, even though height is natural phenomena.

Tomaz includes SQL Server R Services code, so check it out.

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