Benford law - fraud prediction


#1

Has anyone used Benford law in predicting financial services fraud?
When I aggregate data for a daily transactions, Benford law works perfectly. However, when I look at individual merchant then I do not see Benford law working. This might be because of the price points at a merchant. Has anyone had this problem. If yes, how did you deal with it?
Thanks


#2

I have never tried benford’s law.

1. LIBOR RATES

I tried it on LIBOR Rates from 2010 uptil now with a precision of 7 decimal places

I got the following frequency distribution

So Benford’s law is not being followed here

2. RUNIF command R
I ran the runif command in R for the same count of data as the LIBOR rate data ( 490 to be precise )
I got the following frequency distribution

Now, we can see that at least the occurrence of 1 is higher than the rest, which is in accordance with Benford’s law

POINTS

  • From what I can see, the number of observations will definitely be a factor

  • Wikipedia also mentions the following line
    For instance, one can expect that Benford’s law would apply to a list of numbers representing the populations of UK villages, or representing the values of small insurance claims. But if a “village” is defined as a settlement with population between 300 and 999, or a “small insurance claim” is defined as a claim between $50 and $99, then Benford’s law will not apply.link
    This means that we should not have any constraints on the data and allow it follow the gaussian curve

Can you check whether the individual merchants have some limit on the size of the transactions ( it does not accept transactions less than 1000 rs etc ) In that case, we will not be able to leverage Benford’s law

Regards,
Anant