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### Benford's Law - this is great

Posted: **Tue Jan 13, 2015 6:18 pm**

by **JimLombard**

I just happened to be reading an old article about it and it peaked my interest. I guess not too many people (even statisticians) were too familiar with it up until 10-15 years ago, but it is getting very popular as it is being used to detect fraud in corporations, tax documents, etc. by simply looking at the numbers involved.

I know this is a bit out of topic for these forums, but I think it's such an interesting topic, that I wanted to tell people about it. See attached documents below.

### Re: Benford's Law - this is great

Posted: **Thu Jan 15, 2015 6:57 am**

by **Bill_WG**

This is indeed off topic, as far as the forum goes, but is a very interesting topic to me. I also only recently became aware of Benford's Law and am fascinated with it!

I have seen many mentions of it having been used in real legal cases, but have not been able to find and case law for it. Do you happen to know of any such cases? I'd love to read up on them.

### Re: Benford's Law - this is great

Posted: **Sat Jan 17, 2015 5:27 am**

by **OscarG**

Not sure how well this theory applies to the real world. I run a simulation by creating 1.2 million random numbers in the range 1-99999 in excel and then analyzed the first digit (1-9) frequency. I ended up with about 11% for each digit, totally different than what Benford's law suggested.

Am I doing something wrong?

### Re: Benford's Law - this is great

Posted: **Sat Jan 17, 2015 5:52 am**

by **CindyLak**

Oscarg, my findings are similar to yours. I am sure there is a logical explanation, I just don't know what it is.

If anyone here can shed some light, it would be great!

### Re: Benford's Law - this is great

Posted: **Sun Nov 12, 2017 12:03 am**

by **PLeonat**

Wait, isn't that exactly what his premise is? That "made up" numbers are not random, in terms of the first digit?

I may have totally misread this, but I think what you found proves his point.

### Re: Benford's Law - this is great

Posted: **Sun Nov 12, 2017 10:55 pm**

by **CindyLak**

Hmm, you may be right. Have you looked at anything yourself that sort of proves his theory?

### Re: Benford's Law - this is great

Posted: **Mon Nov 13, 2017 3:17 pm**

by **PLeonat**

Yes, I had looked at it a while ago and I had analyzed the populations of 227 countries in 1950. It was a quick and dirty thing, but here is what the results looked like: Pretty good, IMO. The first digit frequencies seem to agree with Benford's law.

- BenfPop1950.PNG (13.2 KiB) Viewed 1931 times

### Re: Benford's Law - this is great

Posted: **Thu Nov 16, 2017 4:42 am**

by **BLarson**

Well, I don't know how helpful it is, but I found another short paper on this site's "techs" section that deals with this subject.

http://triusinc.com/techs/QuickBenford_Karahalios.pdf
It's fairly simple and doesn't go deep into math, but it may provide some additional insight.

### Re: Benford's Law - this is great

Posted: **Thu Nov 16, 2017 6:07 pm**

by **PLeonat**

BLarson wrote: ↑Thu Nov 16, 2017 4:42 am

Well, I don't know how helpful it is, but I found another short paper on this site's "techs" section that deals with this subject.

http://triusinc.com/techs/QuickBenford_Karahalios.pdf
It's fairly simple and doesn't go deep into math, but it may provide some additional insight.

Wow, actually, the plot from the paper you references (see below) displays similar behavior to what I had looked at. Does that constitute Independent verification?

- Benford_Graph_Karahalios.PNG (35.95 KiB) Viewed 1900 times

### Re: Benford's Law - this is great

Posted: **Mon Nov 27, 2017 6:13 pm**

by **CindyLak**

I found this very interesting real-life case study of Benford's Law.

https://acfeinsights.squarespace.com/ac ... case-study