

Benford's law - vhf
https://en.wikipedia.org/wiki/Benford%27s_law

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lukasm
"Benford's Law can be used to show that binary is the best base for doing
floating point math."

[http://blogs.msdn.com/b/ericlippert/archive/2005/01/13/float...](http://blogs.msdn.com/b/ericlippert/archive/2005/01/13/floating-
point-and-benford-s-law-part-two.aspx)

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eudox
>In the United States, evidence based on Benford's Law has been admitted in
criminal cases at the federal, state, and local levels.

This, to me, is the most interesting part of the article.

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lunz
It's said that german finance authorities use it for revealing tax fraud.

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jacquesm
It's a well-known tool in the arsenal of any forensic accountant.

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jds375
It is very surprising that distributions such as Fibonacci and the powers of
two follow this law. Some number sequences that don't are numbers like pi and
e. These numbers are said to be normal numbers, meaning they have an equal
distribution amongst all digits. However, this hasn't been rigorously proven
and is still an open problem.[1]

[http://en.m.wikipedia.org/wiki/Normal_number](http://en.m.wikipedia.org/wiki/Normal_number)

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pavpanchekha
The distribution of the digits of pi and e is not the same as the distribution
of first digits in a _set_ of numbers; only the second is subject to Benford's
Law. While both normal numbers and Benford's Law are interesting mathematical
objects and deal with distributions of digits in a number, that is the
complete extent to which they are related.

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tbrock
I worked at a hedge fund and we used this to figure out whether other funds
were falsifying their returns or not. The most notable deviation was Bernie
Madoff's.

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mikeash
Before or after he got caught?

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bayesianhorse
Benford's law is so well known today, that many a "forger" will evade it
easily. One way is to create random numbers and find a solution that fits both
your goal and Benford's law.

I think this is what the German ADAC did when they falsified test results
around a general "idea" what they wanted to see.

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ajtulloch
Terry Tao has written an excellent (if mathematically advanced) post on
Benford's law that is worth looking at for a more rigorous presentation.

[http://terrytao.wordpress.com/2009/07/03/benfords-law-
zipfs-...](http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-
and-the-pareto-distribution/)

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ericchiang
Probably the best explanation of the intuition behind Benford's law. Worth a
watch if you've got the time:

[https://www.youtube.com/watch?v=XXjlR2OK1kM](https://www.youtube.com/watch?v=XXjlR2OK1kM)

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Terr_
To reuse an old post:

> [I]t has to do with relative growth/shrinkage and the base of the
> positional-numbering system you're using. If you have a random starting
> value (X) multiplied by a second random factor (Y), most of the time the
> result will start with a one.

> You're basically throwing darts at logarithmic graph paper! The area covered
> by squares which "start with 1" is larger than the area covered by square
> which "start with 9".

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brycethornton
Here's a site a friend and I built a while back to test some open datasets
against Benford's Law:

[http://www.testingbenfordslaw.com/](http://www.testingbenfordslaw.com/)

Most seem to match fairly closely. We accept pull requests with new datasets
if anyone wants to contribute.

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pera
> Distance of stars from Earth in light years

that's weird

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darsham
Here's my explanation : assuming random distribution, the probability of
finding a star at a given distance is proportional to the area of the sphere
having that radius. So it follows a square law.

Correct me if I'm wrong, but I think any function with an increasing rate of
change (ie. second derivative > 0) will yield a distribution with the same
ordering of digits as Benford's if random numbers are taken from it.

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jcr
Here's a fairly recent link about using Benford's law to detect fraud.

[http://www.theregister.co.uk/Print/2014/05/14/theorums_1_ben...](http://www.theregister.co.uk/Print/2014/05/14/theorums_1_benford/)

