Comments on: How to cheat with Frank Benford

By: Robin Nelson

Robin Nelson — Thu, 20 Oct 2011 05:05:00 +0000

Interesting blog. It is always good if you can provide additional information about this. Thanks a lot!

By: Dana Aquirre

Dana Aquirre — Wed, 28 Sep 2011 04:39:00 +0000

Thanks for giving such kind of great information .

By: Juliet Meeks

Juliet Meeks — Tue, 19 Jul 2011 11:47:00 +0000

Thank you a lot for your interesting article. I have been looking for such message for a very long time.

By: Steve Mould

Steve Mould — Tue, 28 Jun 2011 13:25:00 +0000

That’s awesome. Thanks Ewerton

By: Ewerton Miglioranza

Ewerton Miglioranza — Tue, 28 Jun 2011 13:21:00 +0000

Just in case someone else want to take a look: http://testingbenfordslaw.com/
Great post dude!

By: Steve Mould

Steve Mould — Fri, 25 Feb 2011 02:01:00 +0000

Finally someone asking the important questions!

By: John Henschen

John Henschen — Fri, 25 Feb 2011 01:59:00 +0000

All this discussion is fine and dandy, but you have yet to touch upon the most important aspect. How will this help me win the lottery?

By: Mold Removal

Mold Removal — Thu, 03 Feb 2011 04:47:00 +0000

I just stumbled upon your site and wanted to say that I have really enjoyed reading your opinions.

By: Steve Mould

Steve Mould — Fri, 21 Jan 2011 13:24:00 +0000

This is brilliant! Love the php. But what your php does is find the distribution of leading digits for a fixed raffle size of 10000000000000000. If you want to find the distribution when you don’t know the size UP TO 10000000000000000 you’ve got to modify the rand line to be like this:

$n = rand(1,rand(1,10000000000000000)).”";

The nested rand is giving you a random raffle size to choose from up to the maximum.

When the max size of the raffle is infinite, the distribution fits Beford exactly. But if it’s finite, so long as it spans several orders of magnitude it’ll fit very closely. And of course the more orders of magnitude you span the better the fit gets.

By: DampeS8N

DampeS8N — Thu, 20 Jan 2011 21:31:00 +0000

That’s not true. If the raffle is of a finite, but unknown, size, then the data will be evenly distributed. It is only when the max size of the raffle is infinite, that your raffle metaphor works. Not for an unknown size.

Consider the results of this PHP snippet. For any maximum number, the distribution will be even.

$i = 0;
$spread = array();
while($i < 1000000)
{
$n = rand(1,10000000000000000)."";
$spread[$n[0]]++;
$i++;
}
ksort($spread);
var_dump($spread);