Re: [libreoffice-users] Benford's Law

At 21:03 18/07/2013 +0000, Toki "Jonathan" Kantoor wrote:
> On 07/15/2013 12:42 PM, Brian Barker wrote:
> > ... don't stop being what they are after some 
> > arbitrary number of significant figures - 
> > whether it be one, three, or any other.
>
> At the fourth significant digit, 0 and 9 occur 
> slightly (¿1:10,000?) more frequently than 1, 2, 
> 3, 4, 5, 6, 7, and 8. For most practical 
> purposes, the fourth digit can be treated as a 
> uniformly random number. At the fifth, and 
> subsequent digits, the numbers are randomly, and uniformly distributed.

It's surely intuitively obvious that this cannot 
be so.  The first digits are very non-uniformly 
distributed, the second ones less so, and so 
on.  What your source is telling you is that the 
fourth digit is very, very nearly uniformly 
distributed and that subsequent digits are so 
nearly so that they may be considered so for all 
practical purposes - not that they really are.  (That would be wrong.)

In any case, if the formula I suggested works 
(and we've seen plenty of evidence that it does 
and none that it doesn't - but I'm still open to 
correction), then according to your theory it 
*will* provide such uniformly distributed digits 
after the fourth.  You've already got what you 
want: the problem appears to be that you cannot 
believe the distribution will turn out the way 
that you say it will!  It's irrational of you to 
suggest removing one set of digits that you claim 
are already uniformly distributed and replacing 
them with another also uniformly distributed 
set!  And if there were any difference, how many 
variates would you have to call upon before any 
difference would be noticeable?  Billions of 
billions of billions?!  More than you are going to use, at any rate.

> > If you want values that follow Benford's Law up 
> > to three digits, you can easily take the true 
> > values from my suggested formula, truncate (or 
> > round?) them after three digits, and add 
> > further random digits selected from a uniform distribution.
>
> And my original post was asking what happened to 
> the macro that automatically did that.

And you now have an even simpler solution: a 
formula that does it.  But you are very welcome 
not to use it if you don't like it.  Even if you 
wanted to make the irrational change, you could 
easily construct a formula to do this.

Brian Barker


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