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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