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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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