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At 12:26 15/07/2013 +0000, Toki "Jonathan" Kantoor wrote:
On 07/14/2013 09:54 PM, Dennis E. Hamilton wrote:
However, Benford's law is about the *first* digit of a wide variety of numbers.

First three digits, not first digit. The fourth and subsequent digits should be uniformly distributed.

The striking thing about variates that follow Benford's Law is indeed that the initial digits are not equally distributed. But such variates don't stop being what they are after some arbitrary number of significant figures - whether it be one, three, or any other. The values come from the distribution - so all their decimal digits are part of the story.

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.

But I'm not at all sure why you would want to do this. Does the source of this suggestion mean merely that, although the early digits are not uniformly distributed, later ones are more nearly so - and that there is little point in worrying about the difference after, say, three digits? If so, there is equally no point in worrying that these later digits might be too right!

Brian Barker

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