Probably this is already contained in the present blog entry, but Fewster article was for me easier to follow.

]]>This would certainly explain how ‘Zipf’s law seems to turn up everywhere’ if it is a manifestation of the Central Limit Theorem.

]]>For 0< n,m in N let’s denote the relative chance of drawing n vs. drawing m by: P(n)/P(m). Then P(n)/P(m) = (log (n+1)/n)/(log (m+1)/m), see the series posted last year on my blog fwaaldijk.wordpress.com. These relative probabilities can be derived heuristically, and are in accordance with Benford's law. The heuristics are interesting I think, but also quite speculative.

A `discrete' or `Zipfian' case can also be stated, which then yields P(n)/P(m)=m/n. But I did not study this in any detail.

I would be happy to receive some feedback on these ideas. Kind regards, Frank

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