
Benford’s law, Zipf’s law, and the Pareto distribution - michael_nielsen
http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/
======
gjm11
There are some very nice insights in here. (As usual from Terry Tao.) For
instance (here I'm simplifying a bit; if you want a more accurate version, go
read TT's article): if you've got two random variables X and Y, and X
approximately obeys a power-law distribution, and Y is independent of X and
has some other not-terribly-demanding properties, then XY also obeys a power-
law distribution, to the same degree of accuracy or (often) better. So, things
made out of products of random variables (e.g., because they arise from an
exponential growth process applied to some starting random thing) tend to have
this sort of distribution, which is where things like Benford's law (first
digits of positive "random" numbers tend to occur unevenly, with k occuring
log(1+1/k) of the time) come from.

