And by the way, the "Zipf mystery" explained ...
(Peter G. Neumman): http://www.csl.sri.com/neumann.html#12a
I frequently see cryptic references to the magic of Zipf
or Pareto or Mandelbrot, with reference to linguistic and other
structures, and sometimes in the context of 80-20 rules relating
to almost anything. (See Note.) There is no surprise at all in
the Zipf/Pareto/Mandelbrot theories once you understand that
each formula can be derived mathematically. In 1959, my old
Russo-Belgian friend Vitold Belevitch [2 Mar 1921--*26 Dec 1999]
(see On the Statistical Laws of Linguistic Distribution, Ann.
Soc. Sci. Bruxelles 73, III, 1959, 310-326) considered a wide
class of more or less well-behaved statistical distributions
(normal or whatever), and performed a functional rearrangement
that represents the frequency as a function of rank-ordered
decreasing frequency, and then did a Taylor expansion of the
resulting formula. Belevitch's lovely result is that "Zipf's
Law" follows directly as the first-order truncation of the
Taylor series ...
- - -
--Lauren--
Lauren Weinstein ([email protected]): http://www.vortex.com/lauren
Founder:
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