Re: [Fis] probability versus power laws

From: Stanley N. Salthe <[email protected]>
Date: Sun 04 Jul 2004 - 22:48:30 CEST

Victoras said:

> Stan, Guy, ... I agree... And one more article on combination
>of Zipf's law and Shannon's entropy as a method to identify functional
>groups within a system: Montemurro M.A. , Zanette D.H., 2001. Entropic
>analysis of the role of words in literary texts.
>(<http://xxx.arxiv.org/abs/cond-mat/0109218>http://xxx.arxiv.org/abs/cond-mat/01
>09218) Let me share my speculations on this point again. I'd think
>power law distributions introduces a notion of SYSTEMS and their
>structures into a field of statistics. In fact whatever we sample or
>observe is not just a POPULATION of events/objects - those are SYSTEMS (or
>their parts) that are sampled. Thus Zipf's law might be useful defining
>not simply whether samples taken represent a population. It probably could
>indicate whether they represent a system being sampled. So let's say if
>Zipf's law is fulfilled, then we can draw sensible conclusions about the
>structure of a system sampled. Otherwise that could mean a composition of
>system's structure being not represented by samples or 'over-sampling' a
>system by biting a piece of yet another system (neighboring or coexisting)
>in samples. Maybe...

     So, given that one can find power laws EVERYWHERE in ALL KINDS of
data, material and linguistic (just as onecan do statistics anywhere), how
do you construe it that the susceptibility of data to being plotted asa
power laws suggest systems? What would be a result of an Xi by i (rank)
plot have to look like in order to falsify your system hypothesis?

STAN

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Received on Sun Jul 4 21:16:24 2004

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