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From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: comp.theory.dynamic-sys,sci.crypt,sci.math.stat
Subject: Re: Can Chaos Be Predictable?
Summary: What do you mean by random?
Keywords: chaos, predictability
Message-ID: <13867@mentor.cc.purdue.edu>
Date: 22 Jun 91 18:29:08 GMT
References: <1991Jun20.194552.15875@cunews.carleton.ca> <1991Jun22.140127.3984@elevia.UUCP>
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In article <1991Jun22.140127.3984@elevia.UUCP>, alain@elevia.UUCP (W.A.Simon) writes:
> In <1991Jun22.133638.3258@elevia.UUCP> alain@elevia.UUCP (W.A.Simon) writes:

			....................

> 	Before I get skewered on a Hilbert curve, let me rephrase
> 	this.  Would the tools of statistical analysis (Chi-Square,
> 	etc...) identify that this sequence is not random ?

If you ask whether the marginal distribution approaches the limiting one,
Beta(.5,.5) for the particular example, the answer is yes.  If you actually
tested it using a two-sided test, you would even find the sample distribution
converged too fast, but it would take quite a large sample to detect that.

But if you looked at pairs, they all lie on a very simple curve, which is
very obvious.  The chaotic nature is that a slight difference at one point
makes a big difference a considerable time in the future.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet)   {purdue,pur-ee}!l.cc!hrubin(UUCP)