I would compare the Shannon entropy of your test vector with the entropy of your expected probability distribution to see if they are close. That is, if you're binary probability distribution is half 1 and half -1, then if your string is long you would expect about half the numbers in your vector to be 1 and half to be -1, i.e. H(s)=1. Moreover, you should also look at the entropy of every subset of the vector and compare that to your distribution as well. For instance, does the sequence (1, 1) show up just as often as (1, -1), (-1, 1) and (-1, 1)? As this problem is specific to a certain random process, I doubt there is a canned test in R.
Also, the sample entropy should converge to the distribution of the underlying process as the sample size increases for all subsets of the sample, probably following a t-distribution (Central Limit Theorem), although I'd need to noodle on this a bit more. You can then construct a test of significance if you know the sample size and how far the sample entropy is from the hypothesized process's distribution. Unfortunately, it's been a while since I've done information encoding, but hopefully this gets you started. You can read up on informational entropy here: http://en.wikipedia.org/wiki/Informational_entropy And if you do find a test in R, I would be interested as well. Best, Robert -----Original Message----- From: Mark Leeds [mailto:[EMAIL PROTECTED] Sent: Wednesday, January 11, 2006 4:46 PM To: R-Stat Help Subject: [R] a series of 1's and -1's Does anyone know of a simple test in any R package that given a series of negative ones and positive ones ( no other values are possible in the series ) returns a test of whether the series is random or not. ( a test at each point would be good but I can use the apply function to implement that ) ? thanks. ********************************************************************** This email and any files transmitted with it are confidentia...{{dropped}} ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html