Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: k (3) Vectors of ones and zeros "combining" together Date: Mon, 23 Jan 2012 22:01:10 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 7 Message-ID: <jfklb6$d6f$1@newscl01ah.mathworks.com> References: <jf510f$nv5$1@newscl01ah.mathworks.com> <jf51ot$q13$1@newscl01ah.mathworks.com> <jf5309$a8$1@newscl01ah.mathworks.com> <jf6n35$3kn$1@newscl01ah.mathworks.com> <jf71oe$bbi$1@newscl01ah.mathworks.com> <jf7l1a$h8i$1@newscl01ah.mathworks.com> <jf9nbq$b9h$1@newscl01ah.mathworks.com> <jfhofo$l7e$1@newscl01ah.mathworks.com> <jfi6j5$2dv$1@newscl01ah.mathworks.com> <jfir93$11i$1@newscl01ah.mathworks.com> <jfjtjr$fij$1@newscl01ah.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: www-06-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: newscl01ah.mathworks.com 1327356070 13519 172.30.248.38 (23 Jan 2012 22:01:10 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Mon, 23 Jan 2012 22:01:10 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:755533 "Matt J" wrote in message <jfjtjr$fij$1@newscl01ah.mathworks.com>... > Thanks, Roger, although I am a little disquieted that it takes 1e7 realizations to get a decently converged histogram. I would think that with only 150 different possible events, the number of required samples would be far less... > ........ - - - - - - - - - - - It's not so surprising, Matt. For N = 5, assuming that all 150 events have equal probability p = 1/150, what you have with n samples is a simple binomial distribution with mean n*p and variance n*p*(1-p) on the count of one of these events. The right quantity to consider in its histogram is the ratio sqrt(variance)/mean which is equal to sqrt((1-p)/(n*p)). As n increases, it drops down only as the reciprocal of the square root of n and the small size of p makes it worse. For larger N the number of events increases and therefore the number of samples needed gets even larger. Also one needs to take into consideration on a histogram that with larger numbers of events, there is an increased opportunity for outliers to appear even for a given value of the above ratio. Roger Stafford