G'day Rainer, On Sat, 25 Sep 2010 16:24:17 +0200 Rainer M Krug <r.m.k...@gmail.com> wrote:
> This is OT, but I need it for my simulation in R. > > I have a special case for sampling with replacement: instead of > sampling once and replacing it immediately, I sample n times, and > then replace all n items. > > > So: > > N entities > x samples with replacement > each sample consists of n sub-samples WITHOUT replacement, which are > all replaced before the next sample is drawn > > My question is: which distribution can I use to describe how often > each entity of the N has been sampled? Surely, unless I am missing something, any given entity would have (marginally) a binomial distribution: A sub-sample of size n either contains the entity or it does not. The probability that a sub-sample contains the entity is a function of N and n alone. x sub-samples are drawn (with replacement), so the number of times that an entity has been sampled is the number of sub-samples in which it appears. This is given by the binomial distribution with parameters x and p, where p is the probability determined in the previous paragraph. I guess the fun starts if you try to determine the joint distribution of two (or more) entities......... HTH. Cheers, Berwin ========================== Full address ============================ Berwin A Turlach Tel.: +61 (8) 6488 3338 (secr) School of Maths and Stats (M019) +61 (8) 6488 3383 (self) The University of Western Australia FAX : +61 (8) 6488 1028 35 Stirling Highway Crawley WA 6009 e-mail: ber...@maths.uwa.edu.au Australia http://www.maths.uwa.edu.au/~berwin ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.