On 1/25/07, Prof Brian Ripley <[EMAIL PROTECTED]> wrote: > That gives a discrete distribution, which may well matter for small > samples. > > Since density() is returning an equal-weighted mixture of (by default) > normal distributions, all you need to do is > > x.new <- rnorm(n, sample(x, size = n, replace=TRUE), bw)
Prof. Ripley, I didn't understand why you used sample(x, size = n, replace=TRUE) I though the mixture should be computed using all the points in x as means, like in x.new <- rnorm(n, x, bw) Could you explain why you propose x.new <- rnorm(n, sample(x, size = n, replace=TRUE), bw) instead? Could you also briefly say in what sense kde is biased? thank you very much, best regards, Roberto > where bw is the bandwidth used by density (d$bw in this example). > (This is known as a 'smoothed bootstrap' in some circles.) > > > > ### Create a bimodal distribution > > x <- c(rnorm(25, -2, 1), rnorm(50, 3, 2)) > > d <- density(x, n = 1000) > > plot(d) > > > > ### Sample from the distribution and show the two > > ### distributions are the same > > x.new <- sample(d$x, size = 100000, # large n for proof of concept > > replace = TRUE, prob = d$y/sum(d$y)) > > dx.new <- density(x.new) > > lines(dx.new$x, dx.new$y, col = "blue") > > BTW, lines(density(x.news), col = "blue") works here, and you do need to > remember that a kde is biased. But my solution matches better than yours. > > -- > Brian D. Ripley, [EMAIL PROTECTED] > Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ > University of Oxford, Tel: +44 1865 272861 (self) > 1 South Parks Road, +44 1865 272866 (PA) > Oxford OX1 3TG, UK Fax: +44 1865 272595 > > ______________________________________________ > [email protected] 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. > ______________________________________________ [email protected] 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.
