R supplies a choice of random-number generators as well as a choice of generating normals. All methods are compromises, and I suspect one of the non-default ones may be better for your purposes. Please investigate the choices.
On 13 Jun 2002, Peter Dalgaard BSA wrote:
rolf@math.unb.ca writes:
There appears to be a mild bug, or at least a deficiency, in rnorm. The bug becomes apparent when one looks at extremes of the squares of the values generated by rnorm; rnorm is not generating quite enough extreme values. The R version that I am using is 1.4.1; I never got around to installing 1.5.0, and now since 1.5.1 is about to come out .... However, checking the 1.5.0 release notes revealed no mention of fixing a bug in rnorm.
...and I see the effect too with an r-patched from a few days back. [snip]
After some discussion with colleagues, I replaced the calls to rnorm()
by calls to myrnorm() defined by
myrnorm <- function(n,mu=0,sigma=1){
mu + sigma*cos(2*pi*runif(n))*sqrt(-2*log(runif(n)))
}
which uses the ``(r,theta)'' method of generating random normals.
When I did so, the resulting values were indeed all ``close to'' 0.05,
as they should be.
I also tried the experiment using rchisq(n,1) instead of rnorm(n) (and
then of course taking m = max of x --- rather than max of x^2). Again
all the resulting values were close to 0.05 as ought to be the case.
(So rchisq() appears to be OK in this regard.)
Also qnorm(runif(n)) seems to be closer to the target. -- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-devel mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-devel-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Brian D. Ripley, ripley@stats.ox.ac.uk 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 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-devel mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-devel-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._