# Bug in rnorm. (PR#1664)

**Peter Dalgaard BSA
**
p.dalgaard@biostat.ku.dk

*13 Jun 2002 23:59:43 +0200*

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
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