Bug in rnorm. (PR#1664)

[ripley@stats.ox.ac.uk]

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
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-- 
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


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