Tested Random Number Generator
On Wed, 11 Jun 2003, Wolfgang Viechtbauer wrote:
Dear All,
The editor of a journal to which I had submitted a publication asked
whether R has a "tested random number generator." My paper included
Monte Carlo simulations generating random normal and random chi-square
values.
help(rnorm) lists
Wichura, M. J. (1988) Algorithm AS 241: The Percentage Points of
the Normal Distribution. Applied Statistics, 37, 477-484.
as a reference, but this algorithm does not discuss the generation of
random values.
help(RNG) indicates that the "Mersenne-Twister" is the default random
number generator with reference:
Matsumoto, M. and Nishimura, T. (1998) Mersenne Twister: A
623-dimensionally equidistributed uniform pseudo-random number
generator, ACM Transactions on Modeling and Computer Simulation,
8, 3-30.
I looked at the paper, but essentially I have no expertise in assessing
whether this random number generator is "good" (which is probably a
tricky concept in the first place when dealing with RNGs). I have almost
blind faith in the developers of R (at least when it comes to something
so fundamental as a RNG) that I feel confident that it is good, but I
guess I need something more substantial at this point to back of my
beliefs! Any suggestions on how I can "show" (without having to go
through a separate study just to make this claim) that the RNG is
"tested"? Any references?
Also, I am a little uncertain about how R generates random observations
from various distributions, such as in rnorm() or rchisq(). Does it
generate random uniforms u ~ U(0,1) and then solve for x in F(x) = u)? I
would imagine that this is rather slow compared to other specialized
methods for various distributions. Any information on this would be
appreciated as well.
Try reading the appropriate help pages (or the code), which give references. Also, don't imagine: check out your suppositions in the RNG literature. (rnorm uses inversion by default, and it is not slow. Someone here claimed that another method was `6 to 7 times faster', but on all bar one of the machines I tried it was less than 1.5x faster and often slower. I never received a reply giving evidence for the claim, so presume it was false.)
I guess some of this relates to the "Validation of R" discussion that occured a while ago on this list, so this info could be of general interest.
There are many much-tested PRNGs that have been found to be seriously deficient! Just point your editor at the reference and that R is developed by people with international standing in that area, then ask his/her credentials for assessing RNGs. But first make sure you have followed standard advice and run your simulations with at least two fundamentally different PRNGs.
Brian D. Ripley, ripley at 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 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595