Thank you.
It looks like the M-M generator is deeply flawed, although R
implementation seems to be faithful.
I can understand that R keeps this generator for historical reasons.
However, R should at least warn that this generator is buggy and should
not be used!
That could be as simple as a Warning message generated by set.seed().
--
Sincerely
André GILLIBERT
> With these matters, one has to be careful to distinguish between
method error and implementation error.
> The reason for changing the RNG setup in R v. 1.7.0 was pretty much
this kind of unfortunate interaction between M-M and K-R. There are even
more egregious examples for the distribution of maxima of normal
variables. Try e.g.
>
> RNGversion("1.6.0") # Marsaglia-Multicarry, Kinderman-Ramage
> s <- replicate(1e6,max(rnorm(10)))
> plot(density(s))
>
> (A further bug in K-R was fixed in 1.7.1, but that is tangential to
this.)
>
> A glimpse of the source of the problem is seen in the
"microcorrelations" in this:
>
> RNGkind("Mar");m <- matrix(runif(4e7),2)
> plot(m[1,],m[2,],xlim=c(0,1e-3),pch=".")
> m <- matrix(runif(4e7),2)
> points(m[1,],m[2,],pch=".")
>
> These examples are from 2003, so the issue has been known for almost
2 decades. However, to the best of our knowledge, the M-M RNG is a
faithful implementation of their > method, so we have left the RNG in
R's arsenal, in case someone needed it for some specific purpose.
>
> - pd
>
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