[Rd] Problem in random number generation for Marsaglia-Multicarry + Ahrens-Dieter

[GILLIBERT, Andre]

Dear R developers,

At the same time I discovered a flaw in Marsaglia-Multicarry + Kinderman-Ramage, I found another in Marsaglia-Multicarry + Ahrens-Dieter.
It is less obvious than for Kinderman-Ramage; so I created a new thread for this bug.

The following code shows the problem (tested on R 4.1.1 x86_64 for Windows 10):

== start of code sample ==
set.seed(1, "Marsaglia-Multicarry", normal.kind="Ahrens-Dieter")
v=rnorm(1e8)

q=qnorm(seq(0.01, 0.99, 0.01))
cv=cut(v, breaks=c(-Inf, q, +Inf))
observed=table(cv)
chisq.test(observed) # p < 2.2e-16
== end of code sample ==

The chisq.test returns a P-value < 2.2e-16 while it was expected to return a non-significant P-value.
The additionnal code below, shows severe irregularities in the distribution of quantiles:

== continuation of code sample ==
expected = chisq.test(observed)$expected
z = (observed - expected)/sqrt(expected)
mean (abs(z) > 6) # 58% of z-scores are greater than 6 while none should be
== end of code sample ==

The bug is specific to the combination Marsaglia-Multicarry + Ahrens-Dieter.
There is no problem with Marsaglia-Multicarry + Inversion or Mersenne-Twister + Ahrens-Dieter

I would expect at least a warning (or an error) from R for such a buggy combination.

--
Sincerely
Andr� GILLIBERT


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