Dear R developers,
In my opinion, I discovered a severe flaw that occur with the combination of
the Marsaglia-Multicarry pseudo-random number generator associated to the
Kinderman-Ramage algorithm to generate normally distributed numbers.
The sample program is very simple (tested on R-4.1.1 x86_64 on Windows 10):
set.seed(1, "Marsaglia-Multicarry", normal.kind="Kinderman-Ramage")
v=rnorm(1e7)
poisson.test(sum(v < (-4)))$conf.int # returns c(34.5, 62.5)
poisson.test(sum(v > (4)))$conf.int # returns c(334.2, 410.7)
pnorm(-4)*1e7 # returns 316.7
There should be approximatively 316 values less than -4 and 316 values greater
than +4, bug there are far too few values less than -4.
Results are similar with other random seeds, and things are even more obvious
with larger sample sizes.
The Kinderman-Ramage algorithm is fine when combined to Mersenne-Twister, and
Marsaglia-Multicarry is fine when combined with the normal.kind="Inversion"
algorithm, but the combination of Marsaglia-Multicarry and Kinderman-Ramage
seems to have severe flaws.
R should at least warn for that combination !
What do you think? Should I file a bug report?
--
Sincerely
Andr� GILLIBERT
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