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wichmann
2008 Aug 17
1
Wichmann-Hill Random Number Generator and the Birthday Problem
...46566.12 for N=10M samples.
For Marsaglia-Multicarry, Super-Duper and Mersene-Twister, M=2^32. D =
11641.53 for N = 10M samples.
My testing results (see below) agree with above analysis. But for
Wichmann-Hill, it wasn't. Wichmann-Hill's cycle is 6.9536e12 (refer to RNG
help by ?RNG and Whichmann's correction in 1984). Thus M <= 6.9536e12. D
>= 7.19052 when N=1e7 and D>= 179.763 for N=5e7.
But in my tests, duplications were surprisingly not observed.
It seems that Wichmann-Hill has a much larger cycle than the one
documented!
Anybody can solve this puzzle?
Regards,
Sheng...