[R] RNG Cycle and Duplication
Shengqiao Li
shli at stat.wvu.edu
Thu Aug 14 23:57:04 CEST 2008
I didn't describe the problem clearly. It's about the number of distinct
values. So just ignore cycle issue.
My tests were:
RNGkind(kind="Knuth-TAOCP");
sum(duplicated(runif(1e7))); #return 46552
RNGkind(kind="Knuth-TAOCP-2002");
sum(duplicated(runif(1e7))); #return 46415
#These collision frequency suggested there were 2^30 distinct values by
birthday problem.
RNGkind(kind="Marsaglia-Multicarry");
sum(duplicated(runif(1e7))); #return 11682
RNGkind(kind="Super-Duper");
sum(duplicated(runif(1e7))); #return 11542
RNGkind(kind="Mersenne-Twister");
sum(duplicated(runif(1e7))); #return 11656
#These indicated there were 2^32 distinct values, which agrees with the
help info.
RNGkind(kind="Wichmann-Hill");
sum(duplicated(runif(1e7))); #return 0
#So for this method, there should be more than 2^32 distinct values.
You may not get the exact numbers, but they should be close. So how to
explain above problem?
I need generate a large sample without any ties, it seems to me
"Wichmann-Hill" is only choice right now.
========================================
Shengqiao Li
The Department of Statistics
PO Box 6330
West Virginia University
Morgantown, WV 26506-6330
========================================
On Thu, 14 Aug 2008, Peter Dalgaard wrote:
> Shengqiao Li wrote:
>> Hello all,
>>
>> I am generating large samples of random numbers. The RNG help page says:
>> "All the supplied uniform generators return 32-bit integer values that are
>> converted to doubles, so they take at most 2^32 distinct values and long
>> runs will return duplicated values." But I find that the cycles are not the
>> same as the 32-bit integer.
>>
>> My test indicated that the cycles for Knuth's methods were 2^30 while
>> Wichmann-Hill's cycle was larger than 2^32! No numbers were duplicated in
>> 10M numbers generated by runif using Wichmann-Hill. The other three methods
>> had cycle length of 2^32.
>>
>> So, anybody can explain this? And any improvement to the implementation can
>> be made to increase the cycle length like the Wichmann-Hill method?
>>
> What test? These are not simple linear congruential generators. Just because
> you get the same value twice, it doesn't mean that the sequence is repeating.
> Perhaps you should read the entire help page rather than just the note.
>
> --
> O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
> c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
> (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
>
>
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