# [Rd] [R] RNG Cycle and Duplication (PR#12540)

shli at stat.wvu.edu shli at stat.wvu.edu
Thu Aug 14 23:45:09 CEST 2008

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I didn't describe the problem clearly. It's about the number of distinct=20
values. So just ignore cycle issue.

My tests were:

RNGkind(kind=3D"Knuth-TAOCP");
sum(duplicated(runif(1e7))); #return 46552

RNGkind(kind=3D"Knuth-TAOCP-2002");
sum(duplicated(runif(1e7))); #return 46415

#These collision frequency suggested there were 2^30 distinct values by=20
birthday problem.

RNGkind(kind=3D"Marsaglia-Multicarry");
sum(duplicated(runif(1e7))); #return 11682

RNGkind(kind=3D"Super-Duper");
sum(duplicated(runif(1e7))); #return 11542

RNGkind(kind=3D"Mersenne-Twister");
sum(duplicated(runif(1e7))); #return 11656

#These indicated there were 2^32 distinct values, which agrees with the=20
help info.

RNGkind(kind=3D"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=20
explain above problem?

I need generate a large sample without any ties, it seems to me=20
"Wichmann-Hill" is only choice right now.

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=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
Shengqiao Li

The Department of Statistics
PO Box 6330
West Virginia University
Morgantown, WV 26506-6330
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
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On Thu, 14 Aug 2008, Peter Dalgaard wrote:

> Shengqiao Li wrote:
>> Hello all,
>>=20
>> I am generating large samples of random numbers. The RNG help page says:=
=20
>> "All the supplied uniform generators return 32-bit integer values that a=
re=20
>> converted to doubles, so they take at most 2^32 distinct values and long=
=20
>> runs will return duplicated values." But I find that the cycles are not =
the=20
>> same as the 32-bit integer.
>>=20
>> My test indicated that the cycles for Knuth's methods were 2^30 while=20
>> Wichmann-Hill's cycle was larger than 2^32! No numbers were duplicated i=
n=20
>> 10M numbers generated by runif using Wichmann-Hill. The other three meth=
ods=20
>> had cycle length of 2^32.
>>=20
>> So, anybody can explain this? And any improvement to the implementation =
can=20
>> be made to increase the cycle length like the Wichmann-Hill method?
>>=20
> What test? These are not simple linear congruential generators. Just beca=
use=20
> you get the same value twice, it doesn't mean that the sequence is repeat=
ing.=20
> Perhaps you should read the entire help page rather than just the note.
>
> --=20
>  O__  ---- Peter Dalgaard             =D8ster 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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