[Rd] RNG Cycle and Duplication (PR#12536)

shli at stat.wvu.edu shli at stat.wvu.edu
Thu Aug 14 18:25:14 CEST 2008

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?

Shengqiao Li

Research Associate
The Department of Statistics
West Virginia University
Morgantown, WV 26506-6330

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