[R] Wichmann-Hill Random Number Generator and the Birthday Problem
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Tue Aug 19 09:11:39 CEST 2008
Prof Brian Ripley wrote:
> Your coincidence calculations may be correct for _independent_ draws
> from a discrete distribution on M values, but independence is not
> satisfied.
> Yet again, you are trying to do things that any good text on
> simulation would warn you against, and which (in a thread on R-devel)
> you have already been told a good way to do.
>
A good example are the "good" old linear congruential random generators.
These will start repeating at the first coincidence, for the pretty
obvious reason that the next random number is a function only of the
previous one. So the number of distinct values in N draws is min(N,
cycle_length). In particular, the number of coincidences is 0 when N is
less than cycle_length.
--
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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