[R] Wichmann-Hill Random Number Generator and the Birthday Problem

[Peter Dalgaard]

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
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