Re: Software roulette statistics

In article <1164775344.018154.251500@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Reef Fish" <large_nassua_grouper@xxxxxxxxx> writes:
...

The property of "mainly on the plain" or hyperplanes is common the
ALL linear congruential generators! They are of the form:

R(i+1) = (A + R(i) B ) mod M,

Different choices of A, B, and M affect the cycle lengths, but the
period of the LCG is AT MOST M, often considerably less than M.

But 2^64 and 2^32 are still huge numbers on 1 dimension. The defect
of ALL LCG, as I said (which is well known) is in HIGH dimension
simulation only, because the n-tuples of coordinates all lie of
hyperplanes (lattices) often with huge "holes" parallelopiped holes
that there are special tests for them.

The Mersenne twister you mentioned is the same kind of LCG, often
recommended with A = 1664525, B = 1013904223, M = 2^32. It's
better and faster than most other LCGs but suffer the same DEFECTS
shared by ALL LCG geneators.

Note that the Mersenne twister is based on the theory of linear recurring
sequences over a finite field, and is totally different from an LCG.
It's more like a souped-up Tausworthe generator.
The most commonly implemented Mersenne twister has a period of
2^19937 - 1, and is for most purposes free of the obvious defects
shared by all LCG generators.
-- Ewart Shaw

...
-- Reef Fish Bob.
--
J.E.H.Shaw [Ewart Shaw] strgh@xxxxxxxxxxxxx TEL: +44 2476 523069
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
http://www.warwick.ac.uk/statsdept http://www.ewartshaw.co.uk
Will read usenet posts up to the first insult (which may be in the Subject)
.

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  • Re: Software roulette statistics
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    (sci.stat.math)