Re: Software roulette statistics


strgh@xxxxxxxxxxxxxxxxxxxxxxxx wrote:
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.

That would be ONE version of what's called the Mersenne twister.

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

YOUR Mersenne twister is the one in
Wikipediahttp://en.wikipedia.org/wiki/Mersenne_twister

$> It was designed to have a colossal period of 219937 - 1

But Wikipedia is not the authority on ANYTHING. It is the authority
on ambiguity and pseudoscience. :-)))


The Mersenne Twister I referenced in my response to Gordon Sande:

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.

can ALSO be found in Wikipedia :-)

http://en.wikipedia.org/wiki/Linear_congruential_generator

Which you prefer to be called the Merseene twister depends on
which Wikipedia page your prefer to use. :-)

If you look under LINEAR CONGRUENTIAL GENERATOR,
you'll find the Mersenne twister I reference.

-- Reef Fish Bob.



...
-- 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)

.

Relevant Pages

  • Re: Software roulette statistics
    ... Gordon Sande wrote: ... That IS a linear congruential generator and IS a Mersenne Twister ... shared by ALL LCG geneators. ...
    (sci.stat.math)
  • Re: Software roulette statistics
    ... ALL linear congruential generators! ... period of the LCG is AT MOST M, ... The Mersenne twister you mentioned is the same kind of LCG, ... If you look under LINEAR CONGRUENTIAL GENERATOR, ...
    (sci.stat.math)
  • Re: Software roulette statistics
    ... Software gambling routines depend on random number generators. ... all multipliers of linear confuences being "defective" in two dimensions. ... period of the LCG is AT MOST M, ... better and faster than most other LCGs but suffer the same DEFECTS ...
    (sci.stat.math)
  • Re: Software roulette statistics
    ... The property of "mainly on the plain" or hyperplanes is common the ... ALL linear congruential generators! ... period of the LCG is AT MOST M, ...
    (sci.stat.math)
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