Art Kendall <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> I tend to be more concerned with the "apparent randomness" of the results than with
>the speed
of the algorithm.
>
> As a thought experiment, what is the cumulative time difference in a run using the
>fastest
vs the slowest algorithm? A
> whole minute? A second? A fractional second?
>
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I agree; the time to generate normal
variates used in most simulations is a
small part of the overall running time.
More important are convenience and fit
to the true distribution.
As for the latter, most methods are
functions of the presumed uniform [0,1)
variates U1,U2,... used in the
generating process, and their fit to
the underlying distribution is a direct
consequence of the suitability of the
U's. There have been few reported
problems, except perhaps when integers
from congruential RNGs are floated
then used via polar coordinates to
provide pairs of normal variates in
the plane. The lattice structure of
pairs of points from the congruential
RNG may cause patterns in the
resulting normal points in the plane.
Most problems with integer RNG's arise
from from their suitability as iid
uniform---usually 32-bit---integers.
After they are floated to [0,1),
problems are much less frequent.
Speed can be an important factor for
exponential variates---for example,
when using them to generate a large
set of ordered uniform [0,1) variates
or when providing points in a Poisson
process.
As long as methods are easy to use,
(via libraries, downloads, etc.),
and seem to produce the required
distributions well within the limits
of single precision, then one may
as well make a choice based on
elegance and speed, criteria for
which there are wide variations
and challenges for improvement.
Assessing the two can be likened
to pairs skating and the downhill.
George Marsaglia
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