Hi Dr. Heiser,
I'd like to use
> Dr. Helms:
as an abbreviation for "Dear" ? :-)
... Ok, I'll use the moment to put some light on my person:
I did not make a PhD yet, since my short academic career fills not all
prerequisites for that :-(( Mainly I was busy as assistant in research
projects for geriatry and rehabilitation and most of statistics and related
math I learned by doing and implementing software. I'm giving introductory
courses for statistics in the dept. of social assistance here in the
university now. Unfortunately with an age of 50 it's difficult here to find
an entry to additional qualification and a practical use of a "Dr." later
...
------------
Well
>
> What did you use as your random number generator. Many of the RNGs that are
> based on the linear congruential method have certain patterns in their
> sequences that give interesting outputs from RNG tests.
thanks for this hint. I just use the RNG of the programming language
(Delphi, former Turbo-Pascal). When I first started analyzing CR I only took
simply integer data: range for x1 and x2: {-100..100} each and every combi -
nation one time.
But that's of little concern for the deriving of the formulae. The set of
y = r*x1 + s*x2
y2 = r*x2 - s*x1
is simply an expression for what we are doing, if we regress y on(?? which
english preposition??) x1 with a correlation of r and after that regressing
x1 on y, assuming all x1,x2,y,y2 are standardized. And for one, who is
familiar with trigonometric formulae, it is obvious that in r and s we
have a cosine and a sine of the same angle. I only left the notation of r and s
since some CR-discutants may not be aware, that a correlation is also a
cosine. ;-)
> These patterns are
> not obvious, but result in unusually good performance (in comparison to
> RNG's that are much closer to true randomness) in the Diehard Parking and 3D
> Spheres tests and in some Monte Carlo simulations.
Yes; the examples, that I recently posted here, are affected from that. These
are the examples, where I sketched the range of expected CR-D-values some days
ago. They surely are affected of the quality of the RNG - and I just draw a
handful of samples.
Expected values on the basis of *good* RNG's is one thing, that (the current
state of) CR is still lacking.
>
> For your y = r*x1 + s*x2, there could also be some local or global
> correlation structures that are not obvious that could be giving you your
> results.
>
> At least right now, Marsaglia's KISS RNG is a pretty good RNG. I am not
> aware of any random number test it has failed.
Yes, I would like to have it; maybe I can translate the algorithm into
Pascal/Delphi one day...
>
> David Heiser
Thanks for your hints!
Sincerely -
Gottfried
--
Gottfried Helms
Univ. Kassel
.
.
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