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From: gunnar@hafro.UUCP (Gunnar Stefansson)
Newsgroups: sci.math
Subject: Re: Need formula for Normal Distribution Simulation
Message-ID: <293@hafro.UUCP>
Date: Thu, 6-Nov-86 02:21:09 EST
Article-I.D.: hafro.293
Posted: Thu Nov  6 02:21:09 1986
Date-Received: Fri, 7-Nov-86 22:06:04 EST
References: <146@helm.UUCP> <5270001@hpfcpf.HP.COM> <401@entropy.UUCP> <2198@ecsvax.UUCP>
Reply-To: gunnar@hafro.UUCP (Gunnar Stefansson)
Organization: Marine Research Institute, Reykjavik
Lines: 47

My mailer can't seem to find this address any better than other
mailers, so here we go to the net.

I have my doubts about using the Box-Muller and like transforms,
which some people have recommended.  The reasons are at least twofold:

1.  It is very ineffective -- there are sines, cosines, logs and
square roots to be evaluated every time.  So it takes MUCH longer
than a random number generator should.  Marsaglia's improvement of
the method is somewhat more effective, but there are still logs and
square roots to be taken every time.

2. It is not at all obvious what happens if your uniform input is not
uniform enough. So to start with, you must be reasonably sure that
your uniform numbers are really iid uniform. Of course, when using
the Unix rand() (or whatever), you're probably not getting very good
random numbers.

Adding up 12 uniforms may be good enough, but that is unlikely. Be
careful that the resulting distribution will have zero probability in
the tails. So if you are interested in e.g. the distribution of a max
of things, it seems likely that it will get messed up.

I'd like to recommend the book 'Statistical Computing' by Kennedy and
Gentle as a general intro -- it's more recent than Knuth. In it,
you'll find lots of good algorithms, many of which can be very well
programmed in C (as opposed to the Fortran that they use). The
feedback-shift-register methods for uniforms seem to be quite
adequate and cheap to use. Further, there are several algorithms for
transforming to normal given, most of them cheaper than the
Box-Muller transform. One in particular (the Marsaglia-Bray
"convenient" method, p. 203) is simple and fast).

I have implemented a u(0,1) and a n(0,1) from that book. Writing the
programs in C turned out to be much simpler than the Fortran
counterparts.

--Gunnar

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Gunnar Stefansson                       {mcvax,seismo}!enea!hafro!gunnar 
Marine Research Institute, Reykjavik    gunnar@hafro.uucp
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Gunnar Stefansson                       {mcvax,seismo}!enea!hafro!gunnar 
Marine Research Institute, Reykjavik    gunnar@hafro.UUCP