From: Bill Stewart <stewarts@ix.netcom.com>
Date: Mon, 22 Apr 1996 10:49:28 +0800
To: cypherpunks@toad.com
Subject: Re: rng hardware running ...
Message-ID: <199604212245.PAA20254@dfw-ix6.ix.netcom.com>
MIME-Version: 1.0
Content-Type: text/plain


>>The dist of 0 vs 1 is documented as being slightly skewed (.05%) toward
>>1s. 
>If the RNG chips aren't too expensive, you could take the output from 2 (or
>more) of them and XOR the outputs together to reduce skew.

There are all sorts of statistics you can look at that may help you
understand the quality of the randomness you're getting.  One of the central
concerns is finding the underlying patterns and the random noise driving them,
though in this case we're looking for the noise and dumping the patterns
rather than the opposite.

Some things that are good to look at are first and second differences of the 
series (e.g. take Y1=X2-X1, Y2=X3-X2, ... and Z1=Y2-Y1, Z2=Y3-Y2... and on up
for higher differences) and look for distributions and patterns there.
You may also want to look at moving averages (take a window of K samples
and slide that through the sample space, for several values of K.)
This stuff is similar to Fourier-series analysis for discrete-valued data.

If you want to read lots of gory details on the math, the book by
Box and Jenkins on Time Series Analysis was one of the best textbooks
~20 years ago.   As my professor put it, if you stare at the numbers long
enough,
you can find all sorts of things in them, which may or may not really be
there :-)
#					Thanks;  Bill
# Bill Stewart, stewarts@ix.netcom.com, +1-415-442-2215