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From: hes@ecsvax.UUCP (Henry Schaffer)
Newsgroups: net.math.stat
Subject: Re: Need tests for random number generators
Message-ID: <467@ecsvax.UUCP>
Date: Mon, 7-Jan-85 09:47:11 EST
Article-I.D.: ecsvax.467
Posted: Mon Jan  7 09:47:11 1985
Date-Received: Tue, 8-Jan-85 05:38:06 EST
References: <553@oddjob.UChicago.UUCP>
Organization: NC State Univ.
Lines: 18

In my opinion, testing the quality of a random number generator
is a rotten job.  Sometimes you can find something wrong, but you
can seldom say enything more than, "So far, no obvious problems."
If you still want to test, it is best to analyze how you are going
to use them, and then test for the particular qualities you need.
Common tests include: Equidistribution- divide your output interval
(e.g. 0-1) into 10 or 20 subintervals, develop a frequency table of a
LARGE number of random numbers, and use the Chi-Square Test.  Lag
Correlations-correlations between adjacent random numbers; correlations
between random numbers i apart (i=1,2,3,...)- where you stop is 
determined by your use, statistically test for the significance of the
correlation coefficient(s).
The problem is that deviations from randomness can be very subtle,
some years ago Marsaglia had an article on Random Numbers Fall Mainly
in the Planes (CACM?) showing the crysalline behavior of n-tuples from
congruential random number generators. Probably the best place to start
reading is Knuth's Volume 2.
--henry schaffer  n. c. state univ.   ...mcnc!ecsvax!hes