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<a name="General-comments-on-random-numbers"></a>
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<p>
Next: <a href="The-Random-Number-Generator-Interface.html#The-Random-Number-Generator-Interface" accesskey="n" rel="next">The Random Number Generator Interface</a>, Up: <a href="Random-Number-Generation.html#Random-Number-Generation" accesskey="u" rel="up">Random Number Generation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="General-comments-on-random-numbers-1"></a>
<h3 class="section">18.1 General comments on random numbers</h3>

<p>In 1988, Park and Miller wrote a paper entitled &ldquo;Random number
generators: good ones are hard to find.&rdquo; [Commun. ACM, 31, 1192&ndash;1201].
Fortunately, some excellent random number generators are available,
though poor ones are still in common use.  You may be happy with the
system-supplied random number generator on your computer, but you should
be aware that as computers get faster, requirements on random number
generators increase.  Nowadays, a simulation that calls a random number
generator millions of times can often finish before you can make it down
the hall to the coffee machine and back.
</p>
<p>A very nice review of random number generators was written by Pierre
L&rsquo;Ecuyer, as Chapter 4 of the book: Handbook on Simulation, Jerry Banks,
ed. (Wiley, 1997).  The chapter is available in postscript from
L&rsquo;Ecuyer&rsquo;s ftp site (see references).  Knuth&rsquo;s volume on Seminumerical
Algorithms (originally published in 1968) devotes 170 pages to random
number generators, and has recently been updated in its 3rd edition
(1997).
It is brilliant, a classic.  If you don&rsquo;t own it, you should stop reading
right now, run to the nearest bookstore, and buy it.
</p>
<p>A good random number generator will satisfy both theoretical and
statistical properties.  Theoretical properties are often hard to obtain
(they require real math!), but one prefers a random number generator
with a long period, low serial correlation, and a tendency <em>not</em> to
&ldquo;fall mainly on the planes.&rdquo;  Statistical tests are performed with
numerical simulations.  Generally, a random number generator is used to
estimate some quantity for which the theory of probability provides an
exact answer.  Comparison to this exact answer provides a measure of
&ldquo;randomness&rdquo;.
</p>
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Next: <a href="The-Random-Number-Generator-Interface.html#The-Random-Number-Generator-Interface" accesskey="n" rel="next">The Random Number Generator Interface</a>, Up: <a href="Random-Number-Generation.html#Random-Number-Generation" accesskey="u" rel="up">Random Number Generation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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