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<title>GNU Scientific Library – Reference Manual: Random Number Distribution References and Further Reading</title>
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<p>
Previous: <a href="Random-Number-Distribution-Examples.html#Random-Number-Distribution-Examples" accesskey="p" rel="previous">Random Number Distribution Examples</a>, Up: <a href="Random-Number-Distributions.html#Random-Number-Distributions" accesskey="u" rel="up">Random Number Distributions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="References-and-Further-Reading-13"></a>
<h3 class="section">20.41 References and Further Reading</h3>
<p>For an encyclopaedic coverage of the subject readers are advised to
consult the book <cite>Non-Uniform Random Variate Generation</cite> by Luc
Devroye. It covers every imaginable distribution and provides hundreds
of algorithms.
</p>
<ul class="no-bullet">
<li><!-- /@w --> Luc Devroye, <cite>Non-Uniform Random Variate Generation</cite>,
Springer-Verlag, ISBN 0-387-96305-7. Available online at
<a href="http://cg.scs.carleton.ca/~luc/rnbookindex.html">http://cg.scs.carleton.ca/~luc/rnbookindex.html</a>.
</li></ul>
<p>The subject of random variate generation is also reviewed by Knuth, who
describes algorithms for all the major distributions.
</p>
<ul class="no-bullet">
<li><!-- /@w --> Donald E. Knuth, <cite>The Art of Computer Programming: Seminumerical
Algorithms</cite> (Vol 2, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896842.
</li></ul>
<p>The Particle Data Group provides a short review of techniques for
generating distributions of random numbers in the “Monte Carlo”
section of its Annual Review of Particle Physics.
</p>
<ul class="no-bullet">
<li><!-- /@w --> <cite>Review of Particle Properties</cite>
R.M. Barnett et al., Physical Review D54, 1 (1996)
<a href="http://pdg.lbl.gov/">http://pdg.lbl.gov/</a>.
</li></ul>
<p>The Review of Particle Physics is available online in postscript and pdf
format.
</p>
<p>An overview of methods used to compute cumulative distribution functions
can be found in <cite>Statistical Computing</cite> by W.J. Kennedy and
J.E. Gentle. Another general reference is <cite>Elements of Statistical
Computing</cite> by R.A. Thisted.
</p>
<ul class="no-bullet">
<li><!-- /@w --> William E. Kennedy and James E. Gentle, <cite>Statistical Computing</cite> (1980),
Marcel Dekker, ISBN 0-8247-6898-1.
</li></ul>
<ul class="no-bullet">
<li><!-- /@w --> Ronald A. Thisted, <cite>Elements of Statistical Computing</cite> (1988),
Chapman & Hall, ISBN 0-412-01371-1.
</li></ul>
<p>The cumulative distribution functions for the Gaussian distribution
are based on the following papers,
</p>
<ul class="no-bullet">
<li><!-- /@w --> <cite>Rational Chebyshev Approximations Using Linear Equations</cite>,
W.J. Cody, W. Fraser, J.F. Hart. Numerische Mathematik 12, 242–251 (1968).
</li></ul>
<ul class="no-bullet">
<li><!-- /@w --> <cite>Rational Chebyshev Approximations for the Error Function</cite>,
W.J. Cody. Mathematics of Computation 23, n107, 631–637 (July 1969).
</li></ul>
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Previous: <a href="Random-Number-Distribution-Examples.html#Random-Number-Distribution-Examples" accesskey="p" rel="previous">Random Number Distribution Examples</a>, Up: <a href="Random-Number-Distributions.html#Random-Number-Distributions" accesskey="u" rel="up">Random Number Distributions</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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