# References and Further Reading¶

For an encyclopaedic coverage of the subject readers are advised to
consult the book *Non-Uniform Random Variate Generation* by Luc Devroye.
It covers every imaginable distribution and provides hundreds of
algorithms.

- Luc Devroye,
*Non-Uniform Random Variate Generation*, Springer-Verlag, ISBN 0-387-96305-7. Available online at http://luc.devroye.org/rnbookindex.html.

The subject of random variate generation is also reviewed by Knuth, who describes algorithms for all the major distributions.

- Donald E. Knuth,
*The Art of Computer Programming: Seminumerical Algorithms*(Vol 2, 3rd Ed, 1997), Addison-Wesley, ISBN 0201896842.

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.

*Review of Particle Properties*R.M. Barnett et al., Physical Review D54, 1 (1996) http://pdg.lbl.gov/.

The Review of Particle Physics is available online in postscript and pdf format.

An overview of methods used to compute cumulative distribution functions
can be found in *Statistical Computing* by W.J. Kennedy and J.E. Gentle.
Another general reference is *Elements of Statistical Computing* by
R.A. Thisted.

- William E. Kennedy and James E. Gentle,
*Statistical Computing*(1980), Marcel Dekker, ISBN 0-8247-6898-1. - Ronald A. Thisted,
*Elements of Statistical Computing*(1988), Chapman & Hall, ISBN 0-412-01371-1.

The cumulative distribution functions for the Gaussian distribution are based on the following papers,

*Rational Chebyshev Approximations Using Linear Equations*, W.J. Cody, W. Fraser, J.F. Hart. Numerische Mathematik 12, 242-251 (1968).*Rational Chebyshev Approximations for the Error Function*, W.J. Cody. Mathematics of Computation 23, n107, 631-637 (July 1969).