References and Further ReadingΒΆ

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.

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).