Non-uniform random variate generation

Pseudo-random number sampling is the numerical practice of generating pseudo-random numbers that are distributed according to a given probability distribution.

In the following, it is taken for granted that there is a pseudo-random number generator producing numbers X that are uniformly distributed. Different algorithms are then used to transform X into a random variable U(X) that is distributed according to a given distribution f(C).

Historically, basic methods of pseudo-random number sampling were developed for Monte-Carlo simulations in the Manhattan project; they were first published by John von Neumann in the early 1950s.

Literature

• Fishman,GS: Monte Carlo. Concepts, Algorithms, and Applications. New York: Springer (1996).
• Knuth,DE: The Art of Computer Programming, Vol. 2 Seminumerical Algorithms, Chapter 3.4.1 (3rd edition, 1997).