Transformation of Uniformly Distributed Random Numbers

- Based on standard pseudo-random numbers
that can
be generated by methods like the linear congruential generator
- it is possible to generate pseudo-random numbers that can be regarded as realizations of random variables having other than uniform distributions.
- Examples are realizations of exponentially, Poisson, binomially or normally distributed random variables .

- For this purpose one can apply algorithms like the so-called
*inversion method*and*rejection-sampling*, whose basic ideas will be explained by some examples. - A much more comprehensive discussion of these algorithms can be
found e.g. in
- L. Devroye (1986)
*Nonuniform Random Variate Generation*. Springer, New York, - G.S. Fishman (1996)
*Monte Carlo: Concepts, Algorithms and Applications*. Springer, New York, - C.P. Robert and G. Casella (1999)
*Monte Carlo Statistical Methods*. Springer, New York.

- L. Devroye (1986)

- Inversion Method
- Transformation Algorithms for Discrete Distributions
- Acceptance-Rejection Method
- Quotients of Uniformly Distributed Random Variables

Ursa Pantle 2006-07-20