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Transformation of Uniformly Distributed Random Numbers
- Based on standard pseudo-random numbers
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
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.