Pseudorandom number generators are essential elements in the toolbox of
stochastic simulation. Their task is to simulate realizations of independent,
identically *U*([0,1[)-distributed random variables. Other distributions will
be obtained by transformation methods, see Devroye (1986), and the software
package C-Rand, see Stadlober and Kremer (1992) and Stadlober and Niederl (1994).

There is a strong need to enlarge this toolbox by widely different pseudorandom number generator s. We refer the reader to Ferrenberg and Landau (1992), L'Ecuyer (1992, 1994), Eddy (1990), and Anderson (1990) for a discussion of some of the deficiencies of traditional generators.

Pseudorandom number generators are like antibiotics. No generator will be
appropriate for all tasks. Any type of generator has some unwanted
side-effects. Hence, we are in need of an arsenal of pseudorandom number generator s with *
distinct properties*. If two strongly different generators yield the same
outcome in a simulation, we will gain confidence in the results.

Many properties of inversive methods are complementary to those of linear algorithms. Inversive generators are easy to initialize. Their excellent properties remain invariant under the choice of parameters. For certain inversive types this robustness was even proved for subsequences. We may work with larger sample sizes on a given architecture. Extensive tables of parameters are available for implementation.

In our opinion, inversive methods should not be viewed as a replacement of
linear methods. In view of their remarkable properties, they are *a valuable completion* of our arsenal of uniform generators.

Peter Hellekalek