ABSTRACT
Realizations of random processes are the raw materials of classical statistical inferences. Most applications of statistical methods in substantive research require a “random sample” or a “random assignment.” Another, quite different way in which observations on random processes may be used is in the development of statistical methods and theory. For some distributions the transformations from the uniform are simple and can be made exactly; in other cases the more complicated transformations must be approximated. A large collection of facts concerning primitive elements has been developed in number theory. Knuth summarized some of the facts pertinent to multiplicative-congruential generators with moduli which are powers of a prime. Tausworthe suggested an interesting linear recurrence equation for generation of pseudorandom numbers. In order to extend the period of a random number generator or otherwise to improve the “randomness” of the generated sequences, a number of authors have suggested various combinations of two or more generators.
