Mixed Congruential Random Number Generators for Binary Machines

Abstract

Random number generators of the mixed congruential type have recently been proposed. They appear to have some advantages over those of the multiplicative type, except that their statistical behavior is unsatisfactory in some cases. It is shown theoretically that a certain class of these mixed generators should be expected to fail statistical tests for randomness. Extensive testing confirms this hypothesis and makes possible a more precise definition of the unsatisfactory class. It is concluded that the advantages of mixed generators can be realized only in special circumstances. On machines with relatively short multiplication times the multiplicative generators are to be preferred.