On a new class of pseudorandom numbers for simulation methods

Abstract

The deficiencies of classical methods for uniform pseudorandom number generation have recently led to the development of alternative methods, such as nonlinear congruential methods. A particularly attractive nonlinear congruential method is the explicit inversive congruential method recently introduced by Eichenauer-Herrmann. We establish several new results on the structural and statistical properties of pseudorandom numbers generated by this method. These results demonstrate that this method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties.