Statistical Independence of a New Class of Inversive Congruential Pseudorandom Numbers

Linear congruential pseudorandom numbers show several undesirable regularities which can render them useless for certain stochastic simulations. This was the motivation for important recent developments in nonlinear congruential methods for generating uniform pseudorandom numbers. It is particularly promising to achieve nonlinearity by employing the operation of multiplicative inversion with respect to a prime modulus. In the present paper a new class of such inversive congruential generators is introduced and analyzed. It is shown that they have excellent statistical independence properties and model true random numbers very closely. The methods of proof rely heavily on Weil-Stepanov bounds for rational exponential sums.