Average Behaviour of Compound Nonlinear Congruential Pseudorandom Numbers

The present paper deals with the compound general nonlinear congruential method for generating uniform pseudorandom numbers, which has been introduced recently. Equidistribution and statistical independence properties of the generated sequences over parts of the period are studied based on the discrepancy of certain point sets. The main result is an upper bound for the average value of these discrepancies, which rests on bounds for certain exponential sums.