AVERAGE EQUIDISTRIBUTION PROPERTIES OF COMPOUND NONLINEAR CONGRUENTIAL PSEUDORANDOM NUMBERS

The present paper deals with the compound nonlinear congruential metho d for generating uniform pseudorandom numbers, which has been introduc ed recently. Equidistribution properties of the generated sequences ov er parts of the period are studied, based on the discrepancy of the co rresponding point sets. Upper and lower bounds for the average value o f these discrepancies are established, which are essentially best poss ible. These results show that the average equidistribution behavior of compound nonlinear congruential pseudorandom numbers fits well the eq uidistribution properties of true random numbers. The method of proof relies heavily on estimates of the average value of incomplete exponen tial sums.