Equidistribution properties of nonlinear congruential pseudorandom numbers

Equidistribution properties of a general class of nonlinear congruential methods for generating uniform pseudorandom numbers are established. The results that are obtained are essentially best possible and show that the generated pseudorandom numbers have an equidistribution behaviour like true random numbers.

[1]  H. Niederreiter.  Nonlinear Methods for Pseudorandom Number and Vector Generation , 1992 .

[2]  Harald Niederreiter,et al.  Recent trends in random number and random vector generation , 1991, Ann. Oper. Res..

[3]  J. Lehn,et al.  Marsaglia’s lattice test and non-linear congruential pseudo random number generators , 1988 .

[4]  A. Weil.  On Some Exponential Sums. , 1948, Proceedings of the National Academy of Sciences of the United States of America.

[5]  H. Niederreiter.  Pseudorandom numbers and quasirandom points , 1993 .

[6]  Rudolf Lide,et al.  Finite fields , 1983 .

[7]  Harald Niederreiter,et al.  Lower bounds for the discrepancy of inversive congruential pseudorandom numbers , 1990 .

[8]  K. Chung,et al.  An estimate concerning the Kolmogoroff limit distribution , 1949 .

[9]  Harald Niederreiter,et al.  Statistical independence of nonlinear congruential pseudorandom numbers , 1988 .

[10]  Harald Niederreiter,et al.  On the statistical independence of nonlinear congruential pseudorandom numbers , 1994, TOMC.

[11]  H. Niederreiter,et al.  Remarks on nonlinear congruential pseudorandom numbers , 1988 .

[12]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[13]  Jürgen Eichenauer-Herrmann,et al.  Inversive congruential pseudorandom numbers : a tutorial , 1992 .

[14]  Todd Cochrane.  On a trigonometric inequality of vinogradov , 1987 .

[15]  Ian H. Sloan.  Random Number Generation and Quasi-Monte Carlo Methods (H, Niederreiter) , 1993, SIAM Rev..