Abstract
Statistical independence properties of recently proposed nonlinear congruential pseudorandom number generators are analyzed by means of the serial test. The results that are established are essentially best possible. The method relies heavily on bounds for exponential sums.
This is a preview of subscription content, access via your institution.
References
Cochrane, T.: On a trigonometric inequality of Vinogradov. J. Number Th.27, 9–16 (1987).
Eichenauer, J., Grothe, H., Lehn, J.: Marsaglia's lattice test and non-linear congruential pseudo random number generators. Metrika35, 241–250 (1988).
Eichenauer, J., Lehn, J.: A non-linear congruential pseudo random number generator. Statist. Hefte27, 315–326 (1986).
Eichenauer, J., Lehn, J., Topuzoğlu, A.: A non-linear congruential pseudo random number generator with power of two modulus. Math. Comp. (To appear.)
Knuth, D. E.: The Art of Computer Programming, vol. 2: Seminumerical Algorithms. 2nd ed. Reading: Addison-Wesley. 1981.
Lidl, R., Niederreiter, H.: Finite Fields. Reading: Addison-Wesley. 1983.
Marsaglia, G.: Random numbers fall mainly in the planes. Proc. Nat. Acad. Sci. U.S.A.61, 25–28 (1968).
Marsaglia, G.: The structure of linear congruential sequences. In: Applications of Number Theory to Numerical Analysis (Ed. by S. K. Zaremba), pp. 249–285. New York: Academic Press. 1972.
Niederreiter, H.: Pseudo-random numbers and optimal coefficients. Adv. Math.26, 99–181 (1977).
Niederreiter, H.: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc.84, 957–1041 (1978).
Niederreiter, H.: Number-theoretic problems in pseudorandom number generation. In: Proc. Symp. on Applications of Number Theory to Numerical Analysis, Lecture Notes No. 537, pp. 18–28. Kyoto: Research Inst. of Math. Sciences. 1984.
Niederreiter, H.: The serial test for pseudo-random numbers generated by the linear congruential method. Numer. Math.46, 51–68 (1985).
Niederreiter, H.: Pseudozufallszahlen und die Theorie der Gleichverteilung. Sitzungsber. Österr. Akad. Wiss. Math.-Naturwiss. Kl.195, 109–138 (1986).
Niederreiter, H.: Remarks on nonlinear congruential pseudorandom numbers. Metrika. (To appear.)
Weil, A.: On some exponential sums. Proc. Nat. Acad. Sci. U.S.A.34, 204–207 (1948).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Niederreiter, H. Statistical independence of nonlinear congruential pseudorandom numbers. Monatshefte für Mathematik 106, 149–159 (1988). https://doi.org/10.1007/BF01298835
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01298835
Keywords
- Number Generator
- Serial Test
- Pseudorandom Number
- Statistical Independence
- Pseudorandom Number Generator