Abstract
Recently, the explicit inversive congruential method with power of two modulus for generating uniform pseudorandom numbers was introduced. Statistical independence properties of the generated sequences have been studied by estimating the discrepancy of all overlapping pairs of successive pseudorandom numbers. In the present paper a similar analysis is performed for the subsets of nonoverlapping pairs. The method of proof relies on a detailed discussion of the properties of certain exponential sums.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eichenauer-Herrmann, J.: Inversive congruential pseudorandom numbers: a tutorial. Int. Statist. Rev.60, 167–176 (1992).
Eichenauer-Herrmann, J.: Pseudorandom number generation by nonlinear methods. Int. Statist. Rev. (to appear).
Eichenauer-Herrmann, J., Ickstadt, K.: Explicit inversive congruential pseudorandom numbers with power of two modulus. Math. Comp. (to appear).
Eichenauer-Herrmann, J., Niederreiter, H.: On the discrepancy of quadratic congruential pseudorandom numbers. J. Comp. Appl. Math.34, 243–249 (1991).
Kiefer, J.: On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm. Pacific J. Math.11, 649–660 (1961).
Niederreiter, H.: The serial test for congruential pseudorandom numbers generated by inversions. Math. Comp.52, 135–144 (1989).
Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. Philadelphia: SIAM. 1992.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eichenauer-Herrmann, J. Nonoverlapping pairs of explicit inversive congruential pseudorandom numbers. Monatshefte für Mathematik 119, 49–61 (1995). https://doi.org/10.1007/BF01292768
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01292768