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Compound inversive congruential
pseudorandom numbers: an average-case analysis


Authors: Jürgen Eichenauer-Herrmann and Frank Emmerich
Journal: Math. Comp. 65 (1996), 215-225
MSC (1991): Primary 65C10; Secondary 11K45
DOI: https://doi.org/10.1090/S0025-5718-96-00675-8
MathSciNet review: 1322889
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Abstract: The present paper deals with the compound (or generalized) inversive 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. The method of proof is based on estimates for exponential sums.


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  • 1 J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers avoid the planes, Math. Comp. 56 (1991), 297--301. MR 91k:65021
  • 2 ------, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167--176.
  • 3 ------, Improved lower bounds for the discrepancy of inversive congruential pseudorandom numbers, Math. Comp. 62 (1994), 783--786. MR 94g:11058
  • 4 ------, On generalized inversive congruential pseudorandom numbers, Math. Comp. 63 (1994), 293--299. MR 94k:11088
  • 5 ------, Pseudorandom number generation by nonlinear methods, Internat. Statist. Rev. 63 (1995), 247--255.
  • 6 ------, A unified approach to the analysis of compound pseudorandom numbers, Finite Fields and their Appl. 1 (1995), 102--114.
  • 7 M. Flahive and H. Niederreiter, On inversive congruential generators for pseudorandom numbers, Finite Fields, Coding Theory, and Advances in Communications and Computing (G. L. Mullen and P. J.-S. Shiue, eds.), Dekker, New York, 1993, pp. 75--80. MR 94a:11117
  • 8 K. Huber, On the period length of generalized inversive pseudorandom number generators, Appl. Algebra Engrg. Comm. Comput. 5 (1994), 255--260. CMP: 94 14
  • 9 J. Kiefer, On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm, Pacific J. Math. 11 (1961), 649--660. MR 24:A1732
  • 10 H. Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions, Math. Comp. 52 (1989), 135--144. MR 90e:65008
  • 11 ------, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers, Math. Comp. 55 (1990), 277--287. MR 91e:65016
  • 12 ------, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323--345. MR 92h:65010
  • 13 ------, Finite fields, pseudorandom numbers, and quasirandom points, Finite Fields, Coding Theory, and Advances in Communications and Computing (G. L. Mullen and P. J.-S. Shiue, eds.), Dekker, New York, 1993, pp. 375--394. MR 94a:11121
  • 14 ------, Nonlinear methods for pseudorandom number and vector generation, Simulation and Optimization (G. Pflug and U. Dieter, eds.), Lecture Notes in Econom. and Math. Systems, vol. 374, Springer, Berlin, 1992, pp. 145--153.
  • 15 ------, Random number generation and quasi-Monte Carlo methods, SIAM, Philadelphia, PA, 1992. MR 93h:65008

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Additional Information

Jürgen Eichenauer-Herrmann
Affiliation: Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgarten- strasse 7, D-64289 Darmstadt, Germany

Frank Emmerich
Affiliation: Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgarten- strasse 7, D-64289 Darmstadt, Germany

DOI: https://doi.org/10.1090/S0025-5718-96-00675-8
Keywords: Uniform pseudorandom numbers, compound inversive congruential method, equidistribution, statistical independence, discrepancy, exponential sums
Received by editor(s): September 19, 1994
Article copyright: © Copyright 1996 American Mathematical Society

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