Structural properties for two classes of combined random number generators

Pierre L'ecuyer, Shu Tezuka

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


We analyze a class of combined random number generators recently proposed by L'Ecuyer, which combines a set of linear congruential generators (LCG’s) with distinct prime moduli. We show that the geometrical behavior of the vectors of points produced by the combined generator can be approximated by the lattice structure of an associated LCG, whose modulus is the product of the moduli of the individual components. The approximation is good if these individual moduli are near each other and if the dimension of the vectors is large enough. The associated LCG is also exactly equivalent to a slightly different combined generator of the form suggested by Wichmann and Hill. We give illustrations, for which we examine the approximation error and assess the quality of the lattice structure of the associated LCG.

Original languageEnglish
Pages (from-to)735-746
Number of pages12
JournalMathematics of Computation
Issue number196
Publication statusPublished - Oct 1991

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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