### Abstract

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 language | English |
---|---|

Pages (from-to) | 735-746 |

Number of pages | 12 |

Journal | Mathematics of Computation |

Volume | 57 |

Issue number | 196 |

DOIs | |

Publication status | Published - Oct 1991 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics of Computation*,

*57*(196), 735-746. https://doi.org/10.1090/S0025-5718-1991-1094954-3

**Structural properties for two classes of combined random number generators.** / L'ecuyer, Pierre; Tezuka, Shu.

Research output: Contribution to journal › Article

*Mathematics of Computation*, vol. 57, no. 196, pp. 735-746. https://doi.org/10.1090/S0025-5718-1991-1094954-3

}

TY - JOUR

T1 - Structural properties for two classes of combined random number generators

AU - L'ecuyer, Pierre

AU - Tezuka, Shu

PY - 1991/10

Y1 - 1991/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966246478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966246478&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1991-1094954-3

DO - 10.1090/S0025-5718-1991-1094954-3

M3 - Article

AN - SCOPUS:84966246478

VL - 57

SP - 735

EP - 746

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 196

ER -