### Abstract

We derive two different general relationships that exist among terms of the linear congruential generator x_{i}+_{1} = ax_{i} + b mod 2^{β} that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.

Original language | English (US) |
---|---|

Pages (from-to) | 381-383 |

Number of pages | 3 |

Journal | Statistics and Probability Letters |

Volume | 15 |

Issue number | 5 |

DOIs | |

State | Published - Dec 8 1992 |

### Fingerprint

### Keywords

- linear congruential generator
- long range corelations
- Monte Carlo simulation
- Random number generator

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

*Statistics and Probability Letters*,

*15*(5), 381-383. https://doi.org/10.1016/0167-7152(92)90158-2

**Intrinsic relations in the structure of linear congruential generators modulo 2β
.** / Percus, Ora E.; Percus, Jerome.

Research output: Contribution to journal › Article

*Statistics and Probability Letters*, vol. 15, no. 5, pp. 381-383. https://doi.org/10.1016/0167-7152(92)90158-2

}

TY - JOUR

T1 - Intrinsic relations in the structure of linear congruential generators modulo 2β

AU - Percus, Ora E.

AU - Percus, Jerome

PY - 1992/12/8

Y1 - 1992/12/8

N2 - We derive two different general relationships that exist among terms of the linear congruential generator xi+1 = axi + b mod 2β that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.

AB - We derive two different general relationships that exist among terms of the linear congruential generator xi+1 = axi + b mod 2β that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.

KW - linear congruential generator

KW - long range corelations

KW - Monte Carlo simulation

KW - Random number generator

UR - http://www.scopus.com/inward/record.url?scp=44049114223&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44049114223&partnerID=8YFLogxK

U2 - 10.1016/0167-7152(92)90158-2

DO - 10.1016/0167-7152(92)90158-2

M3 - Article

AN - SCOPUS:44049114223

VL - 15

SP - 381

EP - 383

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 5

ER -