### BibTeX

@MISC{L'Ecuyer_randomnumber,

author = {Pierre L'Ecuyer},

title = {Random number generation},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables distributed uniformly over the interval

### Citations

2197 | The art of computer programming - Knuth - 1973 |

1958 | Matrix computations - Golub, Loan - 1996 |

1245 |
Simulation Modeling and Analysis
- Law, Kelton
- 2000
(Show Context)
Citation Context ...erators with multiple disjoint streams and substreams. These streams and substreams can provide parallel RNGs and are also important to support the use of variance reduction techniques (Fishman 1996, =-=Law and Kelton 2000-=-, L’Ecuyer et al. 2002). They are usually implemented by partitioning the output sequence of a long-period generator into long disjoint subsequences and subsubsequences whose starting points are found... |

1110 | Statistics for Spatial Data - Cressie - 1993 |

749 | Random Number Generation and Quasi-Monte Carlo Methods, Philadelphia: Society for Industrial and Applied - NIEDERREITER - 1992 |

675 | The Art of Computer Programming, volume 2: Seminumerical Algorithms - Knuth - 1988 |

623 | Non-Uniform Random Variate Generation - Devroye - 1986 |

611 | Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator
- Matsumoto, Nishimura
- 1998
(Show Context)
Citation Context ...linear feedback shift register (LFSR), generalized feedback shift register (GFSR), twisted GFSR (TGFSR), Mersenne twister, the WELL, and xorshift generators (Tezuka 1995, L’Ecuyer 1996, Fishman 1996, =-=Matsumoto and Nishimura 1998-=-, L’Ecuyer and Panneton 2002, L’Ecuyer 2006, Panneton et al. 2006, Panneton and L’Ecuyer 2005, Panneton 2004). A common characterization of all these generators is that they are special cases of a gen... |

420 | Stochastic Simulation - Ripley - 1987 |

409 | Introduction to Finite Fields and Their Applications - Lidl, Niederreiter - 1986 |

324 |
Monte Carlo: Concepts, Algorithms and Applications
- FISHMAN
- 1995
(Show Context)
Citation Context ...Tausworthe or linear feedback shift register (LFSR), generalized feedback shift register (GFSR), twisted GFSR (TGFSR), Mersenne twister, the WELL, and xorshift generators (Tezuka 1995, L’Ecuyer 1996, =-=Fishman 1996-=-, Matsumoto and Nishimura 1998, L’Ecuyer and Panneton 2002, L’Ecuyer 2006, Panneton et al. 2006, Panneton and L’Ecuyer 2005, Panneton 2004). A common characterization of all these generators is that t... |

272 |
Shift-register synthesis and BCH decoding
- Massey
- 1969
(Show Context)
Citation Context ...yed by this sequence, and the characteristic polynomial of that recurrence is called the minimal polynomial of the sequence. This minimal polynomial can be computed by the Berlekamp-Massey algorithm (=-=Massey 1969-=-). The sequences {xn,j, n ≥ 0} may have different minimal polynomials for different values of j, and also different minimal polynomials than the sequences {yn,j, n ≥ 0}. But all these minimal polynomi... |

271 | AGuideto Simulation - Bratley, Fox, et al. - 1987 |

230 | Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis - Fincke, Pohst - 1985 |

229 | Random number generators: Good ones are hard to find - Park, Miller - 1988 |

226 | A simple unpredictable pseudo-random number generator - Blum, Blum, et al. - 1986 |

209 | Various techniques used in connection with random digits - Neumann - 1951 |

149 | Pseudorandomness and Cryptographic Applications - Luby - 1996 |

122 | Quasi-Monte Carlo methods and pseudo-random - Niederreiter - 1978 |

114 | Random Number Generation and Monte Carlo methods - GENTLE - 2003 |

105 | E¢ cient and portable combined random number generators - L’Ecuyer - 1988 |

103 | S.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. Special Publication 800-22 Revision 1a - Rukhin, Soto, et al. - 2010 |

102 | Goodness-of-Fit Statistics for Discrete Multivariate Data - Reed, Cressie - 1988 |

95 | Uniform Random Numbers, Theory and Practice - Tezuka - 1995 |

85 |
A current view of random number generators
- Marsaglia
- 1985
(Show Context)
Citation Context ... these batteries with the following notable exceptions: All F2-linear generators fail the tests that look for linear relationships in the sequences of bits they produce, namely, the matrix-rank test (=-=Marsaglia 1985-=-) for huge binary matrices and the linear complexity tests (Erdmann 1992). The reason for this general failure is obvious: We know from their definitions that these generators produce bit sequences th... |

78 | Good parameters and implementations for combined multiple resursive random number generators - L’Ecuyer - 1999 |

75 | Maximally equidistributed combined Tausworthe generators - L’Ecuyer - 1996 |

71 | Random numbers fall mainly in the planes - Marsaglia - 1968 |

69 | Latin supercube sampling for very highdimensional simulations - Owen - 1998 |

65 | A More Portable Fortran Random Number Generator - Schrage - 1979 |

64 | A universal statistical test for random bit generators - Maurer - 1991 |

63 | An exhaustive analysis of multiplicative congruential random number generators with modulus 2 31 -1 - Fishman, Moore - 1986 |

61 | Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften, 290 - Conway, Sloane - 1988 |

61 | Approximating Integrals via Monte Carlo and Deterministic Methods - Evans, Swartz - 2000 |

60 | Distribution Theory for Tests Based on the Sample Distribution Function - Durbin - 1973 |

60 | A Review of Pseudorandom Number Generators - James - 1990 |

59 | 2002. “Recent advances in randomized quasi-Monte Carlo methods”. In Modeling Uncertainty: an Examination of Stochastic Theory - L’Ecuyer, Lemieux |

56 | Random number generators on vector supercomputers and other advanced architectures - Anderson - 1990 |

56 | E cient and Secure Pseudo-Random Number Generation - Vazirani, Vazirani - 1984 |

52 | Efficient and portable combined Tausworthe random number generators - Tezuka, L’Ecuyer - 1991 |

51 | Simulation Modeling and Analysis. Second edition - Law, Kelton - 1991 |

51 | Random numbers for simulation - L’Ecuyer - 1990 |

51 | Variance Reduction via Lattice Rules - L’Ecuyer, Lemieux - 2000 |

51 | An Object-Oriented Random-Number Package with Many Long Streams and Substreams - L’Ecuyer, Simard, et al. - 2002 |

51 | An efficient method for generating discrete random variables w ith general distributions - Walker - 1974 |

50 | Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure - L’Ecuyer - 1999 |

49 | A guide to simulation, Second edition - Bratley, Bennett, et al. - 1987 |

49 | Monte Carlo simulations: Hidden errors from “good” random number generators - Ferrenberg, Landau, et al. - 1992 |

49 | Tables of Maximally Equidistributed Combined LFSR Generators - L’Ecuyer - 1998 |

49 | Algebra and its Applications - Linear - 1994 |