A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 2<sup>31</sup>— 1

Fishman, George S.; Moore, Louis R.

doi:10.1080/01621459.1982.10477775

Cited by 46 publications

(14 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is evident that the testing allows critically evaluating the efficiency of three different random number algorithms from a spatial simulation perspective, even if it is not an exhaustive alternative to the wide range of existing uniform generator tests (Fishman and Moore, 1982;Fishman and Moore, 1985;Hopkins, 1983;Knuth, 1981;Marsaglia, 1972).…”

Section: Some Practical Resultsmentioning

confidence: 98%

Convergence of realization-based statistics to model-based statistics for the LU unconditional simulation algorithm: some numerical tests

Iaco

Palma

2002

Stochastic Environmental Research and Risk Assessment (SERRA)

View full text Add to dashboard Cite

In geostatistics, stochastic simulation is often used either as an improved interpolation algorithm or as a measure of the spatial uncertainty. Hence, it is crucial to assess how fast realization-based statistics converge towards model-based statistics (i.e. histogram, variogram) since in theory such a match is guaranteed only on average over a number of realizations. This can be strongly affected by the random number generator being used. Moreover, the usual assumption of independence among simulated realizations of a random process may be affected by the random number generator used. Simulation results, obtained by using three different random number generators implemented in Geostatistical Software Library (GSLib), are compared. Some practical aspects are pointed out and some suggestions are given to users of the unconditional LU simulation method.

show abstract

Section: Some Practical Resultsmentioning

confidence: 98%

Convergence of realization-based statistics to model-based statistics for the LU unconditional simulation algorithm: some numerical tests

Iaco

Palma

2002

Stochastic Environmental Research and Risk Assessment (SERRA)

View full text Add to dashboard Cite

show abstract

“…However, it should be noted that De Pagnutti (1988, 1990) and Durst (1989) indicate that certain partitions of a single sequence may lead to dependence between the two streams of deviates. In addition, Fishman and Moore (1982) suggest that DURAND, in particular, is not suitable for the production of 2-and 3-vectors. Crosscorrelation problems may also be avoided by using more sophisticated types of generator, such as the one described by Maclaren (1989).…”

Section: Fig 2 Sample Space ( and N 2 = 5 ) For Realisations Of (5)mentioning

confidence: 99%

Cross-correlation between simultaneously generated sequences of pseudo-random uniform deviates

Anderson

Titterington

1993

Stat Comput

View full text Add to dashboard Cite

Systematic patterns are revealed when sequences of pseudo-random uniform deviates are generated from multiplicative congruential generators. If the initial seeds, x0 and Y0, for two such sequences are related by Yo = (nl/nz)xo, where nl and n2 are relatively prime, positive integers, then an approximate argument suggests that the asymptotic correlation coefficient between corresponding members of the two sequences is (nln2) -1 . This unsettling phenomenon is discussed in the context of related, existing literature.

show abstract

“…The modulus m for the generator is 2 31 -1 = 2,147,483,647 and the multiplier is 397,204,094. (Fishman and Moore, 1982) This generates a sequence of m -1 distinct integers before repeating, in an order that appears random. To obtain real numbers between 0 and 1, the integer obtained in this way is divided by m.…”

Section: Uniform Distributionmentioning

confidence: 99%

SAPHIRE 8 Volume 2 - Technical Reference

Smith¹,

Wood²,

Galyean³

et al. 2011

View full text Add to dashboard Cite

A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 2³¹— 1

Cited by 46 publications

References 12 publications

Convergence of realization-based statistics to model-based statistics for the LU unconditional simulation algorithm: some numerical tests

Convergence of realization-based statistics to model-based statistics for the LU unconditional simulation algorithm: some numerical tests

Cross-correlation between simultaneously generated sequences of pseudo-random uniform deviates

SAPHIRE 8 Volume 2 - Technical Reference

Contact Info

Product

Resources

About

A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 231— 1

Cited by 46 publications

References 12 publications

Convergence of realization-based statistics to model-based statistics for the LU unconditional simulation algorithm: some numerical tests

Convergence of realization-based statistics to model-based statistics for the LU unconditional simulation algorithm: some numerical tests

Cross-correlation between simultaneously generated sequences of pseudo-random uniform deviates

SAPHIRE 8 Volume 2 - Technical Reference

Contact Info

Product

Resources

About

A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 2³¹— 1