Asymptotical behavior of linear congruential generators

Gerlovina V. and Nekrutkin V.

Monte Carlo Methods and Applications, 2005, vol. 11, issue 2, 135-162

Abstract: The paper is devoted to asymptotical analysis of Linear Congruential Generators (LCGs) with increasing moduli and multiplicators. The study is performed within the scope of a stochastic model of LCGs, the technique of weak convergence of distributions is used. It is proved, f.e., that the classical spectral test can be described in terms of a special probability metric inducing a topology of weak convergence. A number of theoretical examples of LCGs with good and bad asymptotical equidistribution properties is presented.

Keywords: Random number generation; linear congruential generators; spectral test; weak convergence of distributions; probability metrics. (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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DOI: 10.1515/156939605777585971

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