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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.
Key Words: Random number generation,; linear congruential generators,; spectral test,; weak convergence of distributions,; probability metrics.
Published Online: --
Published in Print: 2005-06-01
Copyright 2005, Walter de Gruyter
