![]() ![]() Niederreiter, Figures of merit for digital multistep pseudorandom numbers, Math. Weilbächer, The exact determination of rectangle discrepancy for linear congruential pseudorandom numbers, Math. Grothe, The lattice structure of pseudo-random vectors generated by matrix generators, J. Grothe, Calculation of Minkowski-reduced lattice bases, Computing 35(1985)269–276. Afflerbach, The sub-lattice structure of linear congruential random number generators, Manuscripta Math. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. ![]()
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