The Generation of Pseudo-Random Numbers on a Decimal Calculator
Journal of the ACM (JACM)
Serial Correlation in the Generation of Pseudo-Random Numbers
Journal of the ACM (JACM)
A New Pseudo-Random Number Generator
Journal of the ACM (JACM)
Mixed Congruential Random Number Generators for Decimal Machines
Journal of the ACM (JACM)
Mixed Congruential Random Number Generators for Binary Machines
Journal of the ACM (JACM)
Uniform Random Number Generators
Journal of the ACM (JACM)
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
Coding the Lehmer pseudo-random number generator
Communications of the ACM
One-line random number generators and their use in combinations
Communications of the ACM
The GPSS/360 random number generator
Proceedings of the second conference on Applications of simulations
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Pseudo-random number generators of the power residue (sometimes called congruential or multiplicative) type are discussed and results of statistical tests performed on specific examples of this type are presented. Tests were patterned after the methods of MacLaren and Marsaglia (M&M).The main result presented is the discovery of several power residue generators which performed well in these tests. This is important because, of all the generators using standard methods (including power residue) that were tested by M&M, none gave satisfactory results.The overall results here provide further evidence for their conclusion that the types of tests usually encountered in the literature do not provide an adequate index of the behavior of n-tuples of consecutively generated numbers. In any Monte Carlo or simulation problem where n supposedly independent random numbers are required at each step, this behavior is likely to be important.Finally, since the tests presented here differ in certain details from those of M&M, some of their generators were retested as a check. A cross-check shows that results are compatible; in particular, if a generator failed one of their tests badly, it also failed the present author's corresponding test badly.