Distribution Properties of Multiply-with-Carry Random Number Generators

We study the multiply-with-carry family of generators proposed by Marsaglia as a generalization of previous add-with-carry families. We define for them an infinite state space and focus our attention on the (finite) subset of recurrent states. This subset will, in turn, split into possibly several s...

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Bibliographic Details
Published in:Mathematics of computation 1997-04, Vol.66 (218), p.591-607
Main Authors: Couture, Raymond, L'Ecuyer, Pierre
Format: Article
Language:English
Subjects:
Benzodiazepines
Cardinality
Coefficients
Discriminants
Exact sciences and technology
Integers
Mathematical lattices
Mathematical vectors
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical simulation
Random numbers
Sciences and techniques of general use
Uniformity
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Summary:We study the multiply-with-carry family of generators proposed by Marsaglia as a generalization of previous add-with-carry families. We define for them an infinite state space and focus our attention on the (finite) subset of recurrent states. This subset will, in turn, split into possibly several subgenerators. We discuss the uniformity of the d-dimensional distribution of the output of these subgenerators over their full period. In order to improve this uniformity for higher dimensions, we propose a method for finding good parameters in terms of the spectral test. Our results are stated in a general context and are applied to a related complementary multiply-with-carry family of generators.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-97-00827-2