Abstract
Random number generators of the mixed congruential type have recently been proposed. They appear to have some advantages over those of the multiplicative type, except that their statistical behavior is unsatisfactory in some cases. It is shown theoretically that a certain class of these mixed generators should be expected to fail statistical tests for randomness. Extensive testing confirms this hypothesis and makes possible a more precise definition of the unsatisfactory class. It is concluded that the advantages of mixed generators can be realized only in special circumstances. On machines with relatively short multiplication times the multiplicative generators are to be preferred.
- 1 ALLARD, J. L., DOBELL, A. R., AND HULL, W.E. Mixed congruential random number generators for decimal machines. J. ACM 10 (1963), 131-141. Google Scholar
- 2 Covvov, R. R. Serial correlation in the generation of pseudo-random numbers. J. ACM 7 (1960), 72-74. Google Scholar
- 3 GOOD, 1. J. The serial test for sampling numbers and other tests for randomness. Proc. Camb. Phil. Soc. 49 (1953), 276-284.Google Scholar
- 4 GOOD, I .J . On the serial test for random sequences. Ann. Math. Stat. 28 (1957), 262-264.Google Scholar
- 5 GREENBRGER, MARTXN. Notes on a new pseudo-random number generator. J. ACM 8 (1961), 163-167. Google Scholar
- 6 GREENBEIGER, MARTIN. An a priori determination of serial correlation in computer generated random numbers. Math. Comp. 15 (1961), 383-389. See also: corrigenda, Math. Comp. 16 (1962), 126 and 406.Google Scholar
- 7 HULL, W. E., AND DO,ELL, A.R. Random number generators. SIAM Rev. 4 (1962), 230-254.Google Scholar
- 8 KUEHN, HEIDI G. A 48-bit pseudo-random number generator. Comm. ACM 4 (1961), 350-352. Google Scholar
- 9 PEACH, PAUL. Bias in pseudo-random numbers. J. Am. Stat. Assoc. 56 (1961), 610-618.Google Scholar
- 10 ROTENBERG, A. A new pseudo-random number generator. J. ACM 7 (1960), 75-77. Google Scholar
- 11 THOMSON, W. E. A modified congruence method of generating pseudo-random numbers. Comput. J. 1 (1958), 83 and 86.Google Scholar
Index Terms
- Mixed Congruential Random Number Generators for Binary Machines
Recommendations
A Uniform Random Number Generator Based on the Combination of Two Congruential Generators
A method of generating pseudo-random uniform numbers based on the combination of two congruential generators is described. It retains two of the desirable features of congruential generators, namely, the long cycle and the case of implementation on a ...
Bit-Wise Behavior of Random Number Generators
In 1985, G. Marsaglia proposed the m-tuple test, a runs test on bits, as a test of nonrandomness of a sequence of pseudorandom integers. We try this test on the outputs from a large set of pseudorandom number generators and discuss the behavior of the ...
Resolution-stationary random number generators
Besides speed and period length, the quality of uniform random number generators (RNGs) is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F"2-...
Comments