An exhaustive analysis of prime modulus multiplicative congruential random number generators with modulus smaller than 215

Journal of Statistical Computation and Simulation

Volumn 54, Issue 1-3, 1996, Pages 29-35

  Kao, Chiang ^a   Wong, J Y ^b  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b KUNG SHAN INSTITUTE OF TECHNOLOGY   (Taiwan)

Author keywords

Random number; Spectral test

Indexed keywords

EID: 0030485739     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659608811717     Document Type: Article

References (21)

1. Cassels, J. W. S. (1959) An introduction to the geometry of numbers, Springer-Verlag, NY.
2. Chang, P. L., Hwang, S. N. and Kao Chiang, (1993) Some good multipliers for random number generators for 16-bit microcomputers. Computers & Ops. Res. 21, pp. 199-204.
3. Coveyou, R. R. and MacPherson, R. D. (1967) Fourier analysis of uniform random number generators. J. of the ACM, 14, pp 100-119.
4. Fishman, G. S. (1978) Principles of discrete event simulation. Wiley, NY.
5. β: An exhaustive analysis for β = 32 and a partial analysis for β = 48. Math. Comp., 54, pp. 331-344
6. 31 - 1. SIAM J. on Sci. Stat. Compu., 7, pp. 24-45.
7. Hardy, G. H. and Wright, E. M. (1960) The theory of numbers. 4th ed. Clarendon Press, Oxford.
8. Kobayashi, H. (1978) Modeling and analysis: An introduction to system performance evaluation methodology. Addision-Wesley, Reading, Mass.
9. Kao, C. (1989) A random number generator for microcomputers. J. of the Opl. Res. Soc., 40, pp. 687-691.
10. Knuth, D. E., (1981) The art of computer programming, 2: Semi-numerical algorithms. 2nd ed. Addison-Wesley, Reading, Mass.
11. L'Ecuyer, P. (1988) Efficient and portable combined random number generators. Commun. of the ACM, 31, pp. 742-774.
12. L'Ecuyer, P. and Côté, S. (1991) Implementing a random number package with splitting facilities. ACM Trans. on Math. Soft., 17, pp. 98-111.
13. MacLaren, M. D. and Marsaglia, G. (1965) Uniform random number generators. J. of the ACM. 12, pp. 83-89
14. Marsaglia, G. (1968) Random numbers fall mainly in the planes. Proc of the Nat. Acad. Sci., 60, pp. 25-28.
15. Marsaglia, G., (1972) The structure of linear congruential sequences, in Applications of number theory to numerical analysis, edited by S. K. Zeremba. Academic Press, NY, pp. 249-285.
16. Marse, K. and Roberts, S. D. (1983) Implementing a portable FORTRAN uniform (0 1) generator. Simulation, 41, pp 135-139
17. Modianos, D. T., Scott, R. C. and Cornwell, L. W. (1984) Random number generation on microcomputers. Interfaces 14, pp. 81-87.
18. Nance, R. E. and Overstreet, C. Jr. (1975) Implementation of Fortran random number generators on computers with one's complement arithmetic. J. Statist. Comput. Simul., 4, pp. 235-243.
19. Schrage, L. (1979) A more portable Fortran random number generators. ACM Trans. on Math. Soft., 5, pp. 132-138.
20. Wichmann, B. A. and Hill, I. D. (1982) An efficient and portable pseudo-random number generator. Appl. Statist., 31, pp. 188-190.
21. Zeisel, H. (1986) Remark on AS 183: An efficient and portable pseudo-random number generator. Appl. Statist., 35, pp. 89.