Journal of Applied Science and Engineering

Published by Tamkang University Press


Impact Factor



Ching-Jing Kung1 and Hui-Chin Tang This email address is being protected from spambots. You need JavaScript enabled to view it.2

1Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung, Taiwan 833, R.O.C.
2Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan 807, R.O.C.


Received: April 9, 2007
Accepted: October 4, 2008
Publication Date: September 1, 2009

Download Citation: ||  


The criterion issue of spectral test in a linear congruential random number generator is considered. In this paper, we report on four variants of the normalized spectral test, measured both relative to either a theoretical or exact lower bound and aggregative to either a worst-case or average-case method. Computer exhaustive searches are conducted to evaluate and compare their statistical behaviors. It is shown that the spectral test with both theoretical lower bound and average-case aggregation criterion outperforms.

Keywords: Linear Congruential Generator, Spectral Test, Random Number


  1. [1] Lehmer, D. H., Proceedings 2nd Symposium on Largescale Digital Calculating Machinery,Cambridge, Harvard University Press, pp. 141146 (1951).
  2. [2] Fishman, G. S., Monte Carlo: Concepts, Algorithms, and Applications, Springer Series in Operations Research, Springer-Verlag, New York (1996).
  3. [3] Knuth, D. E., The Art of Computer Programming, Semi-numerical Algorithms, 2: 3rd edition, AddisonWesley, Reading MA (1997).
  4. [4] Niederreiter, H., Random number generation and quasi-Monte Carlo methods, SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 63, SIAM, Philadelphia (1992).
  5. [5] Fishman, G. S. and Moore III, L. R., “An Exhaustive Analysis of Multiplicative Congruential Random Number Generators with Modulus 231  1,” SIAM Journal on Scientific and Statistical Computing, Vol. 7, pp. 2445 (1986).
  6. [6] L'Ecuyer, P., Blouin, F. and Couture, R., “A Search for Good Multiple Recursive Random Number Generators,” ACM Transactions on Modeling and Computer Simulation, Vol. 3, pp. 8798 (1993).
  7. [7] Tang, H. C., “A Statistical Analysis of the Screening Measure of Multiple Recursive Random Number Generators of Orders One and Two,” Journal of Statistical Computation and Simulation, Vol. 71, pp. 345356 (2001).
  8. [8] Tang, H. C., “An Analysis of Linear Congruential Random Number Generators when Multiplier Restrictions Exist,” European Journal of Operational Research, Vol. 182, pp. 820828 (2007).
  9. [9] Coveyou, R. R. and MacPherson, R. D., “Fourier Analysis of Uniform Random Number Generators,” Journal of the ACM, Vol. 14, pp. 100119 (1967).
  10. [10] Fincke, U. and Pohst, M., “Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis,” Mathematics of Computation, Vol. 44, pp. 463471 (1985).
  11. [11] Cassels, J. W. S., An Introduction to the Geometry of Number, Springer-Verlag, New York (1959).
  12. [12] L'Ecuyer, P., “Testing Random Number Generators,” Proceeding of the 1992 Winter Simulation Conference, pp. 305313 (1992).