RANDOM NUMBER GENERATORS WITH LONG-PERIOD AND SOUND STATISTICAL PROPERTIES

To generate random numbers (RNs) of long period for large scale simula tion studies, the usual multiplicative congruential RN generator can b e extended to higher order. A multiplicative congruential RN generator of order two with prime modulus 2(31) - 1 attains a maximal period of (2(31) - 1)(2) - 1 when the two multipliers (a(1), a(2)) are chosen p roperly. By fixing a(2) at -742938285, a multiplier recommended for fi rst-order generator in a previous study, approximately 1.1 billion cho ices of a(1) which are able to produce RNs of maximal period are inves tigated in this paper. Via the spectral test of dimensions up to six, 14 sets of multipliers (a(1), a(2)) exhibit good lattice structure in a global sense with a spectral measure greater than 0.84. Ten of these multipliers also pass a battery of tests for detecting departures fro m local randomness and homogeneity. Furthermore, the execution time is promising on 32-bit machines. In sum, the second-order generators dev ised in this paper possess the properties of long period, randomness, homogeneity, repeatability, portability, and efficiency, required for practical use. (C) 1998 Elsevier Science Ltd. All rights reserved.