COMPUTER GENERATION AND TESTING OF RANDOM NUMBERS

The need for random numbers, particularly in regard to Monte Carlo applications, andd the multiplicative mixed congruential methods most commonly used to obtain random numbers are discussed. Both methods involve somewhat arbitrary parameters. Proofs for the lengths of period for both methods and a derivation of an expression for the serial correlation coefficient in terms of the parameters of the mixed congruential method are presented. The results of a series of statistical tests made to determine satisfactory parameters are listed. The length of run test was found to be the most powerful test in that it rejected the largest number of parameters as unsatisfactory. The multiplicative method (for the parameters tested) was superior to the mixed congruential method. The multiplicative method multiplier lambda = 2/sup 18/ + 3 satisfactorily passed all tests and has a short multiply time. (auth)