Generation and Testing of Pseudo-Random Numbers

摘要

The problem of artificially generating numbers which can be considered random is one of great importance in Monte Carlo simulation studies. The paper reviews some of the literature which has been produced on the subject of generating pseudo-random numbers. A new random number generator is proposed. The proposed method of random generation is a slight generalization of the mixed congruential method. Numbers are generated according to the recursion relation X sub (i+1) = a(X sub i) + b + Ci (mod m). Using number theoretic techniques, the author investigated the cycle lengths obtainable by this generator and showed that the parameters may be chosen so that the period of the new procedure is greater than that of the usual mixed congruential generator. The report also discusses the statistical properties of sequences generated via the new technique and shows they compare favorably with those of other standard techniques. (Author)