A Modified PS Method And Its Application In Generating Correlated Normal-distributed Random Numbers

Normal distribution plays an important part in theory of probability statistic and in application, so people are interested in the question that is how to generate normally distributed data. Many methods have been proposed for generating independent normal-distributed data, however there is only one method based on Cholesky decomposition for generating correlated normal-distributed data. This paper studies the generation of correlated normally distribution number and proposes a new method for generating correlated normal-distributed number.Chapter 2 summarizes methods for generating and testing uniform distribution number. A new combined generator is proposed which is constituted of PMMLCG belonged to LCG and MT belonged to modulo 2 generator. Compared results obtained from various statistic tests with MT, the new combined generator is of more superior statistical characteristics. It keeps good non-continuity of MT, at the same time good uniformity and independence will be achieved. These results indicate that the new combined generator is propitious to improve efficiency of emulator, and can satisfy the condition of stochastic simulation.Chapter 3 summarizes and analyzes all kinds of methods for generating independent normal-distributed number. More effective measure for generating independent normally distribution number can be obtained by comparing histogram of each method. This lays a good foundation for generating correlated normal-distributed sequence with good properties.Chapter 4 analyzes classical method for generating correlated normal-distributed number firstly, then obtains a new generated method for correlated normal-distributed by improving PS method. Theoretical proof and numerical experiment are shown. Compared with PS method, new algorithm can generate random number with given expectation, variance and non-negative correlation matrix arbitrarily. Compared with classical algorithm, new algorithm avoids Cholesky decomposition. The obtained data error is much less. So the new method is practical.