Study On Random Number Generator And Random Sampling In Monte Carlo Method

The Monte Carlo method (MCM) differs from the assurance numerical method, it is a numerical method of solving mathematical problems by the simulation of random variables. MCM, also be called statistical experimental method, is a method of approximate solving problems with a series of random numbers. MCM and its program are simple, convergence and convergent speed have nothing to do with the dimension of problem. So MCM has the special advantage in resolving the high dimension problems. Because of its wide application, MCM has become a popular topic today.In this paper, the author introduces the development of MCM, analyzes the principle of MCM and elaborates the random number generator and random sampling. The paper takes MCM as the basic research object; its aim is improving MCM from the theory. By analyzing, researching and improving kinds of random number generators, the author consummates a series of foundational theories of MCM and applies combination generator and bitewise exlusive-or to Mersenne Twister generator. By improvement and combination, the author successfully carries out the improvement of Mersenne Twister generator.In the part of random sampling, the author mainly studies the method of random sampling. To take bivariate related distribution for example, the author discusses the sampling methods of weibull distribution and beta distribution. Firstly, based on the theory of logarithm distribution sampling, the minutely sampling method of bivariate weibull distribution is given. Secondly, the author applies the mixture approach to the sampling of bivariate beta distribution, further more, the validity is tested by experiment.The last part concludes the research in this paper and presents the future research on Monte Carlo method.