Asymptotic statistical analysis of pseudo random numbers

Computer simulation is a widely used powerful tool for solving real world problems. Pseudo random number plays an important role in computer simulation and modeling. It acts like the real random number. We discuss the asymptotic properties of pseudo random numbers as the period size of a random number generator approaches to infinity. Our results show that the pseudo random number converges to the true random number in mean, variance, skewness, kurtosis, moment, and distribution.