Generation of Random Numbers

Abstract

Monte Carlo simulation is a core technology in computational statistics. Monte Carlo methods require numbers that appear to be realizations of random variables. Obtaining these numbers is the process called “generation of random numbers”. Our objective is usually not to generate a truly random sample. Deep understanding of the generation process and strict reproducibility of any application involving the “random” numbers is more important. We often emphasize this perspective by the word “pseudorandom”, although almost anytime we use a phrase similar to “generation of random numbers”, we refer to “pseudorandom” numbers. The quality of a process for random number generation is measured by the extent to which the sample generated appears, from every imaginable perspective, to be a random sample (that is, i.i.d.) from a given probability distribution. Some methods of random number generation are better than others.