Pseudo‐Random Number Generator

Abstract One of the most frequently called functions on a scientific computer is the random number generator. Random numbers are required for many purposes. A major use is in simulation. Large quantities of random numbers are needed to generate the random samples from distributions (theoretical and/or empirical) that are the basis of any stochastic simulation. Another use for random numbers is the Monte Carlo evaluation of multivariate integrals. Ideally, what is required in a simulation is a stream of independently and uniformly distributed random variables taking values between 0 and 1 [i.e. a random sample from the uniform distribution on (0,1)]. At best this ideal can only be realized approximately.