Pseudorandom Number Generators

Abstract

Sequences of pseudorandom numbers are needed for applications of stochastic simulation. Usually they are generated in the computer by a deterministic algorithm which produces a sequence of standard pseudorandom numbers, i.e. a sequence of numbers which “behave” as a realization of a sequence of independent identically distributed random variables having a uniform distribution on the unit interval. In a second step these standard pseudorandom numbers are often transformed in order to fit a given (non-uniform) distribution. For example, Devroy’s book [4] is devoted to this problem. This paper deals only with algorithms producing sequences of standard pseudorandom numbers. Such algorithms are called pseudorandom number generators. Many users of simulation techniques do not think about the pseudorandom number generators implemented in their computers and use the standard software at hand. This habitude is dangerous since the “stochastic quality” of the pseudorandom number sequences is fundamental for the results of stochastic simulation and many pseudorandom number generators in use have serious defects (see e.g. [2], [6], p. 10, and [26], p. 18). The present paper gives a survey on methods for generating deterministic sequences of real numbers which can be used as standard pseudorandom number sequences. Special emphasis is given to generation methods which have been studied by the author’s research group at Darmstadt Technical University.