Chapter 20 - Evaluating pseudo-random number generators

Abstract

The ability to construct a sequence of random numbers is crucial to a variety of computing tasks, from designing arcade games, to generating fractals, to using Monte Carlo techniques. The graphing capabilities of Mathematica (a software package for solving a variety of mathematical problems in algebra, graphics, statistics and calculus) provide a quick, visual route to evaluating some of the characteristics of pseudorandom number generators. This chapter is a tutorial on some simple statistical techniques for testing the output of such generators. Th chapter discusses random numbers on the interval [0, 1] and algorithms that approximate a sequence of statistically independent random numbers distributed uniformly over this interval. Tests of the uniformity of the distribution of a sequence of random numbers are examined. Then several techniques for probing how independent any element of a random number sequence is from the preceding and following elements of that sequence are looked at. The output from several random number generators is explored including that from congruential generators with integer parameters, a generator with an irrational modulus, the RND function in BASIC on a Commodore 64, and the Random[] function in “Mathematica.”