George Forsythe's last paper

TL;DR

This paper discusses von Neumann's sampling method for exponential distributions, Forsythe's generalization for other distributions, and introduces an efficient algorithm for generating pseudo-random normal variables, with historical context.

Contribution

It presents a novel, efficient algorithm for sampling from the normal distribution based on Forsythe's generalization of von Neumann's method.

Findings

Efficient algorithm for normal distribution sampling

Extension of von Neumann's exponential sampling method

Historical overview of sampling techniques

Abstract

We describe von Neumann's elegant idea for sampling from the exponential distribution, Forsythe's generalization for sampling from a probability distribution whose density has the form exp(-G(x)), where G(x) is easy to compute (e.g. a polynomial), and my refinement of these ideas to give an efficient algorithm for generating pseudo-random numbers with a normal distribution. Later developments are also mentioned.