A New Method of Generating Gaussian Random Variables by Computer

摘要

Many scientific computations require the generation by a computer of a large number of seemingly random numbers with a multidimensional normal (gaussian) probability density function. The note describes a variation of the central limit theorem approach, in which N uniform random variables (r.v.) are transformed into N approximately normal r.v. by a Hadamard transformation. The plan of the paper is to first describe the ideal uniform and normal multivariate densities, second to describe the Hadamard transformation used, third to derive the properties of the transformed variables, and fourth, to consider the properties of the transformed variables after they have been subjected to random sign changes.