George Marsaglia

A Convenient Method for Generating Normal Variables

A normal random variable X may be generated in terms of uniform random variables

Evaluating Kolmogorov's Distribution

u_1

Ratios of Normal Variables and Ratios of Sums of Uniform Variables

,

Uniform Random Number Generators

u_2

A fast procedure for generating normal random variables

, in the following simple way: 86 percent of the time, put

The Structure of Linear Congruential Sequences

X = 2(u_1 + u_2 + u_3 - 1.5)

Ferrokinetics: a biologic model for plasma iron exchange in man

,11 percent of the time, put

A simple method for generating gamma variables

X = 1.5(u_1 + u_2 - 1)

Blood Ferrokinetics in Normal Man

, and the remaining 3 percent of the time, use a more complicated procedure so that the resulting mixture is correct. This method takes only half again as long as the very fastest methods, is much simpler, and requires very little storage space.

A Fast, Easily Implemented Method for Sampling from Decreasing or Symmetric Unimodal Density Functions

Kolmogorovs goodness-of-fit measure, Dn , for a sample CDF has consistently been set aside for methods such as the D+n or D-n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of Dn . As far as we know, no easy way to compute that distribution has ever been provided in the 70+ years since Kolmogorovs fundamental paper. We provide one here, a C procedure that provides Pr(Dn