Current Volume | Browse | Search | RSSHome | Instructions for Authors | JSS Style Guide | Editorial Board

Authors: George Marsaglia, Wai Wan Tsang
Title: [download]
(7448)
The Monty Python Method for Generating Gamma Variables
Reference: Vol. 3, Issue 3, Jan 1999
Submitted 1998-05-22, Accepted 1999-01-08
Type: Article
Abstract:

The Monty Python Method for generating random variables takes a decreasing density, cuts it into three pieces, then, using area-preserving transformations, folds it into a rectangle of area 1. A random point (x,y) from that rectangle is used to provide a variate from the given density, most of the time as itself or a linear function of x . The decreasing density is usually the right half of a symmetric density.

The Monty Python method has provided short and fast generators for normal, t and von Mises densities, requiring, on the average, from 1.5 to 1.8 uniform variables. In this article, we apply the method to non-symmetric densities, particularly the important gamma densities. We lose some of the speed and simplicity of the symmetric densities, but still get a method for γα variates that is simple and fast enough to provide beta variates in the form γa/(γab). We use an average of less than 1.7 uniform variates to produce a gamma variate whenever α ≥ 1 . Implementation is simpler and from three to five times as fast as a recent method reputed to be the best for changing α's.

Paper: [download]
(7448)
The Monty Python Method for Generating Gamma Variables
(application/pdf, 74 KB)
Resources: BibTeX | OAI
Creative Commons License
This work is licensed under the licenses
Paper: Creative Commons Attribution 3.0 Unported License
Code: GNU General Public License (at least one of version 2 or version 3)
Current Volume | Browse | Search | RSSHome | Instructions for Authors | JSS Style Guide | Editorial Board