The Monty Python Method for Generating Gamma Variables

George Marsaglia and Wai Wan Tsang

Journal of Statistical Software, 1999, vol. 003, issue i03

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/(γa+γb). 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.

Date: 1999-01-08
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Persistent link: https://EconPapers.repec.org/RePEc:jss:jstsof:v:003:i03

DOI: 10.18637/jss.v003.i03

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