文章基本信息

标题：The Monty Python Method for Generating Gamma Variables
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作者：George Marsaglia ; Wai Wan Tsang
期刊名称：Journal of Statistical Software
印刷版ISSN：1548-7660
电子版ISSN：1548-7660
出版年度：1999
卷号：3
期号：1
页码：1-8
语种：English
出版社：University of California, Los Angeles
摘要：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 γ α variates that is simple and fast enough to provide beta variates in the form γ a /(γ a +γ b ). 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.