File Download
There are no files associated with this item.
Supplementary

Citations:
 Scopus: 0
 Appears in Collections:
Article: The Monty Python method for generating gamma variables
Title  The Monty Python method for generating gamma variables 

Authors  
Issue Date  1998 
Publisher  University of California at Los Angeles, Department of Statistics. The Journal's web site is located at http://www.jstatsoft.org/ 
Citation  Journal Of Statistical Software, 1998, v. 3, p. 18 How to Cite? 
Abstract  The Monty Python Method for generating random variables takes a decreasing density, cuts it into three pieces, then, using areapreserving 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 x 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 nonsymmetric 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. 
Persistent Identifier  http://hdl.handle.net/10722/89055 
ISSN  2015 Impact Factor: 2.379 2015 SCImago Journal Rankings: 2.970 
References 
DC Field  Value  Language 

dc.contributor.author  Marsaglia, G  en_HK 
dc.contributor.author  Tsang, WW  en_HK 
dc.date.accessioned  20100906T09:51:49Z   
dc.date.available  20100906T09:51:49Z   
dc.date.issued  1998  en_HK 
dc.identifier.citation  Journal Of Statistical Software, 1998, v. 3, p. 18  en_HK 
dc.identifier.issn  15487660  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/89055   
dc.description.abstract  The Monty Python Method for generating random variables takes a decreasing density, cuts it into three pieces, then, using areapreserving 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 x 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 nonsymmetric 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.  en_HK 
dc.language  eng  en_HK 
dc.publisher  University of California at Los Angeles, Department of Statistics. The Journal's web site is located at http://www.jstatsoft.org/  en_HK 
dc.relation.ispartof  Journal of Statistical Software  en_HK 
dc.title  The Monty Python method for generating gamma variables  en_HK 
dc.type  Article  en_HK 
dc.identifier.email  Tsang, WW:tsang@cs.hku.hk  en_HK 
dc.identifier.authority  Tsang, WW=rp00179  en_HK 
dc.description.nature  link_to_subscribed_fulltext   
dc.identifier.scopus  eid_2s2.00039646690  en_HK 
dc.identifier.hkuros  40692  en_HK 
dc.identifier.hkuros  51499   
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.00039646690&selection=ref&src=s&origin=recordpage  en_HK 
dc.identifier.volume  3  en_HK 
dc.identifier.spage  1  en_HK 
dc.identifier.epage  8  en_HK 
dc.identifier.scopusauthorid  Marsaglia, G=6603739473  en_HK 
dc.identifier.scopusauthorid  Tsang, WW=7201558521  en_HK 