# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Generating random variates from a bicompositional Dirichlet distribution

(2009)
Abstract
A composition is a vector of positive components summing to a constant. The sample space of a composition is the simplex and the sample space of two compositions, a bicomposition, is a Cartesian product of two simplices. We present a way of generating random variates from a bicompositional Dirichlet distribution defined on the Cartesian product of two simplices using the rejection method. We derive a general solution for finding a dominating density function and a rejection constant, and also compare this solution to using a uniform dominating density function. Finally some examples of generated bicompositional random variates, with varying number of components.
author
organization
publishing date
type
Working Paper
publication status
published
subject
keywords
composition, Dirichlet distribution, bicompositional Dirichlet distribution, random variate generation, rejection method, simplex
pages
10 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
835138bf-2ca3-40b6-8efc-10397897f4ae (old id 1580934)
2010-03-31 13:21:53
date last changed
2016-09-01 10:34:46
```@misc{835138bf-2ca3-40b6-8efc-10397897f4ae,
abstract     = {A composition is a vector of positive components summing to a constant. The sample space of a composition is the simplex and the sample space of two compositions, a bicomposition, is a Cartesian product of two simplices. We present a way of generating random variates from a bicompositional Dirichlet distribution defined on the Cartesian product of two simplices using the rejection method. We derive a general solution for finding a dominating density function and a rejection constant, and also compare this solution to using a uniform dominating density function. Finally some examples of generated bicompositional random variates, with varying number of components.},
author       = {Bergman, Jakob},
keyword      = {composition,Dirichlet distribution,bicompositional Dirichlet distribution,random variate generation,rejection method,simplex},
language     = {eng},
pages        = {10},
publisher    = {ARRAY(0x99461b8)},
title        = {Generating random variates from a bicompositional Dirichlet distribution},
year         = {2009},
}

```