Generating random variates from a bicompositional Dirichlet distribution

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, are presented.

Keywords:

• bicompositional Dirichlet distribution
• composition
• Dirichlet distribution
• random variate generation
• rejection method
• simplex

AMS Subject Classification :

• 65C10
• 65C60
• 62H99

Acknowledgements

The author wishes to thank Professor Jan Lanke for a suggestion that improved the article and also an anonymous reviewer and the associate editor for their valuable comments.