## 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.

number of components, are presented.

Original language | English |
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Pages (from-to) | 797-805 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 82 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2012 |

## Subject classification (UKÄ)

- Probability Theory and Statistics

## Keywords

- Bicompositional Dirichlet distribution
- Composition
- Dirichlet distribution
- Random variate generation
- Rejection method
- Simplex