## Abstract

Let J_{1}> J_{2}> ⋯ be the ranked jumps of a gamma process τ_{α} on the time interval [0 , α] , such that τα=∑k=1∞Jk . In this paper, we design an algorithm that samples from the random vector (J1,⋯,JN,∑k=N+1∞Jk) . Our algorithm provides an analog to the well-established inverse Lévy measure (ILM) algorithm by replacing the numerical inversion of exponential integral with an acceptance-rejection step. This research is motivated by the construction of Dirichlet process prior in Bayesian nonparametric statistics. The prior assigns weight to each atom according to a GEM distribution, and the simulation algorithm enables us to sample from the N largest random weights of the prior. Then we extend the simulation algorithm to a generalised gamma process. The simulation problem of inhomogeneous processes will also be considered. Numerical implementations are provided to illustrate the effectiveness of our algorithms.

Original language | English |
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Article number | 64 |

Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | Methodology and Computing in Applied Probability |

Volume | 25 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2023 |

## Keywords

- 60J25
- 62F15
- 62G05
- Exact simulation
- Gamma process
- Generalised gamma process
- Lévy process
- Poisson-Dirichlet distribution

## ASJC Scopus subject areas

- Statistics and Probability
- General Mathematics