Moderate deviations for Poisson--Dirichlet distribution
| dc.creator | Feng, Shui | |
| dc.creator | Gao, Fuqing | |
| dc.date | 2007-10-18 | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:19Z | |
| dc.date.available | 2026-07-07T10:17:19Z | |
| dc.description | The Poisson--Dirichlet distribution arises in many different areas. The parameter $θ$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $θ$ approaching infinity is practically motivated and has led to new, interesting mathematical structures. Laws of large numbers, fluctuation theorems and large-deviation results have been established. In this paper, moderate-deviation principles are established for the Poisson--Dirichlet distribution, the GEM distribution, the homozygosity, and the Dirichlet process when the parameter $θ$ approaches infinity. These results, combined with earlier work, not only provide a relatively complete picture of the asymptotic behavior of the Poisson--Dirichlet distribution for large $θ$, but also lead to a better understanding of the large deviation problem associated with the scaled homozygosity. They also reveal some new structures that are not observed in existing large-deviation results. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AAP501 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0710.3419 | |
| dc.identifier | http://arxiv.org/abs/0710.3419 | |
| dc.identifier | Annals of Applied Probability 2008, Vol. 18, No. 5, 1794-1824 | |
| dc.identifier | doi:10.1214/07-AAP501 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173811 | |
| dc.subject | Probability | |
| dc.subject | 60F10 (Primary) 92D10 (Secondary) | |
| dc.title | Moderate deviations for Poisson--Dirichlet distribution | |
| dc.type | text |