%0 Generic %1 mpw07 %A McCullagh, Peter %A Pitman, Jim %A Winkel, Matthias %D 2007 %K Poisson_Dirichlet_distribution beta_splitting fragmentation_coalescence %T Gibbs fragmentation trees %U http://front.math.ucdavis.edu/0704.0945 %X We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs type fragmentation tree with Aldous's beta-splitting model, which has an extended parameter range $\beta>-2$ with respect to the $Beta(\beta+1,\beta+1)$ probability distributions on which it is based. In the multifurcating case, we show that Gibbs fragmentation trees are associated with the two-parameter Poisson-Dirichlet models for exchangeable random partitions of $\bN$, with an extended parameter range $0łe\alpha1$, $þeta-2\alpha$ and $\alpha<0$, $þeta=-m\alpha$, $mın\bN$.

@misc{mpw07, abstract = {We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs type fragmentation tree with Aldous's beta-splitting model, which has an extended parameter range $\beta>-2$ with respect to the ${\rm Beta}(\beta+1,\beta+1)$ probability distributions on which it is based. In the multifurcating case, we show that Gibbs fragmentation trees are associated with the two-parameter Poisson-Dirichlet models for exchangeable random partitions of $\bN$, with an extended parameter range $0\le\alpha\le 1$, $\theta\ge -2\alpha$ and $\alpha<0$, $\theta=-m\alpha$, $m\in\bN$.}, added-at = {2008-11-17T06:19:46.000+0100}, arxiv = {0704.0945}, author = {McCullagh, Peter and Pitman, Jim and Winkel, Matthias}, biburl = {https://www.bibsonomy.org/bibtex/2fed2edc3fb27d7b3a9a273d1266e2406/peter.ralph}, interhash = {17c7372c1b612fc6c512b6e8e9240c9b}, intrahash = {fed2edc3fb27d7b3a9a273d1266e2406}, keywords = {Poisson_Dirichlet_distribution beta_splitting fragmentation_coalescence}, timestamp = {2008-11-17T06:19:46.000+0100}, title = {Gibbs fragmentation trees}, url = {http://front.math.ucdavis.edu/0704.0945}, year = 2007 }