{"paper":{"title":"Generalised Poisson-Dirichlet Distributions and the Negative Binomial Point Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross A. Maller, Yuguang F. Ipsen","submitted_at":"2016-11-30T02:56:34Z","abstract_excerpt":"When $S=(S_t)_{t\\ge 0}$ is an $\\alpha$-stable subordinator, the sequence of ordered jumps of $S$, up till time $1$, omitting the $r$ largest of them, and taken as proportions of their sum $^{(r)}S_t$, defines a 2-parameter distribution on the infinite dimensional simplex, $\\nabla_{\\infty}$, which we call the $\\mathrm{PD}_\\alpha^{(r)}$ distribution. When $r=0$ it reduces to the $\\mathrm{PD}_\\alpha$ distribution introduced by Kingman in 1975. We observe a serendipitous connection between $\\mathrm{PD}_\\alpha^{(r)}$ and the negative binomial point process of Gregoire (1984), which we exploit to an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09980","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}