{"paper":{"title":"Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross A. Maller, Yuguang Fan Ipsen","submitted_at":"2018-02-07T22:03:47Z","abstract_excerpt":"The Poisson-Kingman distributions, $\\mathrm{PK}(\\rho)$, on the infinite simplex, can be constructed from a Poisson point process having intensity density $\\rho$ or by taking the ranked jumps up till a specified time of a subordinator with L\\'evy density $\\rho$, as proportions of the subordinator. As a natural extension, we replace the Poisson point process with a negative binomial point process having parameter $r>0$ and L\\'evy density $\\rho$, thereby defining a new class $\\mathrm{PK}^{(r)}(\\rho)$ of distributions on the infinite simplex. The new class contains the two-parameter generalisation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02655","kind":"arxiv","version":1},"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"}