{"paper":{"title":"Stick-breaking PG(\\alpha,\\zeta)-Generalized Gamma Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lancelot F. James","submitted_at":"2013-08-29T19:45:02Z","abstract_excerpt":"This work centers around results related to Proposition 21 of Pitman and Yor's (1997) paper on the two parameter Poisson Dirichlet distribution indexed by (\\alpha,\\theta) for 0<\\alpha<1, also \\alpha=0, and \\theta>-\\alpha, denoted PD(\\alpha,\\theta). We develop explicit stick-breaking representations for a class that contains the PD(\\alpha,\\theta) for the range \\theta=0, and \\theta>0, we call PG(\\alpha,\\zeta). We also construct a larger class, EPG(\\alpha,\\zeta), containing the entire range. These classes are indexed by \\alpha, and an arbitrary non-negative random variable \\zeta. The bulk of this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6570","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"}