{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3L27K5XGCTZU5BX362IGWDUS4U","short_pith_number":"pith:3L27K5XG","schema_version":"1.0","canonical_sha256":"daf5f576e614f34e86fbf6906b0e92e53684944577298dc50d3635d5a1c508a1","source":{"kind":"arxiv","id":"1608.00264","version":1},"attestation_state":"computed","paper":{"title":"Frequency of Frequencies Distributions and Size Dependent Exchangeable Random Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.AP","stat.TH"],"primary_cat":"stat.ME","authors_text":"Mingyuan Zhou, Stefano Favaro, Stephen G Walker","submitted_at":"2016-07-31T21:26:50Z","abstract_excerpt":"Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions. A cluster structure, naturally arising from a completely random measure mixed Poisson process, allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size, a distinct and motivated feature that makes it more flexible than a partition structure. This "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.00264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-31T21:26:50Z","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"title_canon_sha256":"f3a3b40cfe5b06863a028600e500443d3af4008a24e654995690c6e557fa7af9","abstract_canon_sha256":"4b1b1321c04938075074c413ad0a0cb3e3ecbd28d914e6942d4fe9ebff2ce948"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:12.099899Z","signature_b64":"VETKpvEalWPZKNmkWcqYfF+LKruEx0B60Dnf+WkUYrIZCpnd4FKOG9K9R8++nmV1RQKMChRptmg0CjOmD80VCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daf5f576e614f34e86fbf6906b0e92e53684944577298dc50d3635d5a1c508a1","last_reissued_at":"2026-05-18T01:10:12.099445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:12.099445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frequency of Frequencies Distributions and Size Dependent Exchangeable Random Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.AP","stat.TH"],"primary_cat":"stat.ME","authors_text":"Mingyuan Zhou, Stefano Favaro, Stephen G Walker","submitted_at":"2016-07-31T21:26:50Z","abstract_excerpt":"Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions. A cluster structure, naturally arising from a completely random measure mixed Poisson process, allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size, a distinct and motivated feature that makes it more flexible than a partition structure. This "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00264","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.00264","created_at":"2026-05-18T01:10:12.099523+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.00264v1","created_at":"2026-05-18T01:10:12.099523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00264","created_at":"2026-05-18T01:10:12.099523+00:00"},{"alias_kind":"pith_short_12","alias_value":"3L27K5XGCTZU","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3L27K5XGCTZU5BX3","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3L27K5XG","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U","json":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U.json","graph_json":"https://pith.science/api/pith-number/3L27K5XGCTZU5BX362IGWDUS4U/graph.json","events_json":"https://pith.science/api/pith-number/3L27K5XGCTZU5BX362IGWDUS4U/events.json","paper":"https://pith.science/paper/3L27K5XG"},"agent_actions":{"view_html":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U","download_json":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U.json","view_paper":"https://pith.science/paper/3L27K5XG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.00264&json=true","fetch_graph":"https://pith.science/api/pith-number/3L27K5XGCTZU5BX362IGWDUS4U/graph.json","fetch_events":"https://pith.science/api/pith-number/3L27K5XGCTZU5BX362IGWDUS4U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U/action/storage_attestation","attest_author":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U/action/author_attestation","sign_citation":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U/action/citation_signature","submit_replication":"https://pith.science/pith/3L27K5XGCTZU5BX362IGWDUS4U/action/replication_record"}},"created_at":"2026-05-18T01:10:12.099523+00:00","updated_at":"2026-05-18T01:10:12.099523+00:00"}