{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3S2T3ILGPKIDFGOOE7CAGUP5OO","short_pith_number":"pith:3S2T3ILG","schema_version":"1.0","canonical_sha256":"dcb53da1667a903299ce27c40351fd73b87ead01218b167c66df3481410fcbaa","source":{"kind":"arxiv","id":"1211.2299","version":1},"attestation_state":"computed","paper":{"title":"Bayesian approach to cubic natural exponential families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Abdelhamid Hassairi, Marwa Hamza","submitted_at":"2012-11-10T07:13:38Z","abstract_excerpt":"For a natural exponential family (NEF), one can associate in a natural way two standard families of conjugate priors, one on the natural parameter and the other on the mean parameter. These families of conjugate priors have been used to establish some remarkable properties and characterization results of the quadratic NEF's. In the present paper, we show that for a NEF, we can associate a class of NEF's, and for each one of these NEF's, we define a family of conjugate priors on the natural parameter and a family of conjugate priors on the mean parameter which are different of the standard ones"},"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":"1211.2299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-10T07:13:38Z","cross_cats_sorted":[],"title_canon_sha256":"0ac9e978f52e4afa94a07f9799ce78b49292add1746135515ba13aba87647b5d","abstract_canon_sha256":"1ee9f103638021068070d5d4675b744b7634741c0aa3f714f79540080957c7b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:03.805713Z","signature_b64":"HV4cSWIRB6qxREA3DAJAoQWEJ3IjNlGbnsprWztW/XAiicergu4xc8uOEwKVlKm+n+wZL5kNiJfeOaWlGzmOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcb53da1667a903299ce27c40351fd73b87ead01218b167c66df3481410fcbaa","last_reissued_at":"2026-05-18T03:41:03.805061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:03.805061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bayesian approach to cubic natural exponential families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Abdelhamid Hassairi, Marwa Hamza","submitted_at":"2012-11-10T07:13:38Z","abstract_excerpt":"For a natural exponential family (NEF), one can associate in a natural way two standard families of conjugate priors, one on the natural parameter and the other on the mean parameter. These families of conjugate priors have been used to establish some remarkable properties and characterization results of the quadratic NEF's. In the present paper, we show that for a NEF, we can associate a class of NEF's, and for each one of these NEF's, we define a family of conjugate priors on the natural parameter and a family of conjugate priors on the mean parameter which are different of the standard ones"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2299","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":"1211.2299","created_at":"2026-05-18T03:41:03.805154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2299v1","created_at":"2026-05-18T03:41:03.805154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2299","created_at":"2026-05-18T03:41:03.805154+00:00"},{"alias_kind":"pith_short_12","alias_value":"3S2T3ILGPKID","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3S2T3ILGPKIDFGOO","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3S2T3ILG","created_at":"2026-05-18T12:26:53.410803+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/3S2T3ILGPKIDFGOOE7CAGUP5OO","json":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO.json","graph_json":"https://pith.science/api/pith-number/3S2T3ILGPKIDFGOOE7CAGUP5OO/graph.json","events_json":"https://pith.science/api/pith-number/3S2T3ILGPKIDFGOOE7CAGUP5OO/events.json","paper":"https://pith.science/paper/3S2T3ILG"},"agent_actions":{"view_html":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO","download_json":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO.json","view_paper":"https://pith.science/paper/3S2T3ILG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2299&json=true","fetch_graph":"https://pith.science/api/pith-number/3S2T3ILGPKIDFGOOE7CAGUP5OO/graph.json","fetch_events":"https://pith.science/api/pith-number/3S2T3ILGPKIDFGOOE7CAGUP5OO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO/action/storage_attestation","attest_author":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO/action/author_attestation","sign_citation":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO/action/citation_signature","submit_replication":"https://pith.science/pith/3S2T3ILGPKIDFGOOE7CAGUP5OO/action/replication_record"}},"created_at":"2026-05-18T03:41:03.805154+00:00","updated_at":"2026-05-18T03:41:03.805154+00:00"}