{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:7XCNQ262T4UWTM66NRDMWARPDO","short_pith_number":"pith:7XCNQ262","schema_version":"1.0","canonical_sha256":"fdc4d86bda9f2969b3de6c46cb022f1b84642a16fbb52049a4d7970304d01761","source":{"kind":"arxiv","id":"1007.3662","version":2},"attestation_state":"computed","paper":{"title":"An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"G. Afendras, N. Papadatos, V. Papathanasiou","submitted_at":"2010-07-21T13:58:46Z","abstract_excerpt":"For an absolutely continuous (integer-valued) r.v. $X$ of the Pearson (Ord) family, we show that, under natural moment conditions, a Stein-type covariance identity of order $k$ holds (cf. [Goldstein and Reinert, J. Theoret. Probab. 18 (2005) 237--260]). This identity is closely related to the corresponding sequence of orthogonal polynomials, obtained by a Rodrigues-type formula, and provides convenient expressions for the Fourier coefficients of an arbitrary function. Application of the covariance identity yields some novel expressions for the corresponding lower variance bounds for a function"},"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":"1007.3662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-07-21T13:58:46Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"54798ba8b9100317ddcac5cbe68f2b478c73e90adbcf639051d1ffb12401dc73","abstract_canon_sha256":"4f3893631289eb61cea9371acb199947cd6a27066a4d10957faeed2168954838"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:04.856086Z","signature_b64":"TBjXfbFquTngRvT7vC0b2WGyl8Mao0pO5fK+9GqlNMbdIECEzSRnkJHwzesVfZPa3f43VS9E0JpWTDr8+F7iAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdc4d86bda9f2969b3de6c46cb022f1b84642a16fbb52049a4d7970304d01761","last_reissued_at":"2026-05-18T00:58:04.855594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:04.855594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"G. Afendras, N. Papadatos, V. Papathanasiou","submitted_at":"2010-07-21T13:58:46Z","abstract_excerpt":"For an absolutely continuous (integer-valued) r.v. $X$ of the Pearson (Ord) family, we show that, under natural moment conditions, a Stein-type covariance identity of order $k$ holds (cf. [Goldstein and Reinert, J. Theoret. Probab. 18 (2005) 237--260]). This identity is closely related to the corresponding sequence of orthogonal polynomials, obtained by a Rodrigues-type formula, and provides convenient expressions for the Fourier coefficients of an arbitrary function. Application of the covariance identity yields some novel expressions for the corresponding lower variance bounds for a function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3662","kind":"arxiv","version":2},"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":"1007.3662","created_at":"2026-05-18T00:58:04.855675+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.3662v2","created_at":"2026-05-18T00:58:04.855675+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3662","created_at":"2026-05-18T00:58:04.855675+00:00"},{"alias_kind":"pith_short_12","alias_value":"7XCNQ262T4UW","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"7XCNQ262T4UWTM66","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"7XCNQ262","created_at":"2026-05-18T12:26:05.355336+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/7XCNQ262T4UWTM66NRDMWARPDO","json":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO.json","graph_json":"https://pith.science/api/pith-number/7XCNQ262T4UWTM66NRDMWARPDO/graph.json","events_json":"https://pith.science/api/pith-number/7XCNQ262T4UWTM66NRDMWARPDO/events.json","paper":"https://pith.science/paper/7XCNQ262"},"agent_actions":{"view_html":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO","download_json":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO.json","view_paper":"https://pith.science/paper/7XCNQ262","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.3662&json=true","fetch_graph":"https://pith.science/api/pith-number/7XCNQ262T4UWTM66NRDMWARPDO/graph.json","fetch_events":"https://pith.science/api/pith-number/7XCNQ262T4UWTM66NRDMWARPDO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO/action/storage_attestation","attest_author":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO/action/author_attestation","sign_citation":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO/action/citation_signature","submit_replication":"https://pith.science/pith/7XCNQ262T4UWTM66NRDMWARPDO/action/replication_record"}},"created_at":"2026-05-18T00:58:04.855675+00:00","updated_at":"2026-05-18T00:58:04.855675+00:00"}