{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:WJVEFCEV5ZEWFKRQ7FVM2USTYW","short_pith_number":"pith:WJVEFCEV","schema_version":"1.0","canonical_sha256":"b26a428895ee4962aa30f96acd5253c5b5488a6a12051b6181ce4e509530baed","source":{"kind":"arxiv","id":"0904.0966","version":2},"attestation_state":"computed","paper":{"title":"Exact Asymptotics of Bivariate Scale Mixture Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva","submitted_at":"2009-04-06T16:42:41Z","abstract_excerpt":"Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \\in (0,1] as x tends infintiy assuming that R has distribution function in the Gumbel max-domain of attraction and (U_1,U_2) has a specific tail behaviour around some absorbing point. As a special case of our results we retrieve the exact asymptotic behaviour of bivariate polar random vectors. We apply our results to investigate the asymptotic independence and "},"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":"0904.0966","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-04-06T16:42:41Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"15643dbb2b95a286e03ef678caf4ae2f71ede7dc2a62744fe9b98b8240b80838","abstract_canon_sha256":"0ff43e7debbf44762c7dae59b45d8ae7db0db8754cafb1702dc98117a623d0fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:59.890719Z","signature_b64":"Wl5rrGi52UF0VKdY9h8wYkpRnatVHPEZPnR7kxOwqx1qtwxB2jW3UadluV/0S8MEcHT13cXl3xQKXYwJM/6yAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b26a428895ee4962aa30f96acd5253c5b5488a6a12051b6181ce4e509530baed","last_reissued_at":"2026-05-18T03:25:59.890214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:59.890214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Asymptotics of Bivariate Scale Mixture Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva","submitted_at":"2009-04-06T16:42:41Z","abstract_excerpt":"Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \\in (0,1] as x tends infintiy assuming that R has distribution function in the Gumbel max-domain of attraction and (U_1,U_2) has a specific tail behaviour around some absorbing point. As a special case of our results we retrieve the exact asymptotic behaviour of bivariate polar random vectors. We apply our results to investigate the asymptotic independence and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0966","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":"0904.0966","created_at":"2026-05-18T03:25:59.890292+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.0966v2","created_at":"2026-05-18T03:25:59.890292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0966","created_at":"2026-05-18T03:25:59.890292+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJVEFCEV5ZEW","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJVEFCEV5ZEWFKRQ","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJVEFCEV","created_at":"2026-05-18T12:26:02.257875+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/WJVEFCEV5ZEWFKRQ7FVM2USTYW","json":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW.json","graph_json":"https://pith.science/api/pith-number/WJVEFCEV5ZEWFKRQ7FVM2USTYW/graph.json","events_json":"https://pith.science/api/pith-number/WJVEFCEV5ZEWFKRQ7FVM2USTYW/events.json","paper":"https://pith.science/paper/WJVEFCEV"},"agent_actions":{"view_html":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW","download_json":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW.json","view_paper":"https://pith.science/paper/WJVEFCEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.0966&json=true","fetch_graph":"https://pith.science/api/pith-number/WJVEFCEV5ZEWFKRQ7FVM2USTYW/graph.json","fetch_events":"https://pith.science/api/pith-number/WJVEFCEV5ZEWFKRQ7FVM2USTYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW/action/storage_attestation","attest_author":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW/action/author_attestation","sign_citation":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW/action/citation_signature","submit_replication":"https://pith.science/pith/WJVEFCEV5ZEWFKRQ7FVM2USTYW/action/replication_record"}},"created_at":"2026-05-18T03:25:59.890292+00:00","updated_at":"2026-05-18T03:25:59.890292+00:00"}