{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RXB2DC5EJHOZS4ELNDSZHR32OU","short_pith_number":"pith:RXB2DC5E","canonical_record":{"source":{"id":"1102.0771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-03T20:46:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"297763717a5bb6ff7dddfe39053c4a38858a6f6394f601a3a9ea04398eff6bf6","abstract_canon_sha256":"7cecd5dba4b3b2193c6a365a744593b27b70e9d5595274c0ddcf733c5ae49c80"},"schema_version":"1.0"},"canonical_sha256":"8dc3a18ba449dd99708b68e593c77a7525a463c14aaf8b88442548acc86bc519","source":{"kind":"arxiv","id":"1102.0771","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0771","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0771v1","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0771","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"RXB2DC5EJHOZ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RXB2DC5EJHOZS4EL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RXB2DC5E","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RXB2DC5EJHOZS4ELNDSZHR32OU","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-03T20:46:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"297763717a5bb6ff7dddfe39053c4a38858a6f6394f601a3a9ea04398eff6bf6","abstract_canon_sha256":"7cecd5dba4b3b2193c6a365a744593b27b70e9d5595274c0ddcf733c5ae49c80"},"schema_version":"1.0"},"canonical_sha256":"8dc3a18ba449dd99708b68e593c77a7525a463c14aaf8b88442548acc86bc519","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:04.104515Z","signature_b64":"OOpATrAXoT60k3QCBJETJiuraXm3owwmPzjoFxSUKnoRCcsoKpFRzyReY7wYHWQgrXgvbfLrPT2OCDHNgj0gBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dc3a18ba449dd99708b68e593c77a7525a463c14aaf8b88442548acc86bc519","last_reissued_at":"2026-05-18T04:30:04.103996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:04.103996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0771","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvZx6qcC0HF/JAEqYgnETj8NGJjLPvSHaZElING9lhCWG2VyFP57eu2jwR1PjIldkvZ1d1NvQZ3tq2G1s/QBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:26:03.548146Z"},"content_sha256":"3f7fa3663e744198783ab03c8d8b489f12a02ee0e102b0edfbf00ba6b9903664","schema_version":"1.0","event_id":"sha256:3f7fa3663e744198783ab03c8d8b489f12a02ee0e102b0edfbf00ba6b9903664"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RXB2DC5EJHOZS4ELNDSZHR32OU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Regular Variation of Ratios of Jointly Frechet Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Yizao Wang","submitted_at":"2011-02-03T20:46:34Z","abstract_excerpt":"We provide a necessary and sufficient condition for the ratio of two jointly alpha-Frechet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution and is easy to check in practice. Our result motivates the notion of the ratio tail index, which quantifies dependence features that are not characterized by the tail dependence index. As an application, we derive the asymptotic behavior of the quotient correlation coefficient proposed in Zhang (2008) in the dependent case. Our result also serves as an example of a new type of regula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0771","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xILaQoouNoBoT7nBffn/09VlbQrgopYl97dLf1pRXGkbt/V1vlGB8blRhAtC55FRN6Nj9ut0/pXdp1D0DLQJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:26:03.548504Z"},"content_sha256":"db5bb5879dc6c641d6029f112f04c0c93259eca3e954842e226b59e93b45abfd","schema_version":"1.0","event_id":"sha256:db5bb5879dc6c641d6029f112f04c0c93259eca3e954842e226b59e93b45abfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXB2DC5EJHOZS4ELNDSZHR32OU/bundle.json","state_url":"https://pith.science/pith/RXB2DC5EJHOZS4ELNDSZHR32OU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXB2DC5EJHOZS4ELNDSZHR32OU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T10:26:03Z","links":{"resolver":"https://pith.science/pith/RXB2DC5EJHOZS4ELNDSZHR32OU","bundle":"https://pith.science/pith/RXB2DC5EJHOZS4ELNDSZHR32OU/bundle.json","state":"https://pith.science/pith/RXB2DC5EJHOZS4ELNDSZHR32OU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXB2DC5EJHOZS4ELNDSZHR32OU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RXB2DC5EJHOZS4ELNDSZHR32OU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7cecd5dba4b3b2193c6a365a744593b27b70e9d5595274c0ddcf733c5ae49c80","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-03T20:46:34Z","title_canon_sha256":"297763717a5bb6ff7dddfe39053c4a38858a6f6394f601a3a9ea04398eff6bf6"},"schema_version":"1.0","source":{"id":"1102.0771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0771","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0771v1","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0771","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"RXB2DC5EJHOZ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RXB2DC5EJHOZS4EL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RXB2DC5E","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:db5bb5879dc6c641d6029f112f04c0c93259eca3e954842e226b59e93b45abfd","target":"graph","created_at":"2026-05-18T04:30:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We provide a necessary and sufficient condition for the ratio of two jointly alpha-Frechet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution and is easy to check in practice. Our result motivates the notion of the ratio tail index, which quantifies dependence features that are not characterized by the tail dependence index. As an application, we derive the asymptotic behavior of the quotient correlation coefficient proposed in Zhang (2008) in the dependent case. Our result also serves as an example of a new type of regula","authors_text":"Yizao Wang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-03T20:46:34Z","title":"On the Regular Variation of Ratios of Jointly Frechet Random Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0771","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3f7fa3663e744198783ab03c8d8b489f12a02ee0e102b0edfbf00ba6b9903664","target":"record","created_at":"2026-05-18T04:30:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7cecd5dba4b3b2193c6a365a744593b27b70e9d5595274c0ddcf733c5ae49c80","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-03T20:46:34Z","title_canon_sha256":"297763717a5bb6ff7dddfe39053c4a38858a6f6394f601a3a9ea04398eff6bf6"},"schema_version":"1.0","source":{"id":"1102.0771","kind":"arxiv","version":1}},"canonical_sha256":"8dc3a18ba449dd99708b68e593c77a7525a463c14aaf8b88442548acc86bc519","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dc3a18ba449dd99708b68e593c77a7525a463c14aaf8b88442548acc86bc519","first_computed_at":"2026-05-18T04:30:04.103996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:04.103996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OOpATrAXoT60k3QCBJETJiuraXm3owwmPzjoFxSUKnoRCcsoKpFRzyReY7wYHWQgrXgvbfLrPT2OCDHNgj0gBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:04.104515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f7fa3663e744198783ab03c8d8b489f12a02ee0e102b0edfbf00ba6b9903664","sha256:db5bb5879dc6c641d6029f112f04c0c93259eca3e954842e226b59e93b45abfd"],"state_sha256":"a98d69c6c0ba17a06e21b2698e5c1940e09a4a2ce47f77592ea15a6912e250b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+93VqfpTknZBJESA6lmUmG4imOcOwZBdoOPJDQO4sTav03wxHtcUtuN/7yICVFh9KQCIRHrEg8TfZiRF/KvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:26:03.550472Z","bundle_sha256":"50e9c9eea3b95b312a650be46715f0a1a0745adf4b81a6e50c9624e80f836ae3"}}