{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:V7VZTHKK2MGM23WLQPSF4V2Z75","short_pith_number":"pith:V7VZTHKK","schema_version":"1.0","canonical_sha256":"afeb999d4ad30ccd6ecb83e45e5759ff78fd38ebba9213424672fecaa8e1cb92","source":{"kind":"arxiv","id":"1011.2009","version":1},"attestation_state":"computed","paper":{"title":"Comparison of Spearman's rho and Kendall's tau in Normal and Contaminated Normal Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Weichao Xu, Y. S. Hung, Yuexian Zou, Yunhe Hou","submitted_at":"2010-11-09T09:26:30Z","abstract_excerpt":"This paper analyzes the performances of the Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and bivariate contaminated normal populations. The exact analytical formulae of the variance of SR and the covariance between SR and KT are obtained based on the Childs's reduction formula for the quadrivariate normal positive orthant probabilities. Close form expressions with respect to the expectations of SR and KT are established under the bivariate contaminated normal models. The bias, mean square error (MSE) and asymptotic relative efficiency (ARE) of "},"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":"1011.2009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T09:26:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"070d945d6d39704ce4a7c98fa77f14341906053e35a275c5f160e6d79ac7b8d3","abstract_canon_sha256":"a027bf22e43446f4d73a28ab2b830ab481284998c66c55ac0d473de0a8c982c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:42.771954Z","signature_b64":"4ZUY5CF2sHuH16BhADsM5Yq37yg/mqsE7Cg8Yr1F1hU4ZCfXLJIC7zNIeq2LVLpM6472/gaTHHR0MINYFZANDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afeb999d4ad30ccd6ecb83e45e5759ff78fd38ebba9213424672fecaa8e1cb92","last_reissued_at":"2026-05-18T04:36:42.771479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:42.771479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison of Spearman's rho and Kendall's tau in Normal and Contaminated Normal Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Weichao Xu, Y. S. Hung, Yuexian Zou, Yunhe Hou","submitted_at":"2010-11-09T09:26:30Z","abstract_excerpt":"This paper analyzes the performances of the Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and bivariate contaminated normal populations. The exact analytical formulae of the variance of SR and the covariance between SR and KT are obtained based on the Childs's reduction formula for the quadrivariate normal positive orthant probabilities. Close form expressions with respect to the expectations of SR and KT are established under the bivariate contaminated normal models. The bias, mean square error (MSE) and asymptotic relative efficiency (ARE) of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2009","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":"1011.2009","created_at":"2026-05-18T04:36:42.771545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.2009v1","created_at":"2026-05-18T04:36:42.771545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2009","created_at":"2026-05-18T04:36:42.771545+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7VZTHKK2MGM","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7VZTHKK2MGM23WL","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7VZTHKK","created_at":"2026-05-18T12:26:15.391820+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/V7VZTHKK2MGM23WLQPSF4V2Z75","json":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75.json","graph_json":"https://pith.science/api/pith-number/V7VZTHKK2MGM23WLQPSF4V2Z75/graph.json","events_json":"https://pith.science/api/pith-number/V7VZTHKK2MGM23WLQPSF4V2Z75/events.json","paper":"https://pith.science/paper/V7VZTHKK"},"agent_actions":{"view_html":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75","download_json":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75.json","view_paper":"https://pith.science/paper/V7VZTHKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.2009&json=true","fetch_graph":"https://pith.science/api/pith-number/V7VZTHKK2MGM23WLQPSF4V2Z75/graph.json","fetch_events":"https://pith.science/api/pith-number/V7VZTHKK2MGM23WLQPSF4V2Z75/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75/action/storage_attestation","attest_author":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75/action/author_attestation","sign_citation":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75/action/citation_signature","submit_replication":"https://pith.science/pith/V7VZTHKK2MGM23WLQPSF4V2Z75/action/replication_record"}},"created_at":"2026-05-18T04:36:42.771545+00:00","updated_at":"2026-05-18T04:36:42.771545+00:00"}