{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GFYYHY7YNUSGG6TGJWOMQNQ3KT","short_pith_number":"pith:GFYYHY7Y","schema_version":"1.0","canonical_sha256":"317183e3f86d24637a664d9cc8361b54fd12c7595ee7b10d97af07a8ed3d43e1","source":{"kind":"arxiv","id":"2506.06056","version":2},"attestation_state":"computed","paper":{"title":"On Rank Correlation Coefficients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexei Stepanov","submitted_at":"2025-06-06T13:02:47Z","abstract_excerpt":"In the present paper, we propose a new rank correlation coefficient $r_n$, which is a sample analogue of the theoretical correlation coefficient $r$, which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the properties of $r_n$ and compare $r_n$ with known rank Spearman $\\rho_{S,n}$, Kendall $\\tau_n$ and sample Pearson $\\rho_n$ correlation coefficients. Simulation experiments show that when the relationship between $X$ and $Y$ is not close to linear, $r_n$ performs better than other correlation coefficients. We also find analytically the values of $Var(\\tau_n)$ and $V"},"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":"2506.06056","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-06T13:02:47Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5b07473e43f47b71d7abfaac0d007be789dd7da3acc44d8c5ac35e8c06085cf1","abstract_canon_sha256":"873a030778544e5f91a035f2d3be183e7f5a262c3e44806246d6e658ad0bd98d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:23.653365Z","signature_b64":"NnW0KuLEDEuXBP4/Khnc45qO1fxHhC6Jh9s5wzb/Vmr17GcH7Pcye3zIs6Pl7dlDqKifPhpcJtEaSTpwnbqsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"317183e3f86d24637a664d9cc8361b54fd12c7595ee7b10d97af07a8ed3d43e1","last_reissued_at":"2026-07-05T11:18:23.652879Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:23.652879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Rank Correlation Coefficients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexei Stepanov","submitted_at":"2025-06-06T13:02:47Z","abstract_excerpt":"In the present paper, we propose a new rank correlation coefficient $r_n$, which is a sample analogue of the theoretical correlation coefficient $r$, which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the properties of $r_n$ and compare $r_n$ with known rank Spearman $\\rho_{S,n}$, Kendall $\\tau_n$ and sample Pearson $\\rho_n$ correlation coefficients. Simulation experiments show that when the relationship between $X$ and $Y$ is not close to linear, $r_n$ performs better than other correlation coefficients. We also find analytically the values of $Var(\\tau_n)$ and $V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06056","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.06056/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.06056","created_at":"2026-07-05T11:18:23.652937+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.06056v2","created_at":"2026-07-05T11:18:23.652937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06056","created_at":"2026-07-05T11:18:23.652937+00:00"},{"alias_kind":"pith_short_12","alias_value":"GFYYHY7YNUSG","created_at":"2026-07-05T11:18:23.652937+00:00"},{"alias_kind":"pith_short_16","alias_value":"GFYYHY7YNUSGG6TG","created_at":"2026-07-05T11:18:23.652937+00:00"},{"alias_kind":"pith_short_8","alias_value":"GFYYHY7Y","created_at":"2026-07-05T11:18:23.652937+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/GFYYHY7YNUSGG6TGJWOMQNQ3KT","json":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT.json","graph_json":"https://pith.science/api/pith-number/GFYYHY7YNUSGG6TGJWOMQNQ3KT/graph.json","events_json":"https://pith.science/api/pith-number/GFYYHY7YNUSGG6TGJWOMQNQ3KT/events.json","paper":"https://pith.science/paper/GFYYHY7Y"},"agent_actions":{"view_html":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT","download_json":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT.json","view_paper":"https://pith.science/paper/GFYYHY7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.06056&json=true","fetch_graph":"https://pith.science/api/pith-number/GFYYHY7YNUSGG6TGJWOMQNQ3KT/graph.json","fetch_events":"https://pith.science/api/pith-number/GFYYHY7YNUSGG6TGJWOMQNQ3KT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT/action/storage_attestation","attest_author":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT/action/author_attestation","sign_citation":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT/action/citation_signature","submit_replication":"https://pith.science/pith/GFYYHY7YNUSGG6TGJWOMQNQ3KT/action/replication_record"}},"created_at":"2026-07-05T11:18:23.652937+00:00","updated_at":"2026-07-05T11:18:23.652937+00:00"}