{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5LRKUUHZ2IH6CFTHIOX4SJM5OK","short_pith_number":"pith:5LRKUUHZ","canonical_record":{"source":{"id":"1309.4871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-09-19T06:28:30Z","cross_cats_sorted":[],"title_canon_sha256":"fd4c940154114ec1cb739c837e0d50c6959a3111925337085022fa99de9a0d59","abstract_canon_sha256":"0c115662d797f746f1f1fdc252de8bb0bf8af09a72a841ce251da5be36a5d821"},"schema_version":"1.0"},"canonical_sha256":"eae2aa50f9d20fe1166743afc9259d729202051108feb4124c1d8c6f1bc823d3","source":{"kind":"arxiv","id":"1309.4871","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4871","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4871v1","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4871","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"5LRKUUHZ2IH6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5LRKUUHZ2IH6CFTH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5LRKUUHZ","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5LRKUUHZ2IH6CFTHIOX4SJM5OK","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-09-19T06:28:30Z","cross_cats_sorted":[],"title_canon_sha256":"fd4c940154114ec1cb739c837e0d50c6959a3111925337085022fa99de9a0d59","abstract_canon_sha256":"0c115662d797f746f1f1fdc252de8bb0bf8af09a72a841ce251da5be36a5d821"},"schema_version":"1.0"},"canonical_sha256":"eae2aa50f9d20fe1166743afc9259d729202051108feb4124c1d8c6f1bc823d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:57.073057Z","signature_b64":"8kRBdiahfZn8RnNg59dGGKasLtZXPY7xUhU3AQiw9zovHUkQ6kdduIBh+ux5OpZRoDPOFFjYmji8hhnaA1z/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eae2aa50f9d20fe1166743afc9259d729202051108feb4124c1d8c6f1bc823d3","last_reissued_at":"2026-05-18T03:12:57.072325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:57.072325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4871","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":"2026-05-18T03:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eLIlmkmt+tOoU5pzp4fb3CBPQfTQReiBkyathlEq72CLmswFHEfTQdoUiNmo2NXYCDIrXP8CdpAGtV9HAt8UDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:40:03.831631Z"},"content_sha256":"71b94e1db65c331077cb4fc5251578cd57e41345a499d4b41b1a7e6cd24ff9d6","schema_version":"1.0","event_id":"sha256:71b94e1db65c331077cb4fc5251578cd57e41345a499d4b41b1a7e6cd24ff9d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5LRKUUHZ2IH6CFTHIOX4SJM5OK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate ratio estimation with known population proportion of two auxiliary characters for finite population","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"A. A. Adewara, Florentin Smarandache, Rajesh Singh, Sachin Malik","submitted_at":"2013-09-19T06:28:30Z","abstract_excerpt":"In the present study, we propose estimators based on geometric and harmonic mean for estimating population mean using information on two auxiliary attributes in simple random sampling. We have shown that, when we have multi-auxiliary attributes, estimators based on geometric mean and harmonic mean are less biased than Olkin (1958), Naik and Gupta (1996) and Singh (1967) type- estimator under certain conditions. However, the MSE of Olkin(1958) estimator and geometric and harmonic estimators are same up to the first order of approximation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4871","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":"2026-05-18T03:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xLI7eZ5THWFgALd2qBrX6blDn+YbGsZc+yUeDIiyNso2PL38eFi/GAtTxCNaYj5B/2fzroFFgY8PM08gcqTYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:40:03.832358Z"},"content_sha256":"5816a565fcdc76a7408e69d1dc013ae65ccce0f7af3f52b35adbb85c51fe8f9c","schema_version":"1.0","event_id":"sha256:5816a565fcdc76a7408e69d1dc013ae65ccce0f7af3f52b35adbb85c51fe8f9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5LRKUUHZ2IH6CFTHIOX4SJM5OK/bundle.json","state_url":"https://pith.science/pith/5LRKUUHZ2IH6CFTHIOX4SJM5OK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5LRKUUHZ2IH6CFTHIOX4SJM5OK/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":"2026-06-08T10:40:03Z","links":{"resolver":"https://pith.science/pith/5LRKUUHZ2IH6CFTHIOX4SJM5OK","bundle":"https://pith.science/pith/5LRKUUHZ2IH6CFTHIOX4SJM5OK/bundle.json","state":"https://pith.science/pith/5LRKUUHZ2IH6CFTHIOX4SJM5OK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5LRKUUHZ2IH6CFTHIOX4SJM5OK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5LRKUUHZ2IH6CFTHIOX4SJM5OK","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":"0c115662d797f746f1f1fdc252de8bb0bf8af09a72a841ce251da5be36a5d821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-09-19T06:28:30Z","title_canon_sha256":"fd4c940154114ec1cb739c837e0d50c6959a3111925337085022fa99de9a0d59"},"schema_version":"1.0","source":{"id":"1309.4871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4871","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4871v1","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4871","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"5LRKUUHZ2IH6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5LRKUUHZ2IH6CFTH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5LRKUUHZ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:5816a565fcdc76a7408e69d1dc013ae65ccce0f7af3f52b35adbb85c51fe8f9c","target":"graph","created_at":"2026-05-18T03:12:57Z","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":"In the present study, we propose estimators based on geometric and harmonic mean for estimating population mean using information on two auxiliary attributes in simple random sampling. We have shown that, when we have multi-auxiliary attributes, estimators based on geometric mean and harmonic mean are less biased than Olkin (1958), Naik and Gupta (1996) and Singh (1967) type- estimator under certain conditions. However, the MSE of Olkin(1958) estimator and geometric and harmonic estimators are same up to the first order of approximation.","authors_text":"A. A. Adewara, Florentin Smarandache, Rajesh Singh, Sachin Malik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-09-19T06:28:30Z","title":"Multivariate ratio estimation with known population proportion of two auxiliary characters for finite population"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4871","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":"sha256:71b94e1db65c331077cb4fc5251578cd57e41345a499d4b41b1a7e6cd24ff9d6","target":"record","created_at":"2026-05-18T03:12:57Z","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":"0c115662d797f746f1f1fdc252de8bb0bf8af09a72a841ce251da5be36a5d821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2013-09-19T06:28:30Z","title_canon_sha256":"fd4c940154114ec1cb739c837e0d50c6959a3111925337085022fa99de9a0d59"},"schema_version":"1.0","source":{"id":"1309.4871","kind":"arxiv","version":1}},"canonical_sha256":"eae2aa50f9d20fe1166743afc9259d729202051108feb4124c1d8c6f1bc823d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eae2aa50f9d20fe1166743afc9259d729202051108feb4124c1d8c6f1bc823d3","first_computed_at":"2026-05-18T03:12:57.072325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:57.072325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8kRBdiahfZn8RnNg59dGGKasLtZXPY7xUhU3AQiw9zovHUkQ6kdduIBh+ux5OpZRoDPOFFjYmji8hhnaA1z/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:57.073057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71b94e1db65c331077cb4fc5251578cd57e41345a499d4b41b1a7e6cd24ff9d6","sha256:5816a565fcdc76a7408e69d1dc013ae65ccce0f7af3f52b35adbb85c51fe8f9c"],"state_sha256":"844aa27c35d9064e5158d2d3cbb2a4d9ecc8b7ac889d35385eed3b4a203c6c6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NoFqrWTSmNHEhTb/atB23cETL2f2fC6CTLSeCQqT6MUk3xDx0H1CfXMxAIB256J0uW8wy/hmH8M+uoAzcco7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T10:40:03.837130Z","bundle_sha256":"647d249bacd9ecbe3b60fad3af44173b00f5876204a1be5cad3cb9b3197d15d5"}}