{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U4OUK7KQM2QMRWVINY35OPKE3X","short_pith_number":"pith:U4OUK7KQ","canonical_record":{"source":{"id":"1309.3370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-13T05:32:16Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"51feb5d22b0e5c3eadd2e1e023a41e7bc38f61594c165ffe2b31dfb456ce4638","abstract_canon_sha256":"f57a87bb1210e96c428f20f5d51526c2afa6a8daebdf30ced38385eabec5f7f4"},"schema_version":"1.0"},"canonical_sha256":"a71d457d5066a0c8daa86e37d73d44ddf983e449485465a101e19f580590e57f","source":{"kind":"arxiv","id":"1309.3370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3370","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3370v1","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3370","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"U4OUK7KQM2QM","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4OUK7KQM2QMRWVI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4OUK7KQ","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U4OUK7KQM2QMRWVINY35OPKE3X","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-13T05:32:16Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"51feb5d22b0e5c3eadd2e1e023a41e7bc38f61594c165ffe2b31dfb456ce4638","abstract_canon_sha256":"f57a87bb1210e96c428f20f5d51526c2afa6a8daebdf30ced38385eabec5f7f4"},"schema_version":"1.0"},"canonical_sha256":"a71d457d5066a0c8daa86e37d73d44ddf983e449485465a101e19f580590e57f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:22.785889Z","signature_b64":"7/XNoXKyUpme3GxXGmX2I9vR+mn71xxsGIxhc5i0lAMPTTPtFnf/S6U73XLSBwLcd4I73U18IEJ0FUQla0krBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a71d457d5066a0c8daa86e37d73d44ddf983e449485465a101e19f580590e57f","last_reissued_at":"2026-05-18T03:13:22.785227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:22.785227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3370","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":"2026-05-18T03:13:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVIsPcgq8JjeElYcZrOc8ZI1+96ZFemLdc2b6eg/3zfYmlouyi/Otd3OMvkUgIbw/QWNdEMC9VcOmk8YyX79CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:57:16.556792Z"},"content_sha256":"5ea27880e3e85aafe1dbae3fb1cba32f7aea43b6aa012d618a570bfc8a875ab7","schema_version":"1.0","event_id":"sha256:5ea27880e3e85aafe1dbae3fb1cba32f7aea43b6aa012d618a570bfc8a875ab7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U4OUK7KQM2QMRWVINY35OPKE3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalised family of ratio product estimator using transformation equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Rajesh Singh, Viplav K. Singh","submitted_at":"2013-09-13T05:32:16Z","abstract_excerpt":"In this paper we deal with the estimation of population variance of the study variable y using auxiliary information on variable x. A family of ratio and product-type estimators are proposed using suitable transformation on both random variable x(auxiliary variable) and(study variable).Up to the first order of approximation the expression of mean square error and Bias term are obtained. An empirical study is carried out to illustrate the performance of the constructed estimator over others."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3370","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":"2026-05-18T03:13:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qLDAAqNLEfAJK0G2xCRzt9DUDvmd8Plneq5IQnDlDocP2FCYfx9HbYZteTzEC5LxMzCIAJH1HN72wlLfo7M5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:57:16.557430Z"},"content_sha256":"e3c62423dfb66544acebfd93cf25b0df2af3b0a350b0b57ae94b0194e28d20b7","schema_version":"1.0","event_id":"sha256:e3c62423dfb66544acebfd93cf25b0df2af3b0a350b0b57ae94b0194e28d20b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4OUK7KQM2QMRWVINY35OPKE3X/bundle.json","state_url":"https://pith.science/pith/U4OUK7KQM2QMRWVINY35OPKE3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4OUK7KQM2QMRWVINY35OPKE3X/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":"2026-06-07T17:57:16Z","links":{"resolver":"https://pith.science/pith/U4OUK7KQM2QMRWVINY35OPKE3X","bundle":"https://pith.science/pith/U4OUK7KQM2QMRWVINY35OPKE3X/bundle.json","state":"https://pith.science/pith/U4OUK7KQM2QMRWVINY35OPKE3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4OUK7KQM2QMRWVINY35OPKE3X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U4OUK7KQM2QMRWVINY35OPKE3X","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":"f57a87bb1210e96c428f20f5d51526c2afa6a8daebdf30ced38385eabec5f7f4","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-13T05:32:16Z","title_canon_sha256":"51feb5d22b0e5c3eadd2e1e023a41e7bc38f61594c165ffe2b31dfb456ce4638"},"schema_version":"1.0","source":{"id":"1309.3370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3370","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3370v1","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3370","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"U4OUK7KQM2QM","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4OUK7KQM2QMRWVI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4OUK7KQ","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:e3c62423dfb66544acebfd93cf25b0df2af3b0a350b0b57ae94b0194e28d20b7","target":"graph","created_at":"2026-05-18T03:13:22Z","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 this paper we deal with the estimation of population variance of the study variable y using auxiliary information on variable x. A family of ratio and product-type estimators are proposed using suitable transformation on both random variable x(auxiliary variable) and(study variable).Up to the first order of approximation the expression of mean square error and Bias term are obtained. An empirical study is carried out to illustrate the performance of the constructed estimator over others.","authors_text":"Rajesh Singh, Viplav K. Singh","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-13T05:32:16Z","title":"A generalised family of ratio product estimator using transformation equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3370","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":"sha256:5ea27880e3e85aafe1dbae3fb1cba32f7aea43b6aa012d618a570bfc8a875ab7","target":"record","created_at":"2026-05-18T03:13:22Z","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":"f57a87bb1210e96c428f20f5d51526c2afa6a8daebdf30ced38385eabec5f7f4","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-13T05:32:16Z","title_canon_sha256":"51feb5d22b0e5c3eadd2e1e023a41e7bc38f61594c165ffe2b31dfb456ce4638"},"schema_version":"1.0","source":{"id":"1309.3370","kind":"arxiv","version":1}},"canonical_sha256":"a71d457d5066a0c8daa86e37d73d44ddf983e449485465a101e19f580590e57f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a71d457d5066a0c8daa86e37d73d44ddf983e449485465a101e19f580590e57f","first_computed_at":"2026-05-18T03:13:22.785227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:22.785227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/XNoXKyUpme3GxXGmX2I9vR+mn71xxsGIxhc5i0lAMPTTPtFnf/S6U73XLSBwLcd4I73U18IEJ0FUQla0krBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:22.785889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ea27880e3e85aafe1dbae3fb1cba32f7aea43b6aa012d618a570bfc8a875ab7","sha256:e3c62423dfb66544acebfd93cf25b0df2af3b0a350b0b57ae94b0194e28d20b7"],"state_sha256":"c0bbbe55fe65fc76769f3759f46c84addbcda135f56f0bc003c73a1fa6302136"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ZfLWqvc6u8MogVsFExzaH4ToiNLNQoXiUQeIcOgkXtdQgkC4VhdXPH9gzh6QYaUD7eAzD0/bZzhjL/NM2R2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:57:16.561059Z","bundle_sha256":"d038618ba2f1ac274ec89b82487852c73d8ef2c3649934fdf64bf26df7885b9b"}}