{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VNL5OTZIX22IHIZWH5PEWZ6PU4","short_pith_number":"pith:VNL5OTZI","schema_version":"1.0","canonical_sha256":"ab57d74f28beb483a3363f5e4b67cfa7271acde9025d88f53d1d958ed1ccf6ab","source":{"kind":"arxiv","id":"1402.3478","version":1},"attestation_state":"computed","paper":{"title":"A functional derivative useful for the linearization of inequality indexes in the design-based framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Giancarlo Diana, Lucio Barabesi, Pier Francesco Perri","submitted_at":"2014-02-14T14:28:40Z","abstract_excerpt":"Linearization methods are customarily adopted in sampling surveys to obtain approximated variance formulae for estimators of nonlinear functions of finite population totals - such as ratios, correlation coefficients or measures of income inequality - which can be usually rephrased in terms of statistical functionals. In the present paper, by considering the Deville (1991) approach stemming on the concept of design-based influence curve, we provide a general result for linearizing large families of inequality indexes. As an example, the achievement is applied to the Gini, the Amato, the Zenga a"},"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":"1402.3478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-02-14T14:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"932a0c48edd12967f3d90a49e35e7e5ddc12608196834cc3d580ddb74af24f8a","abstract_canon_sha256":"18fddaa8821a231aa1b6c2f6eb8236bef2dcce56d6bfc19c868da961c20a12f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:58.652947Z","signature_b64":"5QjhzwykgcpNkWlSkrWwAqFBVMG9gUvs1VfzdsjM/9C3zQhjNjgjpoBM6sxQBLD/Mf7HJvGlKVJzhMTlbVYXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab57d74f28beb483a3363f5e4b67cfa7271acde9025d88f53d1d958ed1ccf6ab","last_reissued_at":"2026-05-18T02:58:58.652017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:58.652017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A functional derivative useful for the linearization of inequality indexes in the design-based framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Giancarlo Diana, Lucio Barabesi, Pier Francesco Perri","submitted_at":"2014-02-14T14:28:40Z","abstract_excerpt":"Linearization methods are customarily adopted in sampling surveys to obtain approximated variance formulae for estimators of nonlinear functions of finite population totals - such as ratios, correlation coefficients or measures of income inequality - which can be usually rephrased in terms of statistical functionals. In the present paper, by considering the Deville (1991) approach stemming on the concept of design-based influence curve, we provide a general result for linearizing large families of inequality indexes. As an example, the achievement is applied to the Gini, the Amato, the Zenga a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3478","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":"1402.3478","created_at":"2026-05-18T02:58:58.652159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3478v1","created_at":"2026-05-18T02:58:58.652159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3478","created_at":"2026-05-18T02:58:58.652159+00:00"},{"alias_kind":"pith_short_12","alias_value":"VNL5OTZIX22I","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VNL5OTZIX22IHIZW","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VNL5OTZI","created_at":"2026-05-18T12:28:54.890064+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/VNL5OTZIX22IHIZWH5PEWZ6PU4","json":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4.json","graph_json":"https://pith.science/api/pith-number/VNL5OTZIX22IHIZWH5PEWZ6PU4/graph.json","events_json":"https://pith.science/api/pith-number/VNL5OTZIX22IHIZWH5PEWZ6PU4/events.json","paper":"https://pith.science/paper/VNL5OTZI"},"agent_actions":{"view_html":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4","download_json":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4.json","view_paper":"https://pith.science/paper/VNL5OTZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3478&json=true","fetch_graph":"https://pith.science/api/pith-number/VNL5OTZIX22IHIZWH5PEWZ6PU4/graph.json","fetch_events":"https://pith.science/api/pith-number/VNL5OTZIX22IHIZWH5PEWZ6PU4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4/action/storage_attestation","attest_author":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4/action/author_attestation","sign_citation":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4/action/citation_signature","submit_replication":"https://pith.science/pith/VNL5OTZIX22IHIZWH5PEWZ6PU4/action/replication_record"}},"created_at":"2026-05-18T02:58:58.652159+00:00","updated_at":"2026-05-18T02:58:58.652159+00:00"}