{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:J3NAKJ67ZAVWDPP7CFGQ3PLXHQ","short_pith_number":"pith:J3NAKJ67","schema_version":"1.0","canonical_sha256":"4eda0527dfc82b61bdff114d0dbd773c3ddf407a71245f909b1ad62a3d21e3ad","source":{"kind":"arxiv","id":"1405.6884","version":2},"attestation_state":"computed","paper":{"title":"Maximizing the expected range from dependent observations under mean-variance information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nickos Papadatos","submitted_at":"2014-05-27T12:27:17Z","abstract_excerpt":"In this article we derive the best possible upper bound for $E[\\max{X_i}-\\min_i{X_i}]$ under given means and variances on $n$ random variables $X_i$. The random vector $(X_1,...,X_n)$ is allowed to have any dependence structure, provided $E X_i=\\mu_i$ and $Var X_i=\\sigma_i^2$, $0<\\sigma_i<\\infty$. We provide an explicit characterization of the $n$-variate distributions that attain the equality (extremal random vectors), and the tight bound is compared to other existing results.\n  Key words and phrases: Range; Dependent Observations; Tight Expectation Bounds; Extremal Random Vectors; Probabilit"},"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":"1405.6884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-05-27T12:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"b4b958e163a7f0c9efc0376044489adae478741edefcc8b7a34d6d608be71aa6","abstract_canon_sha256":"a21b0d9eda24716d0237483a76b4260d8c0ede04311e37c5d501e32cf1f034a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:04.682225Z","signature_b64":"H/QN0BqOeJCF56VHI9a3ibwdZ/PFrlRkG9Gl6bRHaoYT61afCuDjo0ZS21z7Zg+3oNhZ3XTXLR44J7psySfdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eda0527dfc82b61bdff114d0dbd773c3ddf407a71245f909b1ad62a3d21e3ad","last_reissued_at":"2026-05-18T00:58:04.681815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:04.681815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximizing the expected range from dependent observations under mean-variance information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nickos Papadatos","submitted_at":"2014-05-27T12:27:17Z","abstract_excerpt":"In this article we derive the best possible upper bound for $E[\\max{X_i}-\\min_i{X_i}]$ under given means and variances on $n$ random variables $X_i$. The random vector $(X_1,...,X_n)$ is allowed to have any dependence structure, provided $E X_i=\\mu_i$ and $Var X_i=\\sigma_i^2$, $0<\\sigma_i<\\infty$. We provide an explicit characterization of the $n$-variate distributions that attain the equality (extremal random vectors), and the tight bound is compared to other existing results.\n  Key words and phrases: Range; Dependent Observations; Tight Expectation Bounds; Extremal Random Vectors; Probabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6884","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":""},"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":"1405.6884","created_at":"2026-05-18T00:58:04.681887+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6884v2","created_at":"2026-05-18T00:58:04.681887+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6884","created_at":"2026-05-18T00:58:04.681887+00:00"},{"alias_kind":"pith_short_12","alias_value":"J3NAKJ67ZAVW","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"J3NAKJ67ZAVWDPP7","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"J3NAKJ67","created_at":"2026-05-18T12:28:33.132498+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/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ","json":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ.json","graph_json":"https://pith.science/api/pith-number/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/graph.json","events_json":"https://pith.science/api/pith-number/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/events.json","paper":"https://pith.science/paper/J3NAKJ67"},"agent_actions":{"view_html":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ","download_json":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ.json","view_paper":"https://pith.science/paper/J3NAKJ67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6884&json=true","fetch_graph":"https://pith.science/api/pith-number/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/graph.json","fetch_events":"https://pith.science/api/pith-number/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/action/storage_attestation","attest_author":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/action/author_attestation","sign_citation":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/action/citation_signature","submit_replication":"https://pith.science/pith/J3NAKJ67ZAVWDPP7CFGQ3PLXHQ/action/replication_record"}},"created_at":"2026-05-18T00:58:04.681887+00:00","updated_at":"2026-05-18T00:58:04.681887+00:00"}