{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:6FEHB6XKY3FUSKTSQJI25QLZ4T","short_pith_number":"pith:6FEHB6XK","schema_version":"1.0","canonical_sha256":"f14870faeac6cb492a728251aec179e4de4dcd5e0dadac1a30d851d7898a21d3","source":{"kind":"arxiv","id":"1102.2072","version":1},"attestation_state":"computed","paper":{"title":"On the heavy-tailedness of Student's $t$-statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Fredrik Jonsson","submitted_at":"2011-02-10T10:25:27Z","abstract_excerpt":"Let $\\{X_i\\}_{i\\geq1}$ be an i.i.d. sequence of random variables and define, for $n\\geq2$, \\[T_n=\\cases{n^{-1/2}\\hat{\\sigma}_n^{-1}S_n,\\quad \\hat{\\sigma}_n>0,\\cr 0,\\quad \\hat{\\sigma}_n=0,}with S_n=\\sum_{i=1}^nX_i, \\hat{\\sigma}^2_n=\\frac{1}{n-1}\\sum_{i=1}^n(X_i-n^{-1}S_n)^2.\\] We investigate the connection between the distribution of an observation $X_i$ and finiteness of $\\mathrm{E}|T_n|^r$ for $(n,r)\\in \\mathbb{N}_{\\geq2}\\times\\mathbb{R}^+$. Moreover, assuming $T_n\\stackrel{d}{\\longrightarrow}T$, we prove that for any $r>0$, $\\lim_{n\\to\\infty}\\mathrm{E}|T_n|^r=\\mathrm{E}|T|^r<\\infty$, provide"},"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":"1102.2072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T10:25:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"aa825b0ea55b5648ea650d218a53971ae1dffb88cc4990f6fa6cd6208f47cffc","abstract_canon_sha256":"324a87182a2a27e3d66222265548eaa62b13a115b4d121004532eb6d2d9b8ced"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:34.336274Z","signature_b64":"ae1b/ehrVwAubUIcw6TteRs/1uY8LRy8vVfqn8AxLjSfxluZFeIMTOuHqlgZGFIZomJzqpjJw1pCqjTsbEgBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f14870faeac6cb492a728251aec179e4de4dcd5e0dadac1a30d851d7898a21d3","last_reissued_at":"2026-05-18T04:29:34.335829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:34.335829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the heavy-tailedness of Student's $t$-statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Fredrik Jonsson","submitted_at":"2011-02-10T10:25:27Z","abstract_excerpt":"Let $\\{X_i\\}_{i\\geq1}$ be an i.i.d. sequence of random variables and define, for $n\\geq2$, \\[T_n=\\cases{n^{-1/2}\\hat{\\sigma}_n^{-1}S_n,\\quad \\hat{\\sigma}_n>0,\\cr 0,\\quad \\hat{\\sigma}_n=0,}with S_n=\\sum_{i=1}^nX_i, \\hat{\\sigma}^2_n=\\frac{1}{n-1}\\sum_{i=1}^n(X_i-n^{-1}S_n)^2.\\] We investigate the connection between the distribution of an observation $X_i$ and finiteness of $\\mathrm{E}|T_n|^r$ for $(n,r)\\in \\mathbb{N}_{\\geq2}\\times\\mathbb{R}^+$. Moreover, assuming $T_n\\stackrel{d}{\\longrightarrow}T$, we prove that for any $r>0$, $\\lim_{n\\to\\infty}\\mathrm{E}|T_n|^r=\\mathrm{E}|T|^r<\\infty$, provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2072","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":"1102.2072","created_at":"2026-05-18T04:29:34.335895+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.2072v1","created_at":"2026-05-18T04:29:34.335895+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2072","created_at":"2026-05-18T04:29:34.335895+00:00"},{"alias_kind":"pith_short_12","alias_value":"6FEHB6XKY3FU","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6FEHB6XKY3FUSKTS","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6FEHB6XK","created_at":"2026-05-18T12:26:22.705136+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/6FEHB6XKY3FUSKTSQJI25QLZ4T","json":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T.json","graph_json":"https://pith.science/api/pith-number/6FEHB6XKY3FUSKTSQJI25QLZ4T/graph.json","events_json":"https://pith.science/api/pith-number/6FEHB6XKY3FUSKTSQJI25QLZ4T/events.json","paper":"https://pith.science/paper/6FEHB6XK"},"agent_actions":{"view_html":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T","download_json":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T.json","view_paper":"https://pith.science/paper/6FEHB6XK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.2072&json=true","fetch_graph":"https://pith.science/api/pith-number/6FEHB6XKY3FUSKTSQJI25QLZ4T/graph.json","fetch_events":"https://pith.science/api/pith-number/6FEHB6XKY3FUSKTSQJI25QLZ4T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T/action/storage_attestation","attest_author":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T/action/author_attestation","sign_citation":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T/action/citation_signature","submit_replication":"https://pith.science/pith/6FEHB6XKY3FUSKTSQJI25QLZ4T/action/replication_record"}},"created_at":"2026-05-18T04:29:34.335895+00:00","updated_at":"2026-05-18T04:29:34.335895+00:00"}