{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6FEHB6XKY3FUSKTSQJI25QLZ4T","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":"324a87182a2a27e3d66222265548eaa62b13a115b4d121004532eb6d2d9b8ced","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T10:25:27Z","title_canon_sha256":"aa825b0ea55b5648ea650d218a53971ae1dffb88cc4990f6fa6cd6208f47cffc"},"schema_version":"1.0","source":{"id":"1102.2072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2072","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2072v1","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2072","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"6FEHB6XKY3FU","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6FEHB6XKY3FUSKTS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6FEHB6XK","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:4bd8c82c0cd3c9afe31ca2bf9cff3ce4f33bf06ea1cf98396d488af4cc04fda8","target":"graph","created_at":"2026-05-18T04:29:34Z","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":"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","authors_text":"Fredrik Jonsson","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T10:25:27Z","title":"On the heavy-tailedness of Student's $t$-statistic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2072","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:bc0127c54706122e2de4945537ee016dee801f99348d9a94d289495862b0acbd","target":"record","created_at":"2026-05-18T04:29:34Z","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":"324a87182a2a27e3d66222265548eaa62b13a115b4d121004532eb6d2d9b8ced","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T10:25:27Z","title_canon_sha256":"aa825b0ea55b5648ea650d218a53971ae1dffb88cc4990f6fa6cd6208f47cffc"},"schema_version":"1.0","source":{"id":"1102.2072","kind":"arxiv","version":1}},"canonical_sha256":"f14870faeac6cb492a728251aec179e4de4dcd5e0dadac1a30d851d7898a21d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f14870faeac6cb492a728251aec179e4de4dcd5e0dadac1a30d851d7898a21d3","first_computed_at":"2026-05-18T04:29:34.335829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:34.335829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ae1b/ehrVwAubUIcw6TteRs/1uY8LRy8vVfqn8AxLjSfxluZFeIMTOuHqlgZGFIZomJzqpjJw1pCqjTsbEgBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:34.336274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc0127c54706122e2de4945537ee016dee801f99348d9a94d289495862b0acbd","sha256:4bd8c82c0cd3c9afe31ca2bf9cff3ce4f33bf06ea1cf98396d488af4cc04fda8"],"state_sha256":"78b474825b5c63aee89b2ebe932464630a7725f04f0389529fbc34d4f9354477"}