{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:NWIGS3MQEQQJYDFFXA2RCORURF","short_pith_number":"pith:NWIGS3MQ","schema_version":"1.0","canonical_sha256":"6d90696d9024209c0ca5b835113a34896361cefaf4ffdbfc0856d89cb0f1ac6b","source":{"kind":"arxiv","id":"1905.04955","version":4},"attestation_state":"computed","paper":{"title":"Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Hien Nguyen, Julyan Arbel, Mariia Vladimirova, Stephane Girard","submitted_at":"2019-05-13T10:49:32Z","abstract_excerpt":"We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to potentially heavier-tailed distributions. Sub-Weibull distributions are parameterized by a positive tail index $\\theta$ and reduce to sub-Gaussian distributions for $\\theta=1/2$ and to sub-Exponential distributions for $\\theta=1$. A characterisation of the sub-Weibull property based on moments and on the moment generating function is provided and properties "},"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":"1905.04955","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-05-13T10:49:32Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f0a383251f2f87c6b032b47156b33b95600d47262dc66020d041aa53bc9a4935","abstract_canon_sha256":"eee0eeeffbd4f341d58f930ab9116cc6e4c4f16590dd310122969334243fadc5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:56:39.835086Z","signature_b64":"oCyyu33caYcjx7O77U1P91FQZ83UlHCdcTjEZC8pg3rjS6KMlAI3FnXohc6tPK8/3hBfL+KhOJEVoMPPY6MNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d90696d9024209c0ca5b835113a34896361cefaf4ffdbfc0856d89cb0f1ac6b","last_reissued_at":"2026-07-05T01:56:39.834646Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:56:39.834646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Hien Nguyen, Julyan Arbel, Mariia Vladimirova, Stephane Girard","submitted_at":"2019-05-13T10:49:32Z","abstract_excerpt":"We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to potentially heavier-tailed distributions. Sub-Weibull distributions are parameterized by a positive tail index $\\theta$ and reduce to sub-Gaussian distributions for $\\theta=1/2$ and to sub-Exponential distributions for $\\theta=1$. A characterisation of the sub-Weibull property based on moments and on the moment generating function is provided and properties "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04955","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.04955/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1905.04955","created_at":"2026-07-05T01:56:39.834706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04955v4","created_at":"2026-07-05T01:56:39.834706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04955","created_at":"2026-07-05T01:56:39.834706+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWIGS3MQEQQJ","created_at":"2026-07-05T01:56:39.834706+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWIGS3MQEQQJYDFF","created_at":"2026-07-05T01:56:39.834706+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWIGS3MQ","created_at":"2026-07-05T01:56:39.834706+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.17593","citing_title":"Post-Screening Portfolio Selection","ref_index":129,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF","json":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF.json","graph_json":"https://pith.science/api/pith-number/NWIGS3MQEQQJYDFFXA2RCORURF/graph.json","events_json":"https://pith.science/api/pith-number/NWIGS3MQEQQJYDFFXA2RCORURF/events.json","paper":"https://pith.science/paper/NWIGS3MQ"},"agent_actions":{"view_html":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF","download_json":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF.json","view_paper":"https://pith.science/paper/NWIGS3MQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04955&json=true","fetch_graph":"https://pith.science/api/pith-number/NWIGS3MQEQQJYDFFXA2RCORURF/graph.json","fetch_events":"https://pith.science/api/pith-number/NWIGS3MQEQQJYDFFXA2RCORURF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF/action/storage_attestation","attest_author":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF/action/author_attestation","sign_citation":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF/action/citation_signature","submit_replication":"https://pith.science/pith/NWIGS3MQEQQJYDFFXA2RCORURF/action/replication_record"}},"created_at":"2026-07-05T01:56:39.834706+00:00","updated_at":"2026-07-05T01:56:39.834706+00:00"}