{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3IYMOV7PJALL34RGC5N2OK45JZ","short_pith_number":"pith:3IYMOV7P","schema_version":"1.0","canonical_sha256":"da30c757ef4816bdf226175ba72b9d4e55ff89e78e1067ee6d546b3a2f9ceb61","source":{"kind":"arxiv","id":"1206.6658","version":1},"attestation_state":"computed","paper":{"title":"On Some Asymptotic Properties and an Almost Sure Approximation of the Normalized Inverse-Gaussian Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Luai Al Labadi, Mahmoud Zarepour","submitted_at":"2012-06-28T12:30:38Z","abstract_excerpt":"In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem for the normalized inverse-Gaussian process and its corresponding quantile process. We also derive a finite sum-representation that converges almost surely to the Ferguson and Klass representation of the normalized inverse-Gaussian process. This almost sure approximation can be used to simulate efficie"},"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":"1206.6658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-06-28T12:30:38Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b94192985c887827a7ad8e80213e0b9bbd3e6f1010bf02bac5972acfc10884d2","abstract_canon_sha256":"5dfd3a85e09041c013693d51ce9ac811d46694ff1e15a734a6bbd42d1f6bf87a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:25.324067Z","signature_b64":"rtwuh+GNM1Nu1TtmyijpUDnYb2DateLcuIZX06g6GKW2XmtFBJYI2+uvocBs2dpjwxPSlE39DHQpc4TLuqrLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da30c757ef4816bdf226175ba72b9d4e55ff89e78e1067ee6d546b3a2f9ceb61","last_reissued_at":"2026-05-18T03:52:25.323499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:25.323499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Some Asymptotic Properties and an Almost Sure Approximation of the Normalized Inverse-Gaussian Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Luai Al Labadi, Mahmoud Zarepour","submitted_at":"2012-06-28T12:30:38Z","abstract_excerpt":"In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem for the normalized inverse-Gaussian process and its corresponding quantile process. We also derive a finite sum-representation that converges almost surely to the Ferguson and Klass representation of the normalized inverse-Gaussian process. This almost sure approximation can be used to simulate efficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6658","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":"1206.6658","created_at":"2026-05-18T03:52:25.323585+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.6658v1","created_at":"2026-05-18T03:52:25.323585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6658","created_at":"2026-05-18T03:52:25.323585+00:00"},{"alias_kind":"pith_short_12","alias_value":"3IYMOV7PJALL","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"3IYMOV7PJALL34RG","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"3IYMOV7P","created_at":"2026-05-18T12:26:50.516681+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/3IYMOV7PJALL34RGC5N2OK45JZ","json":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ.json","graph_json":"https://pith.science/api/pith-number/3IYMOV7PJALL34RGC5N2OK45JZ/graph.json","events_json":"https://pith.science/api/pith-number/3IYMOV7PJALL34RGC5N2OK45JZ/events.json","paper":"https://pith.science/paper/3IYMOV7P"},"agent_actions":{"view_html":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ","download_json":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ.json","view_paper":"https://pith.science/paper/3IYMOV7P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.6658&json=true","fetch_graph":"https://pith.science/api/pith-number/3IYMOV7PJALL34RGC5N2OK45JZ/graph.json","fetch_events":"https://pith.science/api/pith-number/3IYMOV7PJALL34RGC5N2OK45JZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ/action/storage_attestation","attest_author":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ/action/author_attestation","sign_citation":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ/action/citation_signature","submit_replication":"https://pith.science/pith/3IYMOV7PJALL34RGC5N2OK45JZ/action/replication_record"}},"created_at":"2026-05-18T03:52:25.323585+00:00","updated_at":"2026-05-18T03:52:25.323585+00:00"}