{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3IYMOV7PJALL34RGC5N2OK45JZ","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":"5dfd3a85e09041c013693d51ce9ac811d46694ff1e15a734a6bbd42d1f6bf87a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-06-28T12:30:38Z","title_canon_sha256":"b94192985c887827a7ad8e80213e0b9bbd3e6f1010bf02bac5972acfc10884d2"},"schema_version":"1.0","source":{"id":"1206.6658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6658","created_at":"2026-05-18T03:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6658v1","created_at":"2026-05-18T03:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6658","created_at":"2026-05-18T03:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"3IYMOV7PJALL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3IYMOV7PJALL34RG","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3IYMOV7P","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:05101bfc04cebbe0dc963d77fb82915a2315ad0a32294b87779ed06cb8ad9cd0","target":"graph","created_at":"2026-05-18T03:52:25Z","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":"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","authors_text":"Luai Al Labadi, Mahmoud Zarepour","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-06-28T12:30:38Z","title":"On Some Asymptotic Properties and an Almost Sure Approximation of the Normalized Inverse-Gaussian Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6658","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":"sha256:65197573dd61c869a51152defad8a0519e8d1ea11f0223f3a8a2d7713de6c795","target":"record","created_at":"2026-05-18T03:52:25Z","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":"5dfd3a85e09041c013693d51ce9ac811d46694ff1e15a734a6bbd42d1f6bf87a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-06-28T12:30:38Z","title_canon_sha256":"b94192985c887827a7ad8e80213e0b9bbd3e6f1010bf02bac5972acfc10884d2"},"schema_version":"1.0","source":{"id":"1206.6658","kind":"arxiv","version":1}},"canonical_sha256":"da30c757ef4816bdf226175ba72b9d4e55ff89e78e1067ee6d546b3a2f9ceb61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da30c757ef4816bdf226175ba72b9d4e55ff89e78e1067ee6d546b3a2f9ceb61","first_computed_at":"2026-05-18T03:52:25.323499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:25.323499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rtwuh+GNM1Nu1TtmyijpUDnYb2DateLcuIZX06g6GKW2XmtFBJYI2+uvocBs2dpjwxPSlE39DHQpc4TLuqrLCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:25.324067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65197573dd61c869a51152defad8a0519e8d1ea11f0223f3a8a2d7713de6c795","sha256:05101bfc04cebbe0dc963d77fb82915a2315ad0a32294b87779ed06cb8ad9cd0"],"state_sha256":"0badf1b99adddfd1a18beaab7b43d406e020cfebcf52202d8960021079407520"}