{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DOYYNIOTVH23B2ZVHRMFEMOOUQ","short_pith_number":"pith:DOYYNIOT","canonical_record":{"source":{"id":"1807.02201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-06T00:10:49Z","cross_cats_sorted":[],"title_canon_sha256":"a40e86a93d4ab17e1402c467789fd522cfb01988ef21abe82f4b0d598138671d","abstract_canon_sha256":"023124eea2a984f762077c47000050a2e95bf12273082a90aa1d4e8934e0c03f"},"schema_version":"1.0"},"canonical_sha256":"1bb186a1d3a9f5b0eb353c585231cea40691d38750160a5483231b4a8eeea7e8","source":{"kind":"arxiv","id":"1807.02201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02201","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02201v1","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02201","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"DOYYNIOTVH23","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOYYNIOTVH23B2ZV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOYYNIOT","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DOYYNIOTVH23B2ZVHRMFEMOOUQ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.02201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-06T00:10:49Z","cross_cats_sorted":[],"title_canon_sha256":"a40e86a93d4ab17e1402c467789fd522cfb01988ef21abe82f4b0d598138671d","abstract_canon_sha256":"023124eea2a984f762077c47000050a2e95bf12273082a90aa1d4e8934e0c03f"},"schema_version":"1.0"},"canonical_sha256":"1bb186a1d3a9f5b0eb353c585231cea40691d38750160a5483231b4a8eeea7e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:22.844735Z","signature_b64":"00SA8FwxrFO7auP7X75Qlnhpd3QKiZD6UU9yFSyUF8CQIML3aX6IHbmLxTrHb8lZbEoikqqdKM1L3Mun7Y7RDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bb186a1d3a9f5b0eb353c585231cea40691d38750160a5483231b4a8eeea7e8","last_reissued_at":"2026-05-18T00:11:22.844222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:22.844222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.02201","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGmkbPWHiWzJw8v6fqKXUNRucu2NdDjmrLghpzUUk/rsIXp06PHlsvMRGSY7bRIclV3Z9ZSjX/ivLOeMC1YBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:18:40.314095Z"},"content_sha256":"a4d2b73e5e563b2370bad38ad7da4ea5a71e24e9e9360deea2d7958d81547ff6","schema_version":"1.0","event_id":"sha256:a4d2b73e5e563b2370bad38ad7da4ea5a71e24e9e9360deea2d7958d81547ff6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DOYYNIOTVH23B2ZVHRMFEMOOUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monte Carlo Methods for Insurance Risk Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ad Ridder, Shaul Bar-Lev","submitted_at":"2018-07-06T00:10:49Z","abstract_excerpt":"In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF) distribution, and that the random number has a NEF counting distribution with a cubic variance function. This specific modelling is supported by data of the aggregated claim distribution of an insurance company. Large tail probabilities are important as they reflect the risk of large losses, however, analytic or numerical expressions are not available. We propose sev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02201","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flE2xIJOS2nP2ltJYnp3Oir9ANtspwh9fKEWVUvJ959CZiei+3bkg9ABQRikOYsjUiMnJMacKyGHQbo9cBGaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:18:40.314459Z"},"content_sha256":"35f7e66a52d8832efcab5b3d960c7c8d7a84b32647359f9e200fc1167b086d78","schema_version":"1.0","event_id":"sha256:35f7e66a52d8832efcab5b3d960c7c8d7a84b32647359f9e200fc1167b086d78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOYYNIOTVH23B2ZVHRMFEMOOUQ/bundle.json","state_url":"https://pith.science/pith/DOYYNIOTVH23B2ZVHRMFEMOOUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOYYNIOTVH23B2ZVHRMFEMOOUQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T19:18:40Z","links":{"resolver":"https://pith.science/pith/DOYYNIOTVH23B2ZVHRMFEMOOUQ","bundle":"https://pith.science/pith/DOYYNIOTVH23B2ZVHRMFEMOOUQ/bundle.json","state":"https://pith.science/pith/DOYYNIOTVH23B2ZVHRMFEMOOUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOYYNIOTVH23B2ZVHRMFEMOOUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DOYYNIOTVH23B2ZVHRMFEMOOUQ","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":"023124eea2a984f762077c47000050a2e95bf12273082a90aa1d4e8934e0c03f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-06T00:10:49Z","title_canon_sha256":"a40e86a93d4ab17e1402c467789fd522cfb01988ef21abe82f4b0d598138671d"},"schema_version":"1.0","source":{"id":"1807.02201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02201","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02201v1","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02201","created_at":"2026-05-18T00:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"DOYYNIOTVH23","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOYYNIOTVH23B2ZV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOYYNIOT","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:35f7e66a52d8832efcab5b3d960c7c8d7a84b32647359f9e200fc1167b086d78","target":"graph","created_at":"2026-05-18T00:11:22Z","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 consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF) distribution, and that the random number has a NEF counting distribution with a cubic variance function. This specific modelling is supported by data of the aggregated claim distribution of an insurance company. Large tail probabilities are important as they reflect the risk of large losses, however, analytic or numerical expressions are not available. We propose sev","authors_text":"Ad Ridder, Shaul Bar-Lev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-06T00:10:49Z","title":"Monte Carlo Methods for Insurance Risk Computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02201","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:a4d2b73e5e563b2370bad38ad7da4ea5a71e24e9e9360deea2d7958d81547ff6","target":"record","created_at":"2026-05-18T00:11:22Z","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":"023124eea2a984f762077c47000050a2e95bf12273082a90aa1d4e8934e0c03f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-06T00:10:49Z","title_canon_sha256":"a40e86a93d4ab17e1402c467789fd522cfb01988ef21abe82f4b0d598138671d"},"schema_version":"1.0","source":{"id":"1807.02201","kind":"arxiv","version":1}},"canonical_sha256":"1bb186a1d3a9f5b0eb353c585231cea40691d38750160a5483231b4a8eeea7e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bb186a1d3a9f5b0eb353c585231cea40691d38750160a5483231b4a8eeea7e8","first_computed_at":"2026-05-18T00:11:22.844222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:22.844222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"00SA8FwxrFO7auP7X75Qlnhpd3QKiZD6UU9yFSyUF8CQIML3aX6IHbmLxTrHb8lZbEoikqqdKM1L3Mun7Y7RDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:22.844735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4d2b73e5e563b2370bad38ad7da4ea5a71e24e9e9360deea2d7958d81547ff6","sha256:35f7e66a52d8832efcab5b3d960c7c8d7a84b32647359f9e200fc1167b086d78"],"state_sha256":"b65cc1915007b565f9d2f45a10df21970e14cf82386d524b48d1f9d1e3f2215f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/G2onXsf2NzrMQ++q5JAxChTyKSao+cQfcZiylKJSbjPyZEgWKXmeyxohQHZkuSMGZk1+Hzs0KGuCZ27wM8tCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:18:40.316372Z","bundle_sha256":"efaf5691834cc382726c0889453af71245bf9b517d38510c059d783cc26a8e78"}}