{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WHG46E323NGGYOAAA3DKDRMINL","short_pith_number":"pith:WHG46E32","canonical_record":{"source":{"id":"1812.04139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-10T22:39:43Z","cross_cats_sorted":[],"title_canon_sha256":"6fae660cfd12670e4bbdd1ebf0fdb301406b3156f58f66f8abbcc3af027a6f64","abstract_canon_sha256":"6bc9c4dbf3c30481e5b353e1bf036963f1c8d841c90191d23a6e8c9c65963342"},"schema_version":"1.0"},"canonical_sha256":"b1cdcf137adb4c6c380006c6a1c5886afbd76311edd6bea6fd82abdb13cebe3f","source":{"kind":"arxiv","id":"1812.04139","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04139","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04139v2","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04139","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"WHG46E323NGG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WHG46E323NGGYOAA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WHG46E32","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WHG46E323NGGYOAAA3DKDRMINL","target":"record","payload":{"canonical_record":{"source":{"id":"1812.04139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-10T22:39:43Z","cross_cats_sorted":[],"title_canon_sha256":"6fae660cfd12670e4bbdd1ebf0fdb301406b3156f58f66f8abbcc3af027a6f64","abstract_canon_sha256":"6bc9c4dbf3c30481e5b353e1bf036963f1c8d841c90191d23a6e8c9c65963342"},"schema_version":"1.0"},"canonical_sha256":"b1cdcf137adb4c6c380006c6a1c5886afbd76311edd6bea6fd82abdb13cebe3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:02.735715Z","signature_b64":"O2ylhYd4yDm3ykI1V419bi1w/utm/FHMk1JN+6ZKLPyLctdHjooMRC+9HsH5lU9YzAvuUtSn4GreAzQ1dpAQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1cdcf137adb4c6c380006c6a1c5886afbd76311edd6bea6fd82abdb13cebe3f","last_reissued_at":"2026-05-17T23:42:02.735041Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:02.735041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.04139","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZuaLzn5AttF9N7h+3KbFPSh3BlWBpEVD4Pify+8QQ2D3VtSRH7s6QGpDsOSR5UrTPbDInrlB3Cya1pafaO5dCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T16:27:17.167383Z"},"content_sha256":"7e9314aae8ec83a533ce3b002f52283ee7982d0e053c54e125080677f27e519d","schema_version":"1.0","event_id":"sha256:7e9314aae8ec83a533ce3b002f52283ee7982d0e053c54e125080677f27e519d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WHG46E323NGGYOAAA3DKDRMINL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inhomogeneous phase--type distributions and heavy tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hansj\\\"org Albrecher, Mogens Bladt","submitted_at":"2018-12-10T22:39:43Z","abstract_excerpt":"We extend the construction principle of phase-type (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In particular, the resulting matrix distributions enable to carry over fitting properties of PH distributions to distributions with heavy tails, providing a general modelling framework for heavy-tail phenomena. We also illustrate the versatility and parsimony of the proposed approach for the modelling of a real-world heavy-tailed fire insurance dataset."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04139","kind":"arxiv","version":2},"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":"2026-05-17T23:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfMwQ32B04tSY5PeVGDsu4KZotSw4UWTUuDeqPrwMZChmeCpT0Bn1tDBPRMrsZTl413SjagNv1iZiSX9Vm4yBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T16:27:17.168020Z"},"content_sha256":"ca26f8feab29050dfd2b4261aff70c04a5ac0e481a0c85c1a07b997262952451","schema_version":"1.0","event_id":"sha256:ca26f8feab29050dfd2b4261aff70c04a5ac0e481a0c85c1a07b997262952451"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHG46E323NGGYOAAA3DKDRMINL/bundle.json","state_url":"https://pith.science/pith/WHG46E323NGGYOAAA3DKDRMINL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHG46E323NGGYOAAA3DKDRMINL/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":"2026-05-22T16:27:17Z","links":{"resolver":"https://pith.science/pith/WHG46E323NGGYOAAA3DKDRMINL","bundle":"https://pith.science/pith/WHG46E323NGGYOAAA3DKDRMINL/bundle.json","state":"https://pith.science/pith/WHG46E323NGGYOAAA3DKDRMINL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHG46E323NGGYOAAA3DKDRMINL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WHG46E323NGGYOAAA3DKDRMINL","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":"6bc9c4dbf3c30481e5b353e1bf036963f1c8d841c90191d23a6e8c9c65963342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-10T22:39:43Z","title_canon_sha256":"6fae660cfd12670e4bbdd1ebf0fdb301406b3156f58f66f8abbcc3af027a6f64"},"schema_version":"1.0","source":{"id":"1812.04139","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04139","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04139v2","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04139","created_at":"2026-05-17T23:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"WHG46E323NGG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WHG46E323NGGYOAA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WHG46E32","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:ca26f8feab29050dfd2b4261aff70c04a5ac0e481a0c85c1a07b997262952451","target":"graph","created_at":"2026-05-17T23:42:02Z","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":"We extend the construction principle of phase-type (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In particular, the resulting matrix distributions enable to carry over fitting properties of PH distributions to distributions with heavy tails, providing a general modelling framework for heavy-tail phenomena. We also illustrate the versatility and parsimony of the proposed approach for the modelling of a real-world heavy-tailed fire insurance dataset.","authors_text":"Hansj\\\"org Albrecher, Mogens Bladt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-10T22:39:43Z","title":"Inhomogeneous phase--type distributions and heavy tails"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04139","kind":"arxiv","version":2},"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":"sha256:7e9314aae8ec83a533ce3b002f52283ee7982d0e053c54e125080677f27e519d","target":"record","created_at":"2026-05-17T23:42:02Z","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":"6bc9c4dbf3c30481e5b353e1bf036963f1c8d841c90191d23a6e8c9c65963342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-10T22:39:43Z","title_canon_sha256":"6fae660cfd12670e4bbdd1ebf0fdb301406b3156f58f66f8abbcc3af027a6f64"},"schema_version":"1.0","source":{"id":"1812.04139","kind":"arxiv","version":2}},"canonical_sha256":"b1cdcf137adb4c6c380006c6a1c5886afbd76311edd6bea6fd82abdb13cebe3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1cdcf137adb4c6c380006c6a1c5886afbd76311edd6bea6fd82abdb13cebe3f","first_computed_at":"2026-05-17T23:42:02.735041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:02.735041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O2ylhYd4yDm3ykI1V419bi1w/utm/FHMk1JN+6ZKLPyLctdHjooMRC+9HsH5lU9YzAvuUtSn4GreAzQ1dpAQCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:02.735715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04139","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e9314aae8ec83a533ce3b002f52283ee7982d0e053c54e125080677f27e519d","sha256:ca26f8feab29050dfd2b4261aff70c04a5ac0e481a0c85c1a07b997262952451"],"state_sha256":"0d6bf81bdd244b889b7cae46e8922632e8d89719f685d0b1370bb82939bac796"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tF0GX24houPVkEVHi/kO4xTLe5zUKg2ZMGeadv3+TIzKo65OlNTxAYN1tErYvc1vIjrzZ11hNjXg46BfFxZAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T16:27:17.171398Z","bundle_sha256":"7e7ce472d3704317bf720f654b2ab1e1af951de88641739da5c07c615a28e31e"}}