{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UHK34VDLBFX7HHQMS43QNSTWCR","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":"8c1b94daabd7e90c731bfe92a8bd78cd686051e3b616c1ab029c7a91ffa5feb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-08-15T08:03:36Z","title_canon_sha256":"f4c4544c2007913332b41021a132e21a6e61f084fb81bbc42d2ea2669eae7dda"},"schema_version":"1.0","source":{"id":"1408.3490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3490","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3490v1","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3490","created_at":"2026-05-18T02:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"UHK34VDLBFX7","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UHK34VDLBFX7HHQM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UHK34VDL","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:cc895cee8c262bf72d045dfacb363cdabd9efc71d4416b13d512a620d6b1734a","target":"graph","created_at":"2026-05-18T02:45:05Z","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":"Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made. In this paper, Frullani's integral formula is shown to result from mixing a lifetime distribution by allowing the logarithm of the scale factor to be uniformly distributed over a finite range. This gives a class of long-tailed distributions related to slash distributions, where the pdf is simply expressed in terms of the survival function of the `parent' distribution. The resulting survival distributions have all moments finite, and can exhibit the bimodal hazard functions sometimes seen in pract","authors_text":"Rose Baker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-08-15T08:03:36Z","title":"Properties and Applications of some Distributions derived from Frullani's integral"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3490","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":"sha256:74aba1abed7b5adf1a483b070a6ebfddfe370937f16526c4529f236dac0ea23d","target":"record","created_at":"2026-05-18T02:45:05Z","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":"8c1b94daabd7e90c731bfe92a8bd78cd686051e3b616c1ab029c7a91ffa5feb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-08-15T08:03:36Z","title_canon_sha256":"f4c4544c2007913332b41021a132e21a6e61f084fb81bbc42d2ea2669eae7dda"},"schema_version":"1.0","source":{"id":"1408.3490","kind":"arxiv","version":1}},"canonical_sha256":"a1d5be546b096ff39e0c973706ca7614520dfa751a57640ced0412a343d6a444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1d5be546b096ff39e0c973706ca7614520dfa751a57640ced0412a343d6a444","first_computed_at":"2026-05-18T02:45:05.744909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:05.744909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7PKAqfVX5f0XETD1Eft0TmCypbYW1s24wUUF4dD1I5gv/3fLtmhJld8WhAbd6dH0cQsHDJPHERQfZCqHHlBzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:05.745510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74aba1abed7b5adf1a483b070a6ebfddfe370937f16526c4529f236dac0ea23d","sha256:cc895cee8c262bf72d045dfacb363cdabd9efc71d4416b13d512a620d6b1734a"],"state_sha256":"6dffef73bdc57d7140f5ac9492b0f7be6800c15183e71b1655e37f64fc015365"}