{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:QKVEBVJFVDE6SMCRFPBTM6TCVQ","short_pith_number":"pith:QKVEBVJF","canonical_record":{"source":{"id":"0809.1894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-09-10T23:02:32Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"9115821abec1dff1943acaaf4500486ed2429e526d39cc1b112d72b2c838bd0b","abstract_canon_sha256":"e23245ca74f2b2720dd11cd0ff27fd540f97a979d689947c81fcefe8eb4844c9"},"schema_version":"1.0"},"canonical_sha256":"82aa40d525a8c9e930512bc3367a62ac3432c636292255e7d6ed8b8a0060ecfc","source":{"kind":"arxiv","id":"0809.1894","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.1894","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"0809.1894v1","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1894","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"QKVEBVJFVDE6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QKVEBVJFVDE6SMCR","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QKVEBVJF","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:QKVEBVJFVDE6SMCRFPBTM6TCVQ","target":"record","payload":{"canonical_record":{"source":{"id":"0809.1894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-09-10T23:02:32Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"9115821abec1dff1943acaaf4500486ed2429e526d39cc1b112d72b2c838bd0b","abstract_canon_sha256":"e23245ca74f2b2720dd11cd0ff27fd540f97a979d689947c81fcefe8eb4844c9"},"schema_version":"1.0"},"canonical_sha256":"82aa40d525a8c9e930512bc3367a62ac3432c636292255e7d6ed8b8a0060ecfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:13.998174Z","signature_b64":"4PNECtuNWBJbpLkz6riESk95QfC1ohYUmAgUfPJSz/RLc/qUrLzqpyqO6E/P8WIPVsIe1m9sf4lZPV6pWxtrDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82aa40d525a8c9e930512bc3367a62ac3432c636292255e7d6ed8b8a0060ecfc","last_reissued_at":"2026-05-18T04:42:13.997604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:13.997604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.1894","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":"2026-05-18T04:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zcqewNFBy2FjuZBPfwn/VTyVCZm1exiMOwtLOg+vtAYZgOvyzfEHSIwJ0Ck5VcJmNu20eP8tFmTX6QQ/NGmUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:12:25.142729Z"},"content_sha256":"fd53c05916941a49415c3c0e23d271748b2f37dc687bbcdfbbc46e480959b313","schema_version":"1.0","event_id":"sha256:fd53c05916941a49415c3c0e23d271748b2f37dc687bbcdfbbc46e480959b313"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:QKVEBVJFVDE6SMCRFPBTM6TCVQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Generalization of the Exponential-Poisson Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"stat.ME","authors_text":"Francisco Cribari-Neto, Wagner Barreto-Souza","submitted_at":"2008-09-10T23:02:32Z","abstract_excerpt":"The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new distribution can be decreasing or increasing. The failure rate can also be upside-down bathtub shaped. A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival and failure rate functions; we also obtain the density of the $i$th order statistic. We derive the $r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1894","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":"2026-05-18T04:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5GJA6w0GdXWk+NF2nhXbCHT/CQCds5gdJR9yVD/Q/e+D070kpvrLAnI7IeE9zBz9ymK+ujags8IInk7Md80CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:12:25.143077Z"},"content_sha256":"f47a0916aacb22ce8666f3d07180805eaca8f2596bfa6ce8f062e4be511900f2","schema_version":"1.0","event_id":"sha256:f47a0916aacb22ce8666f3d07180805eaca8f2596bfa6ce8f062e4be511900f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKVEBVJFVDE6SMCRFPBTM6TCVQ/bundle.json","state_url":"https://pith.science/pith/QKVEBVJFVDE6SMCRFPBTM6TCVQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKVEBVJFVDE6SMCRFPBTM6TCVQ/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":"2026-06-02T03:12:25Z","links":{"resolver":"https://pith.science/pith/QKVEBVJFVDE6SMCRFPBTM6TCVQ","bundle":"https://pith.science/pith/QKVEBVJFVDE6SMCRFPBTM6TCVQ/bundle.json","state":"https://pith.science/pith/QKVEBVJFVDE6SMCRFPBTM6TCVQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKVEBVJFVDE6SMCRFPBTM6TCVQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QKVEBVJFVDE6SMCRFPBTM6TCVQ","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":"e23245ca74f2b2720dd11cd0ff27fd540f97a979d689947c81fcefe8eb4844c9","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-09-10T23:02:32Z","title_canon_sha256":"9115821abec1dff1943acaaf4500486ed2429e526d39cc1b112d72b2c838bd0b"},"schema_version":"1.0","source":{"id":"0809.1894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.1894","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"0809.1894v1","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1894","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"QKVEBVJFVDE6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QKVEBVJFVDE6SMCR","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QKVEBVJF","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:f47a0916aacb22ce8666f3d07180805eaca8f2596bfa6ce8f062e4be511900f2","target":"graph","created_at":"2026-05-18T04:42:13Z","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":"The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new distribution can be decreasing or increasing. The failure rate can also be upside-down bathtub shaped. A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival and failure rate functions; we also obtain the density of the $i$th order statistic. We derive the $r","authors_text":"Francisco Cribari-Neto, Wagner Barreto-Souza","cross_cats":["stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-09-10T23:02:32Z","title":"A Generalization of the Exponential-Poisson Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1894","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:fd53c05916941a49415c3c0e23d271748b2f37dc687bbcdfbbc46e480959b313","target":"record","created_at":"2026-05-18T04:42:13Z","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":"e23245ca74f2b2720dd11cd0ff27fd540f97a979d689947c81fcefe8eb4844c9","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2008-09-10T23:02:32Z","title_canon_sha256":"9115821abec1dff1943acaaf4500486ed2429e526d39cc1b112d72b2c838bd0b"},"schema_version":"1.0","source":{"id":"0809.1894","kind":"arxiv","version":1}},"canonical_sha256":"82aa40d525a8c9e930512bc3367a62ac3432c636292255e7d6ed8b8a0060ecfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82aa40d525a8c9e930512bc3367a62ac3432c636292255e7d6ed8b8a0060ecfc","first_computed_at":"2026-05-18T04:42:13.997604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:13.997604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4PNECtuNWBJbpLkz6riESk95QfC1ohYUmAgUfPJSz/RLc/qUrLzqpyqO6E/P8WIPVsIe1m9sf4lZPV6pWxtrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:13.998174Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.1894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd53c05916941a49415c3c0e23d271748b2f37dc687bbcdfbbc46e480959b313","sha256:f47a0916aacb22ce8666f3d07180805eaca8f2596bfa6ce8f062e4be511900f2"],"state_sha256":"345ae968cd7213c10f4cbe069836051757a1547aa5ee08542537096322590be1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AIQvhOaMbd7nRsTq6CDr8EorjmnGTWtWOYt3Embp7Wj/+/Ew/zEpX4bnOSSS5hs/R3qMACidG9Q7gJ2+YfcFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:12:25.145119Z","bundle_sha256":"12dfd101eeb3d923bd2672e5f24a39417c18d192bcab2d0d1b2b344144032bcd"}}