{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OX5WWZYYAU2DG2OW2OQ6PECAYV","short_pith_number":"pith:OX5WWZYY","canonical_record":{"source":{"id":"1908.08764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2019-08-23T11:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"15b40f217c2d155a2efc0672d55705504c0fff478cc6304bd779057db9abed19","abstract_canon_sha256":"5e155a0336b552cedb47326374963269a439b490f632ec86da861c91d6042052"},"schema_version":"1.0"},"canonical_sha256":"75fb6b671805343369d6d3a1e79040c543fd275f2db6edb241d65c6d59d0651d","source":{"kind":"arxiv","id":"1908.08764","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08764","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08764v1","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08764","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"pith_short_12","alias_value":"OX5WWZYYAU2D","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"pith_short_16","alias_value":"OX5WWZYYAU2DG2OW","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"pith_short_8","alias_value":"OX5WWZYY","created_at":"2026-07-04T23:59:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OX5WWZYYAU2DG2OW2OQ6PECAYV","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2019-08-23T11:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"15b40f217c2d155a2efc0672d55705504c0fff478cc6304bd779057db9abed19","abstract_canon_sha256":"5e155a0336b552cedb47326374963269a439b490f632ec86da861c91d6042052"},"schema_version":"1.0"},"canonical_sha256":"75fb6b671805343369d6d3a1e79040c543fd275f2db6edb241d65c6d59d0651d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:23.940276Z","signature_b64":"s22XSIwREZ4woN1LsgohZ4xwWfB6O/klqUVicJaODBnGRWZK4x5GIrbJL+GrJ6q3rXHjwChUXgxyN+SJYDUIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75fb6b671805343369d6d3a1e79040c543fd275f2db6edb241d65c6d59d0651d","last_reissued_at":"2026-07-04T23:59:23.939907Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:23.939907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08764","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":"2026-07-04T23:59:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PIpeE+ZpU8HesR5n20OV5gZqdkjpR7uVqw6FBQXxaayyJKkU/QU4LISDdhHszpuCA8QuWOr7IH64ZEEHfD8iCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:16:08.836417Z"},"content_sha256":"5d80cfc4e5116fbb17024722b6ef8b42124ecbef58129b775bf037af543b798e","schema_version":"1.0","event_id":"sha256:5d80cfc4e5116fbb17024722b6ef8b42124ecbef58129b775bf037af543b798e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OX5WWZYYAU2DG2OW2OQ6PECAYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Poisson-exponential-Tweedie models for ultra-overdispersed data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Afif Masmoudi, Celestin C. Kokonendji, Rahma Abid","submitted_at":"2019-08-23T11:39:22Z","abstract_excerpt":"We introduce a new class of Poisson-exponential-Tweedie (PET) mixture in the framework of generalized linear models for ultra-overdispersed count data. The mean-variance relationship is of the form $m+m^{2}+\\phi m^{p}$, where $\\phi$ and $p$ are the dispersion and Tweedie power parameters, respectively. The proposed model is equivalent to the exponential-Poisson-Tweedie models arising from geometric sums of Poisson-Tweedie random variables. In this respect, the PET models encompass the geometric versions of Hermite, Neyman Type A, P\\'{o}lya-Aeppli, negative binomial and Poisson inverse Gaussian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08764","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08764/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:59:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVKwWO5gW0Y1hOI8EvBI3NNEmWgDaCbgG/JTJSVEOZap/YOUmpBjh5b6ZRIVDr2bKu8zVkUjQUczCEIWv2a0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:16:08.837191Z"},"content_sha256":"de7c08289406217b491866e0655337a2ee5bf2689d2eb9e112f26ebd3b1e3a94","schema_version":"1.0","event_id":"sha256:de7c08289406217b491866e0655337a2ee5bf2689d2eb9e112f26ebd3b1e3a94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OX5WWZYYAU2DG2OW2OQ6PECAYV/bundle.json","state_url":"https://pith.science/pith/OX5WWZYYAU2DG2OW2OQ6PECAYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OX5WWZYYAU2DG2OW2OQ6PECAYV/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":"2026-08-16T06:16:08Z","links":{"resolver":"https://pith.science/pith/OX5WWZYYAU2DG2OW2OQ6PECAYV","bundle":"https://pith.science/pith/OX5WWZYYAU2DG2OW2OQ6PECAYV/bundle.json","state":"https://pith.science/pith/OX5WWZYYAU2DG2OW2OQ6PECAYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OX5WWZYYAU2DG2OW2OQ6PECAYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OX5WWZYYAU2DG2OW2OQ6PECAYV","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":"5e155a0336b552cedb47326374963269a439b490f632ec86da861c91d6042052","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2019-08-23T11:39:22Z","title_canon_sha256":"15b40f217c2d155a2efc0672d55705504c0fff478cc6304bd779057db9abed19"},"schema_version":"1.0","source":{"id":"1908.08764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08764","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08764v1","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08764","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"pith_short_12","alias_value":"OX5WWZYYAU2D","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"pith_short_16","alias_value":"OX5WWZYYAU2DG2OW","created_at":"2026-07-04T23:59:23Z"},{"alias_kind":"pith_short_8","alias_value":"OX5WWZYY","created_at":"2026-07-04T23:59:23Z"}],"graph_snapshots":[{"event_id":"sha256:de7c08289406217b491866e0655337a2ee5bf2689d2eb9e112f26ebd3b1e3a94","target":"graph","created_at":"2026-07-04T23:59:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.08764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new class of Poisson-exponential-Tweedie (PET) mixture in the framework of generalized linear models for ultra-overdispersed count data. The mean-variance relationship is of the form $m+m^{2}+\\phi m^{p}$, where $\\phi$ and $p$ are the dispersion and Tweedie power parameters, respectively. The proposed model is equivalent to the exponential-Poisson-Tweedie models arising from geometric sums of Poisson-Tweedie random variables. In this respect, the PET models encompass the geometric versions of Hermite, Neyman Type A, P\\'{o}lya-Aeppli, negative binomial and Poisson inverse Gaussian","authors_text":"Afif Masmoudi, Celestin C. Kokonendji, Rahma Abid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2019-08-23T11:39:22Z","title":"On Poisson-exponential-Tweedie models for ultra-overdispersed data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08764","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":"sha256:5d80cfc4e5116fbb17024722b6ef8b42124ecbef58129b775bf037af543b798e","target":"record","created_at":"2026-07-04T23:59:23Z","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":"5e155a0336b552cedb47326374963269a439b490f632ec86da861c91d6042052","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2019-08-23T11:39:22Z","title_canon_sha256":"15b40f217c2d155a2efc0672d55705504c0fff478cc6304bd779057db9abed19"},"schema_version":"1.0","source":{"id":"1908.08764","kind":"arxiv","version":1}},"canonical_sha256":"75fb6b671805343369d6d3a1e79040c543fd275f2db6edb241d65c6d59d0651d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75fb6b671805343369d6d3a1e79040c543fd275f2db6edb241d65c6d59d0651d","first_computed_at":"2026-07-04T23:59:23.939907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:23.939907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s22XSIwREZ4woN1LsgohZ4xwWfB6O/klqUVicJaODBnGRWZK4x5GIrbJL+GrJ6q3rXHjwChUXgxyN+SJYDUIDw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:23.940276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d80cfc4e5116fbb17024722b6ef8b42124ecbef58129b775bf037af543b798e","sha256:de7c08289406217b491866e0655337a2ee5bf2689d2eb9e112f26ebd3b1e3a94"],"state_sha256":"f84d7af9a87c1ef0dedbd979e2b48b8a499abff66d9f58f433ff42b1e9b6437b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zFTcWEFgG7cQqdnwtZMZEhb18L1y9LR+xqQrlKdlroep/qn/S6+RJKwsnxAFtywytGxb/Ga1/jW3JYOUZNgBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T06:16:08.843410Z","bundle_sha256":"c791f9d48b0643df8fe63b246ea4d39396c0a28f1f1f1c5578f1d72e42a7a061"}}