{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IKSOX6V3467UKIAB2WPEWONQCP","short_pith_number":"pith:IKSOX6V3","canonical_record":{"source":{"id":"1009.2022","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-09-10T14:35:47Z","cross_cats_sorted":["stat.CO","stat.TH"],"title_canon_sha256":"e8a0f7c7c9053d1795ebd667729f2ec084aad52992cd2a3d1bb2ba8990f47de5","abstract_canon_sha256":"82dab9b1e2b4c8d2934ffdf4bb6a8c648be0e6a3cb95980a18da7784217c6f34"},"schema_version":"1.0"},"canonical_sha256":"42a4ebfabbe7bf452001d59e4b39b013fb96f4112f50d46f74e7dd602f485407","source":{"kind":"arxiv","id":"1009.2022","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2022","created_at":"2026-05-17T23:58:15Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2022v3","created_at":"2026-05-17T23:58:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2022","created_at":"2026-05-17T23:58:15Z"},{"alias_kind":"pith_short_12","alias_value":"IKSOX6V3467U","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IKSOX6V3467UKIAB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IKSOX6V3","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IKSOX6V3467UKIAB2WPEWONQCP","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2022","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-09-10T14:35:47Z","cross_cats_sorted":["stat.CO","stat.TH"],"title_canon_sha256":"e8a0f7c7c9053d1795ebd667729f2ec084aad52992cd2a3d1bb2ba8990f47de5","abstract_canon_sha256":"82dab9b1e2b4c8d2934ffdf4bb6a8c648be0e6a3cb95980a18da7784217c6f34"},"schema_version":"1.0"},"canonical_sha256":"42a4ebfabbe7bf452001d59e4b39b013fb96f4112f50d46f74e7dd602f485407","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:15.566256Z","signature_b64":"AyXxt1Qil9by1w2FhTT1MmWZsH4zk1g3rLCAK7JwikVXAt0hKIO43U8NmXmaCXEwOshtuVeOnztTaK/SpSP9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42a4ebfabbe7bf452001d59e4b39b013fb96f4112f50d46f74e7dd602f485407","last_reissued_at":"2026-05-17T23:58:15.565702Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:15.565702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2022","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1E3JqJZ0QD/zP8UTJipYtmEQOZ0UNsaniAEthpRp7uxVRAPy7BFPaDBBKb06e30t2/CQF2sBGzcMgoi+18fCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:05:35.883051Z"},"content_sha256":"ccc4b077fc7492f966c69be5ffa47a8bd86d34132651743742c80e359ff2b5e6","schema_version":"1.0","event_id":"sha256:ccc4b077fc7492f966c69be5ffa47a8bd86d34132651743742c80e359ff2b5e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IKSOX6V3467UKIAB2WPEWONQCP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Luis Mendo","submitted_at":"2010-09-10T14:35:47Z","abstract_excerpt":"Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\\hat p<p$ and $\\hat p>p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p$ tends to $0$, and which guaran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2022","kind":"arxiv","version":3},"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":"2026-05-17T23:58:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PCJBB/iec/saK6H0Ooa5M81TobvYy+vLnHT31OwZ2eK2BlM4PyxnwPdsrthHnY/8r5t4AIo41lIeeFu7SrtGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:05:35.883821Z"},"content_sha256":"9bdf73843c55067129ab8c7ae37c6108f1229727adbb65a2e22a1e0b47fbea11","schema_version":"1.0","event_id":"sha256:9bdf73843c55067129ab8c7ae37c6108f1229727adbb65a2e22a1e0b47fbea11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKSOX6V3467UKIAB2WPEWONQCP/bundle.json","state_url":"https://pith.science/pith/IKSOX6V3467UKIAB2WPEWONQCP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKSOX6V3467UKIAB2WPEWONQCP/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":"2026-06-11T20:05:35Z","links":{"resolver":"https://pith.science/pith/IKSOX6V3467UKIAB2WPEWONQCP","bundle":"https://pith.science/pith/IKSOX6V3467UKIAB2WPEWONQCP/bundle.json","state":"https://pith.science/pith/IKSOX6V3467UKIAB2WPEWONQCP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKSOX6V3467UKIAB2WPEWONQCP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IKSOX6V3467UKIAB2WPEWONQCP","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":"82dab9b1e2b4c8d2934ffdf4bb6a8c648be0e6a3cb95980a18da7784217c6f34","cross_cats_sorted":["stat.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-09-10T14:35:47Z","title_canon_sha256":"e8a0f7c7c9053d1795ebd667729f2ec084aad52992cd2a3d1bb2ba8990f47de5"},"schema_version":"1.0","source":{"id":"1009.2022","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2022","created_at":"2026-05-17T23:58:15Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2022v3","created_at":"2026-05-17T23:58:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2022","created_at":"2026-05-17T23:58:15Z"},{"alias_kind":"pith_short_12","alias_value":"IKSOX6V3467U","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IKSOX6V3467UKIAB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IKSOX6V3","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:9bdf73843c55067129ab8c7ae37c6108f1229727adbb65a2e22a1e0b47fbea11","target":"graph","created_at":"2026-05-17T23:58:15Z","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":"Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\\hat p<p$ and $\\hat p>p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p$ tends to $0$, and which guaran","authors_text":"Luis Mendo","cross_cats":["stat.CO","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-09-10T14:35:47Z","title":"Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2022","kind":"arxiv","version":3},"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:ccc4b077fc7492f966c69be5ffa47a8bd86d34132651743742c80e359ff2b5e6","target":"record","created_at":"2026-05-17T23:58:15Z","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":"82dab9b1e2b4c8d2934ffdf4bb6a8c648be0e6a3cb95980a18da7784217c6f34","cross_cats_sorted":["stat.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-09-10T14:35:47Z","title_canon_sha256":"e8a0f7c7c9053d1795ebd667729f2ec084aad52992cd2a3d1bb2ba8990f47de5"},"schema_version":"1.0","source":{"id":"1009.2022","kind":"arxiv","version":3}},"canonical_sha256":"42a4ebfabbe7bf452001d59e4b39b013fb96f4112f50d46f74e7dd602f485407","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42a4ebfabbe7bf452001d59e4b39b013fb96f4112f50d46f74e7dd602f485407","first_computed_at":"2026-05-17T23:58:15.565702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:15.565702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AyXxt1Qil9by1w2FhTT1MmWZsH4zk1g3rLCAK7JwikVXAt0hKIO43U8NmXmaCXEwOshtuVeOnztTaK/SpSP9BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:15.566256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2022","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccc4b077fc7492f966c69be5ffa47a8bd86d34132651743742c80e359ff2b5e6","sha256:9bdf73843c55067129ab8c7ae37c6108f1229727adbb65a2e22a1e0b47fbea11"],"state_sha256":"4bfe342dce2e3bdd0d6e64a4aaea2744b2a4d33f39fa7f4062eeae114edf0080"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/so9KelTzbPnyO292NYB/xqbRO8wgpcL9D2FHa0Jt+HwP7RQj6b+Psqn9CPGufDnuHDxJs9LwuYMjiRrlV0CCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:05:35.888253Z","bundle_sha256":"bb89197c600a4d6b5809a01c4812515b13636ef94097318d5e1db2ceff3a62ce"}}