{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C3THFQHCG5S5IZQCKL4RA2IMRC","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":"75d09b096f88661e28a2e275be66adcd4962b49fa08d60107e8b391f613e281f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T18:47:24Z","title_canon_sha256":"00188c1727e27f88d35840b3f0728e5a790579893d81804dc82cf8ef0b692530"},"schema_version":"1.0","source":{"id":"1503.09160","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.09160","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1503.09160v3","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09160","created_at":"2026-05-18T01:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"C3THFQHCG5S5","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C3THFQHCG5S5IZQC","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C3THFQHC","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:d230a00cd8a9a8f3cca184fd9b5f0ffa2a64bd20370a1e3a398d6a98951eb294","target":"graph","created_at":"2026-05-18T01:29:21Z","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 use the Stein-Chen method to study the extremal behaviour of the problem of extremes for univariate and bivariate geometric laws. We obtain a rate for the convergence to the Gumbel distribution of the law of the maximum of i. i. d. geometric random variables, and show that convergence is faster when approximating by a discretised Gumbel. We similarly find a rate of convergence for the law of maxima of bivariate Marshall-Olkin geometric random pairs when approximating by a discrete limit law. We introduce marked point processes of exceedances (MPPEs), both with univariate and bivariate Marsh","authors_text":"Alessandra Cipriani, Anne Feidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T18:47:24Z","title":"Rates of convergence for extremes of geometric random variables and marked point processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09160","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:f356aaf4ceb24d3f4584d738833dc36ba6a4bec12be27ebe3f4824af8aa2c6b4","target":"record","created_at":"2026-05-18T01:29:21Z","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":"75d09b096f88661e28a2e275be66adcd4962b49fa08d60107e8b391f613e281f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T18:47:24Z","title_canon_sha256":"00188c1727e27f88d35840b3f0728e5a790579893d81804dc82cf8ef0b692530"},"schema_version":"1.0","source":{"id":"1503.09160","kind":"arxiv","version":3}},"canonical_sha256":"16e672c0e23765d4660252f910690c8883b01ed0b8e41ccc55ebf4ff3e420eb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16e672c0e23765d4660252f910690c8883b01ed0b8e41ccc55ebf4ff3e420eb3","first_computed_at":"2026-05-18T01:29:21.208430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:21.208430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QKMY+K4QVC1m2WOBu7K9i8zc8Sli/tIznoiqQaiMTqHuBmt6OT0CLFC+PnrYY0KEr8mElSD9cnE4bzzR7ZqSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:21.209152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.09160","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f356aaf4ceb24d3f4584d738833dc36ba6a4bec12be27ebe3f4824af8aa2c6b4","sha256:d230a00cd8a9a8f3cca184fd9b5f0ffa2a64bd20370a1e3a398d6a98951eb294"],"state_sha256":"caafd0c6fef3d2e7cb5e5b523a3c34336f2408e93ab75ec4547c90197751dc34"}