{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:C3THFQHCG5S5IZQCKL4RA2IMRC","short_pith_number":"pith:C3THFQHC","schema_version":"1.0","canonical_sha256":"16e672c0e23765d4660252f910690c8883b01ed0b8e41ccc55ebf4ff3e420eb3","source":{"kind":"arxiv","id":"1503.09160","version":3},"attestation_state":"computed","paper":{"title":"Rates of convergence for extremes of geometric random variables and marked point processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alessandra Cipriani, Anne Feidt","submitted_at":"2015-03-31T18:47:24Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.09160","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-31T18:47:24Z","cross_cats_sorted":[],"title_canon_sha256":"00188c1727e27f88d35840b3f0728e5a790579893d81804dc82cf8ef0b692530","abstract_canon_sha256":"75d09b096f88661e28a2e275be66adcd4962b49fa08d60107e8b391f613e281f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:21.209152Z","signature_b64":"QKMY+K4QVC1m2WOBu7K9i8zc8Sli/tIznoiqQaiMTqHuBmt6OT0CLFC+PnrYY0KEr8mElSD9cnE4bzzR7ZqSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e672c0e23765d4660252f910690c8883b01ed0b8e41ccc55ebf4ff3e420eb3","last_reissued_at":"2026-05-18T01:29:21.208430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:21.208430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rates of convergence for extremes of geometric random variables and marked point processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alessandra Cipriani, Anne Feidt","submitted_at":"2015-03-31T18:47:24Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09160","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.09160","created_at":"2026-05-18T01:29:21.208544+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.09160v3","created_at":"2026-05-18T01:29:21.208544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09160","created_at":"2026-05-18T01:29:21.208544+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3THFQHCG5S5","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3THFQHCG5S5IZQC","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3THFQHC","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC","json":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC.json","graph_json":"https://pith.science/api/pith-number/C3THFQHCG5S5IZQCKL4RA2IMRC/graph.json","events_json":"https://pith.science/api/pith-number/C3THFQHCG5S5IZQCKL4RA2IMRC/events.json","paper":"https://pith.science/paper/C3THFQHC"},"agent_actions":{"view_html":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC","download_json":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC.json","view_paper":"https://pith.science/paper/C3THFQHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.09160&json=true","fetch_graph":"https://pith.science/api/pith-number/C3THFQHCG5S5IZQCKL4RA2IMRC/graph.json","fetch_events":"https://pith.science/api/pith-number/C3THFQHCG5S5IZQCKL4RA2IMRC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC/action/storage_attestation","attest_author":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC/action/author_attestation","sign_citation":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC/action/citation_signature","submit_replication":"https://pith.science/pith/C3THFQHCG5S5IZQCKL4RA2IMRC/action/replication_record"}},"created_at":"2026-05-18T01:29:21.208544+00:00","updated_at":"2026-05-18T01:29:21.208544+00:00"}