{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LWXQCRKKQ3UYOWRWDVJGMUCY6P","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":"87b64850c7ecae3c553919f555242a810d1d3b1b773c1ced0d8d3e93df29afb0","cross_cats_sorted":["math.PR","q-fin.RM","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2010-08-05T18:01:46Z","title_canon_sha256":"064b7d1700d569e4e629e8b787a0731c5ee4f07c7ae53b117d05259f061caf87"},"schema_version":"1.0","source":{"id":"1008.1032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1032","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1032v1","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1032","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"LWXQCRKKQ3UY","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LWXQCRKKQ3UYOWRW","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LWXQCRKK","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:3305bcf168373fcb9217578ab9dc3b9f42241f278ff32f6efb1966608c3cf704","target":"graph","created_at":"2026-05-18T04:42:34Z","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 approximate the distribution of total expenditure of a retail company over warranty claims incurred in a fixed period [0, T], say the following quarter. We consider two kinds of warranty policies, namely, the non-renewing free replacement warranty policy and the non-renewing pro-rata warranty policy. Our approximation holds under modest assumptions on the distribution of the sales process of the warranted item and the nature of arrivals of warranty claims. We propose a method of using historical data to statistically estimate the parameters of the approximate distribution. Our methodology i","authors_text":"Abhimanyu Mitra, Sidney I. Resnick","cross_cats":["math.PR","q-fin.RM","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2010-08-05T18:01:46Z","title":"Modeling total expenditure on warranty claims"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1032","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":"sha256:583c50b578a2108660bff4e2f018f6119cd38c633b9198456f1d19b75a1a2ce1","target":"record","created_at":"2026-05-18T04:42:34Z","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":"87b64850c7ecae3c553919f555242a810d1d3b1b773c1ced0d8d3e93df29afb0","cross_cats_sorted":["math.PR","q-fin.RM","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2010-08-05T18:01:46Z","title_canon_sha256":"064b7d1700d569e4e629e8b787a0731c5ee4f07c7ae53b117d05259f061caf87"},"schema_version":"1.0","source":{"id":"1008.1032","kind":"arxiv","version":1}},"canonical_sha256":"5daf01454a86e9875a361d52665058f3c3884a4b20facf687761536d01b80739","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5daf01454a86e9875a361d52665058f3c3884a4b20facf687761536d01b80739","first_computed_at":"2026-05-18T04:42:34.731071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:34.731071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1RvObKs3I54JY9pOrXogFu4s+iztTZiEOdIUYli9uv9xFgkyDVyj1n6RXcv2nWpru5FelhkgIwVgmsYdcWvYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:34.731709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:583c50b578a2108660bff4e2f018f6119cd38c633b9198456f1d19b75a1a2ce1","sha256:3305bcf168373fcb9217578ab9dc3b9f42241f278ff32f6efb1966608c3cf704"],"state_sha256":"a95f644068deed7f180f403e2a910a428e1e92c286ce3c6ed47fbeb673b6a854"}