{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K47HVK36PPXNKAUKDFOPSG5WMW","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":"db8c6275100b7baa045ea8db048869265779c14ef28e7e1c52d6741f883cda58","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-10T19:02:02Z","title_canon_sha256":"b623e916bdfc9f276983ab8099f752c182499e8d8177f7c0f6ab39c1a86bafad"},"schema_version":"1.0","source":{"id":"1901.03348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03348","created_at":"2026-05-17T23:56:31Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03348v1","created_at":"2026-05-17T23:56:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03348","created_at":"2026-05-17T23:56:31Z"},{"alias_kind":"pith_short_12","alias_value":"K47HVK36PPXN","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K47HVK36PPXNKAUK","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K47HVK36","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:37d1f4a6273d872be0f6f904e89db64205c1c65e82756083d1692e4d7896d5d8","target":"graph","created_at":"2026-05-17T23:56:31Z","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":"The ratio $P(S_n=x)/P(Z_n=x)$ is investigated for three cases: (a) when $S_n$ is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and $Z_n$ is Poisson rv; (b) when $S_n$ is a statistic of 2-runs and $Z_n$ is negative binomial rv; and (c) when $S_n$ is statistic of $N(1,1)$-events and $Z_n$ is a binomial r.v. We also consider the approximation of $P(S_n\\geqslant x)$ by Poisson distribution with parameter depending on $x$.","authors_text":"Palaniappan Vellaisamy, Vydas \\v{C}ekanavi\\v{c}ius","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-10T19:02:02Z","title":"On large deviations for sums of discrete m-dependent random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03348","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":"sha256:1551c93e1c28972fde05ab476224904e7556c293ced360a3fe5573167860ced0","target":"record","created_at":"2026-05-17T23:56:31Z","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":"db8c6275100b7baa045ea8db048869265779c14ef28e7e1c52d6741f883cda58","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-10T19:02:02Z","title_canon_sha256":"b623e916bdfc9f276983ab8099f752c182499e8d8177f7c0f6ab39c1a86bafad"},"schema_version":"1.0","source":{"id":"1901.03348","kind":"arxiv","version":1}},"canonical_sha256":"573e7aab7e7beed5028a195cf91bb665a7bd3625c27b0cc7404d21d5b947d96d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"573e7aab7e7beed5028a195cf91bb665a7bd3625c27b0cc7404d21d5b947d96d","first_computed_at":"2026-05-17T23:56:31.491683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:31.491683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09IXQ5HRquLFxQfKxtm0eAMwGk0lWKAPkZ1aka9aG7RP7QWzCqCgywdG2+XhtrgXKrZ4Y4gA6ElGicaCfYnGCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:31.492231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.03348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1551c93e1c28972fde05ab476224904e7556c293ced360a3fe5573167860ced0","sha256:37d1f4a6273d872be0f6f904e89db64205c1c65e82756083d1692e4d7896d5d8"],"state_sha256":"9ae070a5567e327b9597149b9f51ef43a85cb35007d829351d68d256d04fff81"}