{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PU6537WMAUW4BCPOFAEQIKZ35O","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":"ac32094758d44f9534ea4049204ab94a1ede14bc005870f7c8e95b319e78f0fc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-29T10:22:07Z","title_canon_sha256":"ae08666a9927542b071462bf79cf831df5220ba46d5817c6ff2fe673442b8b39"},"schema_version":"1.0","source":{"id":"1207.6763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6763","created_at":"2026-05-18T03:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6763v1","created_at":"2026-05-18T03:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6763","created_at":"2026-05-18T03:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"PU6537WMAUW4","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PU6537WMAUW4BCPO","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PU6537WM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:ba87d6d449bd701def3db035e439258f65749a16664ede71854433ab367f8ef9","target":"graph","created_at":"2026-05-18T03:49:48Z","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":"In this note we derive the exact null distribution for the test statistic proposed by Anis and Mitra (2011) for testing exponentiality against NBUE alternatives. As a special case, we obtain the exact null distribution for the test statistic proposed by Hollander and Proschan (1975). Selected critical values for different size are tabulated for these two statistics. Some remarks concerning the benefits of using the exact distribution are made.","authors_text":"Kinjal Basu, M.Z. Anis","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-29T10:22:07Z","title":"The exact null distribution of the generalized Hollander-Proschan type test for NBUE alternatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6763","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":"sha256:6b303599b264d57276162148c9e8eedf00de5da500473f3364e49fe5e3352417","target":"record","created_at":"2026-05-18T03:49:48Z","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":"ac32094758d44f9534ea4049204ab94a1ede14bc005870f7c8e95b319e78f0fc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-29T10:22:07Z","title_canon_sha256":"ae08666a9927542b071462bf79cf831df5220ba46d5817c6ff2fe673442b8b39"},"schema_version":"1.0","source":{"id":"1207.6763","kind":"arxiv","version":1}},"canonical_sha256":"7d3dddfecc052dc089ee2809042b3bebb18061eb6b89be4964889008702d30f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d3dddfecc052dc089ee2809042b3bebb18061eb6b89be4964889008702d30f4","first_computed_at":"2026-05-18T03:49:48.806048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:48.806048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RjNWcW74X3PKZ351Jf1KBETo7DNcvg34Y9a6fw7IEFxD9ChMok3SecgYzttOQgupj+liv8RbRElicBe+XeEUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:48.806963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b303599b264d57276162148c9e8eedf00de5da500473f3364e49fe5e3352417","sha256:ba87d6d449bd701def3db035e439258f65749a16664ede71854433ab367f8ef9"],"state_sha256":"1f05944f019c7ae3fd0f314ec0262a865d6a7ee0e261d20b748d0df71dd5a674"}