{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:D6HBVT7O77NGBMHXZH2B7P47SE","short_pith_number":"pith:D6HBVT7O","canonical_record":{"source":{"id":"1110.3436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-15T19:32:21Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"08f352839d1cd2f6e5df439d742914a21baefb5d30342f993e8388de81da5f87","abstract_canon_sha256":"6654bd4543747dcbf638e99115030b08d0fefc9b911cb39d4a0b662f77f85733"},"schema_version":"1.0"},"canonical_sha256":"1f8e1acfeeffda60b0f7c9f41fbf9f913e17234af4f7176702352b7e5a646919","source":{"kind":"arxiv","id":"1110.3436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3436","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3436v1","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3436","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"D6HBVT7O77NG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D6HBVT7O77NGBMHX","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D6HBVT7O","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:D6HBVT7O77NGBMHXZH2B7P47SE","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-15T19:32:21Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"08f352839d1cd2f6e5df439d742914a21baefb5d30342f993e8388de81da5f87","abstract_canon_sha256":"6654bd4543747dcbf638e99115030b08d0fefc9b911cb39d4a0b662f77f85733"},"schema_version":"1.0"},"canonical_sha256":"1f8e1acfeeffda60b0f7c9f41fbf9f913e17234af4f7176702352b7e5a646919","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.848058Z","signature_b64":"sUe7usB0OlzZLomAew5ExiB2Ww5DLZ0V1CzoCnRZirHFsWidjbxNTewQzaOb2GwFWzoeqMbJ8wYYzzU/f3uQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f8e1acfeeffda60b0f7c9f41fbf9f913e17234af4f7176702352b7e5a646919","last_reissued_at":"2026-05-17T23:52:08.847637Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.847637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3436","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"15H3s1kJZ3HUxr0038QFrZRcRrHTF9Vks93knKRE3iUFG+iBCSKJG4qPl0LH3OIxNI2fKEP710Mk9Vs18Xm4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:30:21.728212Z"},"content_sha256":"c64999b4405706c6d441bc62ed5aaf56766b8f6fb090d133bf50ab4f0d36c0dc","schema_version":"1.0","event_id":"sha256:c64999b4405706c6d441bc62ed5aaf56766b8f6fb090d133bf50ab4f0d36c0dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:D6HBVT7O77NGBMHXZH2B7P47SE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Entropy Estimator with an Application to Test of Normality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Amor Keziou, Issam Elhattab, Salim Bouzebda, Tewfik Lounis","submitted_at":"2011-10-15T19:32:21Z","abstract_excerpt":"In the present paper we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is proposed. A small power comparison is provided. A simulation study for the comparison, in terms of mean squared error, of all estimators under study is performed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3436","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MiM2DGVcmi6mwAi6cVr+5QdF+pIBeIoqyELUD637/u5ca+7TZM4nwdOs3Q0s20GMDl4eviBr+cXCsh1HjxHGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:30:21.728576Z"},"content_sha256":"975b2a8aeb8beb97497ee81107a9761f75ae93db695fcdd9147c27e1bc878dcc","schema_version":"1.0","event_id":"sha256:975b2a8aeb8beb97497ee81107a9761f75ae93db695fcdd9147c27e1bc878dcc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6HBVT7O77NGBMHXZH2B7P47SE/bundle.json","state_url":"https://pith.science/pith/D6HBVT7O77NGBMHXZH2B7P47SE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6HBVT7O77NGBMHXZH2B7P47SE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T08:30:21Z","links":{"resolver":"https://pith.science/pith/D6HBVT7O77NGBMHXZH2B7P47SE","bundle":"https://pith.science/pith/D6HBVT7O77NGBMHXZH2B7P47SE/bundle.json","state":"https://pith.science/pith/D6HBVT7O77NGBMHXZH2B7P47SE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6HBVT7O77NGBMHXZH2B7P47SE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D6HBVT7O77NGBMHXZH2B7P47SE","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":"6654bd4543747dcbf638e99115030b08d0fefc9b911cb39d4a0b662f77f85733","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-15T19:32:21Z","title_canon_sha256":"08f352839d1cd2f6e5df439d742914a21baefb5d30342f993e8388de81da5f87"},"schema_version":"1.0","source":{"id":"1110.3436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3436","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3436v1","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3436","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"D6HBVT7O77NG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D6HBVT7O77NGBMHX","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D6HBVT7O","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:975b2a8aeb8beb97497ee81107a9761f75ae93db695fcdd9147c27e1bc878dcc","target":"graph","created_at":"2026-05-17T23:52:08Z","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 the present paper we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is proposed. A small power comparison is provided. A simulation study for the comparison, in terms of mean squared error, of all estimators under study is performed.","authors_text":"Amor Keziou, Issam Elhattab, Salim Bouzebda, Tewfik Lounis","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-15T19:32:21Z","title":"New Entropy Estimator with an Application to Test of Normality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3436","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:c64999b4405706c6d441bc62ed5aaf56766b8f6fb090d133bf50ab4f0d36c0dc","target":"record","created_at":"2026-05-17T23:52:08Z","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":"6654bd4543747dcbf638e99115030b08d0fefc9b911cb39d4a0b662f77f85733","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-15T19:32:21Z","title_canon_sha256":"08f352839d1cd2f6e5df439d742914a21baefb5d30342f993e8388de81da5f87"},"schema_version":"1.0","source":{"id":"1110.3436","kind":"arxiv","version":1}},"canonical_sha256":"1f8e1acfeeffda60b0f7c9f41fbf9f913e17234af4f7176702352b7e5a646919","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f8e1acfeeffda60b0f7c9f41fbf9f913e17234af4f7176702352b7e5a646919","first_computed_at":"2026-05-17T23:52:08.847637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:08.847637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sUe7usB0OlzZLomAew5ExiB2Ww5DLZ0V1CzoCnRZirHFsWidjbxNTewQzaOb2GwFWzoeqMbJ8wYYzzU/f3uQDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:08.848058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c64999b4405706c6d441bc62ed5aaf56766b8f6fb090d133bf50ab4f0d36c0dc","sha256:975b2a8aeb8beb97497ee81107a9761f75ae93db695fcdd9147c27e1bc878dcc"],"state_sha256":"9631a17f85dd6ade5e1659ccdbf169a085532ffc812b0eef71dbdd57a3f7f292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/tLIc4sL5HdAOBBP5rqCAx+yl8lkn6NRK3298bUwlePndnBsHKc4cdEzmAQNzUAYBLOhId8yu/oDIgXQla7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T08:30:21.730441Z","bundle_sha256":"18702c21b5bb7da794e58c4a722fa3814619371c8a7d8b820ece3773c07f7123"}}