{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:62DU2HSKMY6WMONDWEVB45TWDZ","short_pith_number":"pith:62DU2HSK","canonical_record":{"source":{"id":"1605.09652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-05-31T15:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"639cb2cd3c3b96d2c6e31909639fedaf029d9f4caeb016d25d5f43f8eb41cb75","abstract_canon_sha256":"649f7809b89594a6fcce5dc078ed11fd8fa3b22310a84799b94b3bf2c181011e"},"schema_version":"1.0"},"canonical_sha256":"f6874d1e4a663d6639a3b12a1e76761e4bfd7be9b7b8dcaaad40bdd36aeba27d","source":{"kind":"arxiv","id":"1605.09652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09652","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09652v1","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09652","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"62DU2HSKMY6W","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"62DU2HSKMY6WMOND","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"62DU2HSK","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:62DU2HSKMY6WMONDWEVB45TWDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1605.09652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-05-31T15:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"639cb2cd3c3b96d2c6e31909639fedaf029d9f4caeb016d25d5f43f8eb41cb75","abstract_canon_sha256":"649f7809b89594a6fcce5dc078ed11fd8fa3b22310a84799b94b3bf2c181011e"},"schema_version":"1.0"},"canonical_sha256":"f6874d1e4a663d6639a3b12a1e76761e4bfd7be9b7b8dcaaad40bdd36aeba27d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:10.405506Z","signature_b64":"mz1ePCTBrK0vQDraxMjry1ImpMQpYkxB70phzZRgMsXepZxG4F9ROXx3mm0UnENAtfK2AY54JYdyYSMPGsDVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6874d1e4a663d6639a3b12a1e76761e4bfd7be9b7b8dcaaad40bdd36aeba27d","last_reissued_at":"2026-05-18T01:13:10.405152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:10.405152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.09652","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":"2026-05-18T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JssGn0EmY3gHMtbto7YOPmNZocCVExYYb7bSI899Sz6rXJhis46ZxOWu4Rj/tdfpiB8amguWW/KI8/WCOCbPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:12:32.406385Z"},"content_sha256":"186bf2b7e2cb4ce2171ca245ef32918d572ae46e13024925c7a74ab47d8e6ab2","schema_version":"1.0","event_id":"sha256:186bf2b7e2cb4ce2171ca245ef32918d572ae46e13024925c7a74ab47d8e6ab2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:62DU2HSKMY6WMONDWEVB45TWDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some estimators of the PMF and CDF of the Logarithmic Series Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"Indrani Mukherjee, Monojit Das, Sudhansu S. Maiti","submitted_at":"2016-05-31T15:00:31Z","abstract_excerpt":"This article addresses the different methods of estimation of the probability mass function (PMF) and the cumulative distribution function (CDF) for the Logarithmic Series distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), percentile estimator (PCE), least square estimator (LSE), weighted least square estimator (WLSE). Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09652","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":"2026-05-18T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FO0g+pS1RebiOkQbb/cErNcafblQlzFYZQMWfZZ+u9e3ZrhBlnyqlRdfwhUTYzsxyXfwXxJ2/EXMC665VoSeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:12:32.406739Z"},"content_sha256":"230721f6f59ac04730602e29ae527af20267fcf0cf25a1021569a63caf7b7ac5","schema_version":"1.0","event_id":"sha256:230721f6f59ac04730602e29ae527af20267fcf0cf25a1021569a63caf7b7ac5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62DU2HSKMY6WMONDWEVB45TWDZ/bundle.json","state_url":"https://pith.science/pith/62DU2HSKMY6WMONDWEVB45TWDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62DU2HSKMY6WMONDWEVB45TWDZ/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":"2026-06-02T04:12:32Z","links":{"resolver":"https://pith.science/pith/62DU2HSKMY6WMONDWEVB45TWDZ","bundle":"https://pith.science/pith/62DU2HSKMY6WMONDWEVB45TWDZ/bundle.json","state":"https://pith.science/pith/62DU2HSKMY6WMONDWEVB45TWDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62DU2HSKMY6WMONDWEVB45TWDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:62DU2HSKMY6WMONDWEVB45TWDZ","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":"649f7809b89594a6fcce5dc078ed11fd8fa3b22310a84799b94b3bf2c181011e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-05-31T15:00:31Z","title_canon_sha256":"639cb2cd3c3b96d2c6e31909639fedaf029d9f4caeb016d25d5f43f8eb41cb75"},"schema_version":"1.0","source":{"id":"1605.09652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09652","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09652v1","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09652","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"62DU2HSKMY6W","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"62DU2HSKMY6WMOND","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"62DU2HSK","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:230721f6f59ac04730602e29ae527af20267fcf0cf25a1021569a63caf7b7ac5","target":"graph","created_at":"2026-05-18T01:13:10Z","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":"This article addresses the different methods of estimation of the probability mass function (PMF) and the cumulative distribution function (CDF) for the Logarithmic Series distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), percentile estimator (PCE), least square estimator (LSE), weighted least square estimator (WLSE). Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation.","authors_text":"Indrani Mukherjee, Monojit Das, Sudhansu S. Maiti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-05-31T15:00:31Z","title":"Some estimators of the PMF and CDF of the Logarithmic Series Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09652","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":"sha256:186bf2b7e2cb4ce2171ca245ef32918d572ae46e13024925c7a74ab47d8e6ab2","target":"record","created_at":"2026-05-18T01:13:10Z","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":"649f7809b89594a6fcce5dc078ed11fd8fa3b22310a84799b94b3bf2c181011e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2016-05-31T15:00:31Z","title_canon_sha256":"639cb2cd3c3b96d2c6e31909639fedaf029d9f4caeb016d25d5f43f8eb41cb75"},"schema_version":"1.0","source":{"id":"1605.09652","kind":"arxiv","version":1}},"canonical_sha256":"f6874d1e4a663d6639a3b12a1e76761e4bfd7be9b7b8dcaaad40bdd36aeba27d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6874d1e4a663d6639a3b12a1e76761e4bfd7be9b7b8dcaaad40bdd36aeba27d","first_computed_at":"2026-05-18T01:13:10.405152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:10.405152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mz1ePCTBrK0vQDraxMjry1ImpMQpYkxB70phzZRgMsXepZxG4F9ROXx3mm0UnENAtfK2AY54JYdyYSMPGsDVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:10.405506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:186bf2b7e2cb4ce2171ca245ef32918d572ae46e13024925c7a74ab47d8e6ab2","sha256:230721f6f59ac04730602e29ae527af20267fcf0cf25a1021569a63caf7b7ac5"],"state_sha256":"a8a81c2e4b5b4a16ffcf28e520a16fc17f03508de9f77215dc097026435f8f92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCMv6NaKWOGJcGgL8DmXgY7Fe7hAhlheA+4q1npUK/+CFhRMUKmz/+55/4A3fdmtLvWFxxS3FDhWeyX1F9AxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:12:32.408713Z","bundle_sha256":"add794847d873e935679c0e831692acbe210b7b7e387fb2f9c61924dd10c16c4"}}