{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PE5PZ6SMTUWTHIZR7CNBBDLMYX","short_pith_number":"pith:PE5PZ6SM","canonical_record":{"source":{"id":"1708.08676","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2017-08-29T10:03:14Z","cross_cats_sorted":[],"title_canon_sha256":"44562d45a1d1fe429322e46bff84d7668cbbd88d5bbfbf84124e0b27bd7224ae","abstract_canon_sha256":"bb42f4c12e4dc9b3659721a6d3cc4edfc6bd2aea0532e724e44a6de70e18bee0"},"schema_version":"1.0"},"canonical_sha256":"793afcfa4c9d2d33a331f89a108d6cc5cdc2171d7ff32f187a01648b01bc8e93","source":{"kind":"arxiv","id":"1708.08676","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08676","created_at":"2026-05-18T00:36:26Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08676v1","created_at":"2026-05-18T00:36:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08676","created_at":"2026-05-18T00:36:26Z"},{"alias_kind":"pith_short_12","alias_value":"PE5PZ6SMTUWT","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PE5PZ6SMTUWTHIZR","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PE5PZ6SM","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PE5PZ6SMTUWTHIZR7CNBBDLMYX","target":"record","payload":{"canonical_record":{"source":{"id":"1708.08676","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2017-08-29T10:03:14Z","cross_cats_sorted":[],"title_canon_sha256":"44562d45a1d1fe429322e46bff84d7668cbbd88d5bbfbf84124e0b27bd7224ae","abstract_canon_sha256":"bb42f4c12e4dc9b3659721a6d3cc4edfc6bd2aea0532e724e44a6de70e18bee0"},"schema_version":"1.0"},"canonical_sha256":"793afcfa4c9d2d33a331f89a108d6cc5cdc2171d7ff32f187a01648b01bc8e93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:26.070225Z","signature_b64":"hxBgi8qKbq9mChz+4bZir+mgAo88ecM83NyrQa0+ihuGO+l2mlXjtbNIrRqaA+5McdtJ1T1lonl8qoRzeaDJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"793afcfa4c9d2d33a331f89a108d6cc5cdc2171d7ff32f187a01648b01bc8e93","last_reissued_at":"2026-05-18T00:36:26.069559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:26.069559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.08676","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":"2026-05-18T00:36:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wua02EJa+yE1GqZKgk1tRatrvA9TeY++xsL7ewyNOghOW19tzsBp65vPp2WV4BooE9e7gZOySoSn+rERGvboBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:54:05.697268Z"},"content_sha256":"2cb6bb8c48db8817d9d2eca50d4c85bd18ed8f1dc8e1303742c2993a33925921","schema_version":"1.0","event_id":"sha256:2cb6bb8c48db8817d9d2eca50d4c85bd18ed8f1dc8e1303742c2993a33925921"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PE5PZ6SMTUWTHIZR7CNBBDLMYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Jade Giguelay, Sylvie Huet","submitted_at":"2017-08-29T10:03:14Z","abstract_excerpt":"We develop here several goodness-of-fit tests for testing the k-monotonicity of a discrete density, based on the empirical distribution of the observations. Our tests are non-parametric, easy to implement and are proved to be asymptotically of the desired level and consistent. We propose an estimator of the degree of k-monotonicity of the distribution based on the non-parametric goodness-of-fit tests. We apply our work to the estimation of the total number of classes in a population. A large simulation study allows to assess the performances of our procedures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08676","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":"2026-05-18T00:36:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFYve7HBPL0RjoB0L3h35g+D1dMGKQwzalN3Vhh0HnWC3S8bi7Gn6SxsCqpnRXAfaZY7+Y4EjN+jAXwPs21pCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:54:05.697625Z"},"content_sha256":"b9f330e429d0bf56a272087f539a9e9b426256d630c609275277fa36f90b9f8a","schema_version":"1.0","event_id":"sha256:b9f330e429d0bf56a272087f539a9e9b426256d630c609275277fa36f90b9f8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PE5PZ6SMTUWTHIZR7CNBBDLMYX/bundle.json","state_url":"https://pith.science/pith/PE5PZ6SMTUWTHIZR7CNBBDLMYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PE5PZ6SMTUWTHIZR7CNBBDLMYX/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":"2026-06-03T09:54:05Z","links":{"resolver":"https://pith.science/pith/PE5PZ6SMTUWTHIZR7CNBBDLMYX","bundle":"https://pith.science/pith/PE5PZ6SMTUWTHIZR7CNBBDLMYX/bundle.json","state":"https://pith.science/pith/PE5PZ6SMTUWTHIZR7CNBBDLMYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PE5PZ6SMTUWTHIZR7CNBBDLMYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PE5PZ6SMTUWTHIZR7CNBBDLMYX","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":"bb42f4c12e4dc9b3659721a6d3cc4edfc6bd2aea0532e724e44a6de70e18bee0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2017-08-29T10:03:14Z","title_canon_sha256":"44562d45a1d1fe429322e46bff84d7668cbbd88d5bbfbf84124e0b27bd7224ae"},"schema_version":"1.0","source":{"id":"1708.08676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08676","created_at":"2026-05-18T00:36:26Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08676v1","created_at":"2026-05-18T00:36:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08676","created_at":"2026-05-18T00:36:26Z"},{"alias_kind":"pith_short_12","alias_value":"PE5PZ6SMTUWT","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PE5PZ6SMTUWTHIZR","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PE5PZ6SM","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:b9f330e429d0bf56a272087f539a9e9b426256d630c609275277fa36f90b9f8a","target":"graph","created_at":"2026-05-18T00:36:26Z","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 develop here several goodness-of-fit tests for testing the k-monotonicity of a discrete density, based on the empirical distribution of the observations. Our tests are non-parametric, easy to implement and are proved to be asymptotically of the desired level and consistent. We propose an estimator of the degree of k-monotonicity of the distribution based on the non-parametric goodness-of-fit tests. We apply our work to the estimation of the total number of classes in a population. A large simulation study allows to assess the performances of our procedures.","authors_text":"Jade Giguelay, Sylvie Huet","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2017-08-29T10:03:14Z","title":"Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08676","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":"sha256:2cb6bb8c48db8817d9d2eca50d4c85bd18ed8f1dc8e1303742c2993a33925921","target":"record","created_at":"2026-05-18T00:36:26Z","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":"bb42f4c12e4dc9b3659721a6d3cc4edfc6bd2aea0532e724e44a6de70e18bee0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2017-08-29T10:03:14Z","title_canon_sha256":"44562d45a1d1fe429322e46bff84d7668cbbd88d5bbfbf84124e0b27bd7224ae"},"schema_version":"1.0","source":{"id":"1708.08676","kind":"arxiv","version":1}},"canonical_sha256":"793afcfa4c9d2d33a331f89a108d6cc5cdc2171d7ff32f187a01648b01bc8e93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"793afcfa4c9d2d33a331f89a108d6cc5cdc2171d7ff32f187a01648b01bc8e93","first_computed_at":"2026-05-18T00:36:26.069559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:26.069559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hxBgi8qKbq9mChz+4bZir+mgAo88ecM83NyrQa0+ihuGO+l2mlXjtbNIrRqaA+5McdtJ1T1lonl8qoRzeaDJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:26.070225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cb6bb8c48db8817d9d2eca50d4c85bd18ed8f1dc8e1303742c2993a33925921","sha256:b9f330e429d0bf56a272087f539a9e9b426256d630c609275277fa36f90b9f8a"],"state_sha256":"15136635a875bcbfe49dad0c2aa383191f9974d87df570878932462360c9871d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7V+A4z6fmdRITlArSwpzOJrpP17Q0HFloe9K9Fd19LaVwWFBgA2CC1J5Adk/8hjuMbOnacAWJYwu/263xlAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:54:05.699563Z","bundle_sha256":"3f16515566b7d320e04ba3f7a49a87ed4718779d6403a1cb9e386bf993cf6fcc"}}