{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SSL3TZMXK2PKOOY5TAFLA76UAZ","short_pith_number":"pith:SSL3TZMX","schema_version":"1.0","canonical_sha256":"9497b9e597569ea73b1d980ab07fd40678df9421c324f636c3b438c1aca01cff","source":{"kind":"arxiv","id":"1509.06365","version":1},"attestation_state":"computed","paper":{"title":"Expanding the Computation of Mixture Models by the use of Hermite Polynomials and Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Andrew Clark","submitted_at":"2015-09-21T14:56:35Z","abstract_excerpt":"Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from the same parametric family, e.g. Gaussians or Poissons. In this paper it is shown that by using Hermite polynomials and ideals, the modeling of a mixture process can be extended to include different families in terms of their cumulative distribution functions (cdfs)"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.06365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-09-21T14:56:35Z","cross_cats_sorted":[],"title_canon_sha256":"4ebcf452dc6e0efebf31a7f9c753a73ecd3347f8719bc5eafdb0813b8cb9a9ce","abstract_canon_sha256":"71d19daff4f77eed7e4ecbf0f1dcd8afafbffd71bcf5c66c7757c661674e4a71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:20.462924Z","signature_b64":"I9x96ZJAzgB4B7tDtkCfMnG/jTYREjWR07QB/nF0wYit/XibTv7Xw8dVWxQnLc/cflI2FgGlNIbDXJXelI/qAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9497b9e597569ea73b1d980ab07fd40678df9421c324f636c3b438c1aca01cff","last_reissued_at":"2026-05-18T01:32:20.462271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:20.462271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expanding the Computation of Mixture Models by the use of Hermite Polynomials and Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Andrew Clark","submitted_at":"2015-09-21T14:56:35Z","abstract_excerpt":"Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from the same parametric family, e.g. Gaussians or Poissons. In this paper it is shown that by using Hermite polynomials and ideals, the modeling of a mixture process can be extended to include different families in terms of their cumulative distribution functions (cdfs)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06365","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.06365","created_at":"2026-05-18T01:32:20.462372+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.06365v1","created_at":"2026-05-18T01:32:20.462372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06365","created_at":"2026-05-18T01:32:20.462372+00:00"},{"alias_kind":"pith_short_12","alias_value":"SSL3TZMXK2PK","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SSL3TZMXK2PKOOY5","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SSL3TZMX","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ","json":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ.json","graph_json":"https://pith.science/api/pith-number/SSL3TZMXK2PKOOY5TAFLA76UAZ/graph.json","events_json":"https://pith.science/api/pith-number/SSL3TZMXK2PKOOY5TAFLA76UAZ/events.json","paper":"https://pith.science/paper/SSL3TZMX"},"agent_actions":{"view_html":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ","download_json":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ.json","view_paper":"https://pith.science/paper/SSL3TZMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.06365&json=true","fetch_graph":"https://pith.science/api/pith-number/SSL3TZMXK2PKOOY5TAFLA76UAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/SSL3TZMXK2PKOOY5TAFLA76UAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ/action/storage_attestation","attest_author":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ/action/author_attestation","sign_citation":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ/action/citation_signature","submit_replication":"https://pith.science/pith/SSL3TZMXK2PKOOY5TAFLA76UAZ/action/replication_record"}},"created_at":"2026-05-18T01:32:20.462372+00:00","updated_at":"2026-05-18T01:32:20.462372+00:00"}