{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PJGVFAOJZ7H4AWM5WMMLBMDRVJ","short_pith_number":"pith:PJGVFAOJ","schema_version":"1.0","canonical_sha256":"7a4d5281c9cfcfc0599db318b0b071aa55544bcfce4183109a0d1fc2da9e3224","source":{"kind":"arxiv","id":"1506.02778","version":5},"attestation_state":"computed","paper":{"title":"A note on mixture representations for the Linnik and Mittag-Leffler distributions and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Zeifman, Victor Korolev","submitted_at":"2015-06-09T05:12:17Z","abstract_excerpt":"We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the representation of the Linnik distribution as a normal scale mixture with the Mittag-Leffler mixing distribution. As a corollary, we obtain the known representation of the Linnik distribution as a scale mixture of Laplace distributions. Another corollary of the main representation is the theorem establishing that the distributions of random sums of independent identi"},"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":"1506.02778","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-09T05:12:17Z","cross_cats_sorted":[],"title_canon_sha256":"2bf2ac5f70fb3224f7e876cf89d806fd9f3c7447524695e982b64c5cbf3c24fa","abstract_canon_sha256":"33de66acb268314ace1b03055fb36e1307d2c3cd6a9b7e490a67cf99f9fc0a8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.141858Z","signature_b64":"ObJAf2ftQIU96dlWkO1TVQT4+zvLbrCUCD5O2Ebym3i41vg3u7zZG7dnHSsi/qpNa8Uyp41On6WBLV3ssg9NAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a4d5281c9cfcfc0599db318b0b071aa55544bcfce4183109a0d1fc2da9e3224","last_reissued_at":"2026-05-18T01:11:55.141488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.141488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on mixture representations for the Linnik and Mittag-Leffler distributions and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Zeifman, Victor Korolev","submitted_at":"2015-06-09T05:12:17Z","abstract_excerpt":"We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the representation of the Linnik distribution as a normal scale mixture with the Mittag-Leffler mixing distribution. As a corollary, we obtain the known representation of the Linnik distribution as a scale mixture of Laplace distributions. Another corollary of the main representation is the theorem establishing that the distributions of random sums of independent identi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02778","kind":"arxiv","version":5},"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":"1506.02778","created_at":"2026-05-18T01:11:55.141545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.02778v5","created_at":"2026-05-18T01:11:55.141545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02778","created_at":"2026-05-18T01:11:55.141545+00:00"},{"alias_kind":"pith_short_12","alias_value":"PJGVFAOJZ7H4","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PJGVFAOJZ7H4AWM5","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PJGVFAOJ","created_at":"2026-05-18T12:29:37.295048+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/PJGVFAOJZ7H4AWM5WMMLBMDRVJ","json":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ.json","graph_json":"https://pith.science/api/pith-number/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/graph.json","events_json":"https://pith.science/api/pith-number/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/events.json","paper":"https://pith.science/paper/PJGVFAOJ"},"agent_actions":{"view_html":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ","download_json":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ.json","view_paper":"https://pith.science/paper/PJGVFAOJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.02778&json=true","fetch_graph":"https://pith.science/api/pith-number/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/graph.json","fetch_events":"https://pith.science/api/pith-number/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/action/storage_attestation","attest_author":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/action/author_attestation","sign_citation":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/action/citation_signature","submit_replication":"https://pith.science/pith/PJGVFAOJZ7H4AWM5WMMLBMDRVJ/action/replication_record"}},"created_at":"2026-05-18T01:11:55.141545+00:00","updated_at":"2026-05-18T01:11:55.141545+00:00"}