{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:DHAOAHMZL5M2BK2BP2Q7GYLR2T","short_pith_number":"pith:DHAOAHMZ","schema_version":"1.0","canonical_sha256":"19c0e01d995f59a0ab417ea1f36171d4cb4ca36d9b597aa70922e795faf371f9","source":{"kind":"arxiv","id":"1009.4926","version":2},"attestation_state":"computed","paper":{"title":"On classical and free stable laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","stat.TH"],"primary_cat":"math.ST","authors_text":"Nizar Demni (PMA)","submitted_at":"2010-09-24T19:56:16Z","abstract_excerpt":"We derive the representative Bernstein measure of the density of $(X_{\\alpha})^{-\\alpha/(1-\\alpha)}, 0 < \\alpha < 1$, where $X_{\\alpha}$ is a positive stable random variable, as a Fox-H function. When $1-\\alpha = 1/j$ for some integer $j \\geq 2$, the Fox H-function reduces to a Meijer G-function so that the Kanter's random variable (see below) is closely related to a product of $(j-1)$ independent Beta random variables. When $\\alpha$ tends to 0, the Bernstein measure becomes degenerate thereby agrees with Cressie's result for the asymptotic behaviour of stable distributions for small values of"},"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":"1009.4926","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-09-24T19:56:16Z","cross_cats_sorted":["math.CA","stat.TH"],"title_canon_sha256":"508e4b5996514a443252a54169632bf564088d4c5ea2ec29017e37b11a616566","abstract_canon_sha256":"874d06fb4e662aa52a89573841c724be16b26d82d56528f107db4c2df36eaed5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:43.522461Z","signature_b64":"HWGBD092N2h1kz1rYPeo5eFbwnkdSS8pXDxu6jbOYcFZl4DagXYtor0AGa2igRH0mHXl2uHanfvfhcsDHqj8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19c0e01d995f59a0ab417ea1f36171d4cb4ca36d9b597aa70922e795faf371f9","last_reissued_at":"2026-05-18T04:31:43.522043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:43.522043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On classical and free stable laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","stat.TH"],"primary_cat":"math.ST","authors_text":"Nizar Demni (PMA)","submitted_at":"2010-09-24T19:56:16Z","abstract_excerpt":"We derive the representative Bernstein measure of the density of $(X_{\\alpha})^{-\\alpha/(1-\\alpha)}, 0 < \\alpha < 1$, where $X_{\\alpha}$ is a positive stable random variable, as a Fox-H function. When $1-\\alpha = 1/j$ for some integer $j \\geq 2$, the Fox H-function reduces to a Meijer G-function so that the Kanter's random variable (see below) is closely related to a product of $(j-1)$ independent Beta random variables. When $\\alpha$ tends to 0, the Bernstein measure becomes degenerate thereby agrees with Cressie's result for the asymptotic behaviour of stable distributions for small values of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4926","kind":"arxiv","version":2},"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":"1009.4926","created_at":"2026-05-18T04:31:43.522106+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4926v2","created_at":"2026-05-18T04:31:43.522106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4926","created_at":"2026-05-18T04:31:43.522106+00:00"},{"alias_kind":"pith_short_12","alias_value":"DHAOAHMZL5M2","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DHAOAHMZL5M2BK2B","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DHAOAHMZ","created_at":"2026-05-18T12:26:06.534383+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/DHAOAHMZL5M2BK2BP2Q7GYLR2T","json":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T.json","graph_json":"https://pith.science/api/pith-number/DHAOAHMZL5M2BK2BP2Q7GYLR2T/graph.json","events_json":"https://pith.science/api/pith-number/DHAOAHMZL5M2BK2BP2Q7GYLR2T/events.json","paper":"https://pith.science/paper/DHAOAHMZ"},"agent_actions":{"view_html":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T","download_json":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T.json","view_paper":"https://pith.science/paper/DHAOAHMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4926&json=true","fetch_graph":"https://pith.science/api/pith-number/DHAOAHMZL5M2BK2BP2Q7GYLR2T/graph.json","fetch_events":"https://pith.science/api/pith-number/DHAOAHMZL5M2BK2BP2Q7GYLR2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T/action/storage_attestation","attest_author":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T/action/author_attestation","sign_citation":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T/action/citation_signature","submit_replication":"https://pith.science/pith/DHAOAHMZL5M2BK2BP2Q7GYLR2T/action/replication_record"}},"created_at":"2026-05-18T04:31:43.522106+00:00","updated_at":"2026-05-18T04:31:43.522106+00:00"}