{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:N5PWRDRKUWZSCHO6SGIKBASDXA","short_pith_number":"pith:N5PWRDRK","canonical_record":{"source":{"id":"1105.6031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-05-30T16:31:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8915a06eb64ece5d4f7b0b4cd6e5185795e4897f3dac81e0412015c02fc3ab55","abstract_canon_sha256":"7c9220aebd7d9a81ec6e6fa067b53272fddf8cfc8dc006c9d3363f5fea79b58e"},"schema_version":"1.0"},"canonical_sha256":"6f5f688e2aa5b3211dde9190a08243b8269bb2a2d584e22e1507380de12b2135","source":{"kind":"arxiv","id":"1105.6031","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6031","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6031v1","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6031","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"N5PWRDRKUWZS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N5PWRDRKUWZSCHO6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N5PWRDRK","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:N5PWRDRKUWZSCHO6SGIKBASDXA","target":"record","payload":{"canonical_record":{"source":{"id":"1105.6031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-05-30T16:31:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8915a06eb64ece5d4f7b0b4cd6e5185795e4897f3dac81e0412015c02fc3ab55","abstract_canon_sha256":"7c9220aebd7d9a81ec6e6fa067b53272fddf8cfc8dc006c9d3363f5fea79b58e"},"schema_version":"1.0"},"canonical_sha256":"6f5f688e2aa5b3211dde9190a08243b8269bb2a2d584e22e1507380de12b2135","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:01.059966Z","signature_b64":"n1pRFC/BE3iy9zQuNSIg6PLddbJr0L512PfckbG9rAop+CCrkzguUe/O9Zp98UEU6e1BLOhCrScyUQNkWazuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f5f688e2aa5b3211dde9190a08243b8269bb2a2d584e22e1507380de12b2135","last_reissued_at":"2026-05-18T04:21:01.059349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:01.059349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.6031","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":"2026-05-18T04:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGT+U62zxPFXsKoT0qPLBv6GDJwQIhLo+hLwUDCUWXKMN3SOr/In2diMFFbQCXP3dIP+0P7FE65g8DZnkQAVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:53:41.302844Z"},"content_sha256":"2d6ace059aa9712f75affd992a5c626f5c62225a5f059f063cc95ebb70b7d7a5","schema_version":"1.0","event_id":"sha256:2d6ace059aa9712f75affd992a5c626f5c62225a5f059f063cc95ebb70b7d7a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:N5PWRDRKUWZSCHO6SGIKBASDXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupled risk measures and their empirical estimation when losses follow heavy-tailed distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Abdelhakim Necir, Ri\\v{c}ardas Zitikis","submitted_at":"2011-05-30T16:31:56Z","abstract_excerpt":"Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios, or even more complex combinations, of two L-functionals. In the present paper we call such combinations `coupled risk measures' and develop a statistical inferential theory for them when losses follow heavy-tailed distributions. Our theory implies -at a stroke- statistical inferential results for absol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6031","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":"2026-05-18T04:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxBVc+fyZIPnTM5JHruBJ+4vMrniSB+p2l2YwFEeEtII0jMODaHxM8PUSc9C7EW5jJkC8/C1B+ipSNx2JGWXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:53:41.303188Z"},"content_sha256":"54e27732345e9e10fb2e461b927cac568db8efec4154d8e7625240e9534bf4ab","schema_version":"1.0","event_id":"sha256:54e27732345e9e10fb2e461b927cac568db8efec4154d8e7625240e9534bf4ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5PWRDRKUWZSCHO6SGIKBASDXA/bundle.json","state_url":"https://pith.science/pith/N5PWRDRKUWZSCHO6SGIKBASDXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5PWRDRKUWZSCHO6SGIKBASDXA/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":"2026-06-08T21:53:41Z","links":{"resolver":"https://pith.science/pith/N5PWRDRKUWZSCHO6SGIKBASDXA","bundle":"https://pith.science/pith/N5PWRDRKUWZSCHO6SGIKBASDXA/bundle.json","state":"https://pith.science/pith/N5PWRDRKUWZSCHO6SGIKBASDXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5PWRDRKUWZSCHO6SGIKBASDXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N5PWRDRKUWZSCHO6SGIKBASDXA","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":"7c9220aebd7d9a81ec6e6fa067b53272fddf8cfc8dc006c9d3363f5fea79b58e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-05-30T16:31:56Z","title_canon_sha256":"8915a06eb64ece5d4f7b0b4cd6e5185795e4897f3dac81e0412015c02fc3ab55"},"schema_version":"1.0","source":{"id":"1105.6031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6031","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6031v1","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6031","created_at":"2026-05-18T04:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"N5PWRDRKUWZS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N5PWRDRKUWZSCHO6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N5PWRDRK","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:54e27732345e9e10fb2e461b927cac568db8efec4154d8e7625240e9534bf4ab","target":"graph","created_at":"2026-05-18T04:21:01Z","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":"Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios, or even more complex combinations, of two L-functionals. In the present paper we call such combinations `coupled risk measures' and develop a statistical inferential theory for them when losses follow heavy-tailed distributions. Our theory implies -at a stroke- statistical inferential results for absol","authors_text":"Abdelhakim Necir, Ri\\v{c}ardas Zitikis","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-05-30T16:31:56Z","title":"Coupled risk measures and their empirical estimation when losses follow heavy-tailed distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6031","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":"sha256:2d6ace059aa9712f75affd992a5c626f5c62225a5f059f063cc95ebb70b7d7a5","target":"record","created_at":"2026-05-18T04:21:01Z","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":"7c9220aebd7d9a81ec6e6fa067b53272fddf8cfc8dc006c9d3363f5fea79b58e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-05-30T16:31:56Z","title_canon_sha256":"8915a06eb64ece5d4f7b0b4cd6e5185795e4897f3dac81e0412015c02fc3ab55"},"schema_version":"1.0","source":{"id":"1105.6031","kind":"arxiv","version":1}},"canonical_sha256":"6f5f688e2aa5b3211dde9190a08243b8269bb2a2d584e22e1507380de12b2135","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f5f688e2aa5b3211dde9190a08243b8269bb2a2d584e22e1507380de12b2135","first_computed_at":"2026-05-18T04:21:01.059349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:01.059349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n1pRFC/BE3iy9zQuNSIg6PLddbJr0L512PfckbG9rAop+CCrkzguUe/O9Zp98UEU6e1BLOhCrScyUQNkWazuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:01.059966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.6031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d6ace059aa9712f75affd992a5c626f5c62225a5f059f063cc95ebb70b7d7a5","sha256:54e27732345e9e10fb2e461b927cac568db8efec4154d8e7625240e9534bf4ab"],"state_sha256":"fc41fc1cd8e400318b2f86a37217704732a95ff8b14c3fa67ff47193d49bda37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mMk7PSSa4nQLeulvXvp5nhTidxEBZ4jcxTYW/0mLcBvqbe1BuwXNX0Qzw64ajYO73gaQX7raKsEziFbbOLO6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:53:41.305044Z","bundle_sha256":"ee44036ddc0b8b64a4ee91de7fd7ec0b4a095a52621fbf6d0a9b5cac1f1f715b"}}