{"id":"https://openalex.org/W2162708400","doi":"https://doi.org/10.1007/s00186-010-0316-3","title":"On probabilistic constraints induced by rectangular sets and multivariate normal distributions","display_name":"On probabilistic constraints induced by rectangular sets and multivariate normal distributions","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2162708400","doi":"https://doi.org/10.1007/s00186-010-0316-3","mag":"2162708400"},"language":"en","primary_location":{"id":"doi:10.1007/s00186-010-0316-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00186-010-0316-3","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.18452/8404","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080745391","display_name":"Wim van Ackooij","orcid":"https://orcid.org/0000-0002-9943-3572"},"institutions":[{"id":"https://openalex.org/I4210143116","display_name":"\u00c9lectricit\u00e9 de France (France)","ror":"https://ror.org/03wb8xz10","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210143116"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Wim Van Ackooij","raw_affiliation_strings":["\u00c9lectricit\u00e9 de France R&D, 1, avenue du G\u00e9n\u00e9ral de Gaulle, 92141, Clamart CEDEX, France","\u00c9lectricit\u00e9 de France R&D, Clamart CEDEX, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9lectricit\u00e9 de France R&D, 1, avenue du G\u00e9n\u00e9ral de Gaulle, 92141, Clamart CEDEX, France","institution_ids":["https://openalex.org/I4210143116"]},{"raw_affiliation_string":"\u00c9lectricit\u00e9 de France R&D, Clamart CEDEX, France","institution_ids":["https://openalex.org/I4210143116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111442239","display_name":"Ren\u00e9 Henrion","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ren\u00e9 Henrion","raw_affiliation_strings":["Weierstrass Institute, Berlin, Germany","Weierstrass Institute, Mohrenstra\u00dfe 39, 10117, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]},{"raw_affiliation_string":"Weierstrass Institute, Mohrenstra\u00dfe 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113572512","display_name":"Andris M\u00f6ller","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andris M\u00f6ller","raw_affiliation_strings":["Weierstrass Institute, Berlin, Germany","Weierstrass Institute, Mohrenstra\u00dfe 39, 10117, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]},{"raw_affiliation_string":"Weierstrass Institute, Mohrenstra\u00dfe 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043826678","display_name":"Riadh Zorgati","orcid":"https://orcid.org/0000-0001-8600-3541"},"institutions":[{"id":"https://openalex.org/I4210143116","display_name":"\u00c9lectricit\u00e9 de France (France)","ror":"https://ror.org/03wb8xz10","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210143116"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Riadh Zorgati","raw_affiliation_strings":["\u00c9lectricit\u00e9 de France R&D, 1, avenue du G\u00e9n\u00e9ral de Gaulle, 92141, Clamart CEDEX, France","\u00c9lectricit\u00e9 de France R&D, Clamart CEDEX, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9lectricit\u00e9 de France R&D, 1, avenue du G\u00e9n\u00e9ral de Gaulle, 92141, Clamart CEDEX, France","institution_ids":["https://openalex.org/I4210143116"]},{"raw_affiliation_string":"\u00c9lectricit\u00e9 de France R&D, Clamart CEDEX, France","institution_ids":["https://openalex.org/I4210143116"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111442239"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":4.5233,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.94542521,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"71","issue":"3","first_page":"535","last_page":"549"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.8115681409835815},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.7620261907577515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6245650053024292},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47367149591445923},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4652678966522217},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.45014458894729614},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.43152570724487305},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.425995796918869},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.39631253480911255},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.3664754629135132},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3617544174194336},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34877902269363403},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12489920854568481}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.8115681409835815},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.7620261907577515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6245650053024292},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47367149591445923},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4652678966522217},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.45014458894729614},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.43152570724487305},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.425995796918869},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.39631253480911255},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3664754629135132},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3617544174194336},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34877902269363403},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12489920854568481},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00186-010-0316-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00186-010-0316-3","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.155.3636","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.155.3636","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://edoc.hu-berlin.de/series/speps/2009-6/PDF/6.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:compst:v:71:y:2010:i:3:p:535-549","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s00186-010-0316-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:edoc.hu-berlin.de:18452/9056","is_oa":false,"landing_page_url":"http://edoc.hu-berlin.de/18452/9056","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"book"},{"id":"doi:10.18452/8404","is_oa":true,"landing_page_url":"https://doi.org/10.18452/8404","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"book"}],"best_oa_location":{"id":"doi:10.18452/8404","is_oa":true,"landing_page_url":"https://doi.org/10.18452/8404","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"book"},"sustainable_development_goals":[{"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6","score":0.8600000143051147}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W200336680","https://openalex.org/W1486993561","https://openalex.org/W1536391780","https://openalex.org/W1891298814","https://openalex.org/W2029225872","https://openalex.org/W2039743397","https://openalex.org/W2061750459","https://openalex.org/W2127294592","https://openalex.org/W2142453884","https://openalex.org/W2798344481"],"related_works":["https://openalex.org/W170825502","https://openalex.org/W1555219153","https://openalex.org/W2052718200","https://openalex.org/W3195391652","https://openalex.org/W1582593418","https://openalex.org/W1498343739","https://openalex.org/W2384906603","https://openalex.org/W3023138785","https://openalex.org/W3022473826","https://openalex.org/W4288910996"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}