{"id":"https://openalex.org/W3010533237","doi":"https://doi.org/10.1109/iscc50000.2020.9219581","title":"On the Computation of Integrals of Bivariate Gaussian Distribution","display_name":"On the Computation of Integrals of Bivariate Gaussian Distribution","publication_year":2020,"publication_date":"2020-07-01","ids":{"openalex":"https://openalex.org/W3010533237","doi":"https://doi.org/10.1109/iscc50000.2020.9219581","mag":"3010533237"},"language":"en","primary_location":{"id":"doi:10.1109/iscc50000.2020.9219581","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscc50000.2020.9219581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE Symposium on Computers and Communications (ISCC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02555869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087598746","display_name":"Vincent Savaux","orcid":"https://orcid.org/0000-0002-3483-4869"},"institutions":[{"id":"https://openalex.org/I4210143287","display_name":"Institut de Recherche Technologique B-com","ror":"https://ror.org/03cejhk28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210143287"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Vincent Savaux","raw_affiliation_strings":["b<>com, Rennes, France","bcom, Rennes, France"],"affiliations":[{"raw_affiliation_string":"b<>com, Rennes, France","institution_ids":["https://openalex.org/I4210143287"]},{"raw_affiliation_string":"bcom, Rennes, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013280214","display_name":"Luc Le Magoarou","orcid":"https://orcid.org/0000-0002-2871-4406"},"institutions":[{"id":"https://openalex.org/I4210143287","display_name":"Institut de Recherche Technologique B-com","ror":"https://ror.org/03cejhk28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210143287"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Luc Le Magoarou","raw_affiliation_strings":["b<>com, Rennes, France","bcom, Rennes, France"],"affiliations":[{"raw_affiliation_string":"b<>com, Rennes, France","institution_ids":["https://openalex.org/I4210143287"]},{"raw_affiliation_string":"bcom, Rennes, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087598746"],"corresponding_institution_ids":["https://openalex.org/I4210143287"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.03510591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9266999959945679,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9266999959945679,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.7266327142715454},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6919615864753723},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.6866118311882019},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.6527597308158875},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5518400073051453},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5161296129226685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5130676031112671},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.472510427236557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.328859806060791},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2843972444534302},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1512945592403412},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13394013047218323},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0661625862121582}],"concepts":[{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7266327142715454},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6919615864753723},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6866118311882019},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.6527597308158875},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5518400073051453},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5161296129226685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5130676031112671},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.472510427236557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.328859806060791},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2843972444534302},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1512945592403412},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13394013047218323},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0661625862121582}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/iscc50000.2020.9219581","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscc50000.2020.9219581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE Symposium on Computers and Communications (ISCC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-02555869v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02555869","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Symposium on Computers and Communications (ISCC), Jul 2020, Rennes, France","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02555869v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02555869","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Symposium on Computers and Communications (ISCC), Jul 2020, Rennes, France","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W250076511","https://openalex.org/W1517060137","https://openalex.org/W1965392255","https://openalex.org/W2022261649","https://openalex.org/W2045638068","https://openalex.org/W2122759946","https://openalex.org/W2151666308","https://openalex.org/W2801640676","https://openalex.org/W3196620053","https://openalex.org/W4256225108","https://openalex.org/W4301459447"],"related_works":["https://openalex.org/W1721599012","https://openalex.org/W1893285581","https://openalex.org/W2901858382","https://openalex.org/W4384273653","https://openalex.org/W2095736209","https://openalex.org/W4372063917","https://openalex.org/W4232399475","https://openalex.org/W3090632489","https://openalex.org/W2953080444","https://openalex.org/W3119134791"],"abstract_inverted_index":{"This":[0,57],"paper":[1],"deals":[2],"with":[3,91],"the":[4,34,40,64,94],"computation":[5],"of":[6,8,21,33,68,82,93],"integrals":[7],"centred":[9],"bivariate":[10,69],"Gaussian":[11,71],"densities":[12],"over":[13],"any":[14],"domain":[15],"defined":[16],"as":[17,63],"an":[18,29],"angular":[19,65],"sector":[20],"\u211d":[22],"<sup":[23],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[24],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[25],".":[26],"Based":[27],"on":[28],"accessible":[30],"geometrical":[31],"approach":[32,81],"problem,":[35],"we":[36,86],"suggest":[37],"to":[38,48,77],"transform":[39],"double":[41],"integral":[42],"into":[43],"a":[44,49,79],"single":[45],"one,":[46],"leading":[47],"tractable":[50],"closed-form":[51],"expression":[52],"only":[53],"involving":[54],"trigonometric":[55],"functions.":[56],"solution":[58],"can":[59],"also":[60],"be":[61],"seen":[62],"cumulative":[66],"distribution":[67],"centered":[70],"variables":[72],"(X,":[73],"Y).":[74],"We":[75],"aim":[76],"provide":[78],"didactic":[80],"our":[83],"results,":[84],"and":[85],"validate":[87],"them":[88],"by":[89],"comparing":[90],"those":[92],"literature.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
