{"id":"https://openalex.org/W2096646376","doi":"https://doi.org/10.1109/tit.1971.1054592","title":"On the expansion of a bivariate distribution and its relationship to the output of a nolinearity","display_name":"On the expansion of a bivariate distribution and its relationship to the output of a nolinearity","publication_year":1971,"publication_date":"1971-01-01","ids":{"openalex":"https://openalex.org/W2096646376","doi":"https://doi.org/10.1109/tit.1971.1054592","mag":"2096646376"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1971.1054592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1971.1054592","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089412910","display_name":"Stamatis Cambanis","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]},{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Cambanis","raw_affiliation_strings":["Univ. of North Carolina, NC","Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","Department of Statistics, North Carolina State University, Chapel Hill, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of North Carolina, NC","institution_ids":[]},{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Statistics, North Carolina State University, Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109000558","display_name":"Bede Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bede Liu","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0178,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87531951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"1","first_page":"17","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.920799970626831,"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"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9150999784469604,"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/bivariate-analysis","display_name":"Bivariate analysis","score":0.8873696327209473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7098919153213501},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5942896008491516},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5830109119415283},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5084542036056519},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5016090869903564},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4978458881378174},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45458611845970154},{"id":"https://openalex.org/keywords/series-expansion","display_name":"Series expansion","score":0.4431424140930176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3261457085609436},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.26664698123931885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1263885796070099},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.059375613927841187}],"concepts":[{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.8873696327209473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7098919153213501},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5942896008491516},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5830109119415283},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5084542036056519},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5016090869903564},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4978458881378174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45458611845970154},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.4431424140930176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3261457085609436},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26664698123931885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1263885796070099},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.059375613927841187},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1971.1054592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1971.1054592","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1991302453","https://openalex.org/W2002851938","https://openalex.org/W2040292626","https://openalex.org/W2041041695","https://openalex.org/W2068581004","https://openalex.org/W2071104439","https://openalex.org/W2121055926","https://openalex.org/W2121139863","https://openalex.org/W2143890950","https://openalex.org/W2160465108","https://openalex.org/W2168498958","https://openalex.org/W2753933954","https://openalex.org/W2798461040","https://openalex.org/W3145497163"],"related_works":["https://openalex.org/W4362510888","https://openalex.org/W1989722484","https://openalex.org/W2370613025","https://openalex.org/W1909086734","https://openalex.org/W2065297222","https://openalex.org/W2075698138","https://openalex.org/W2566221162","https://openalex.org/W1975843096","https://openalex.org/W2029158491","https://openalex.org/W2016747299"],"abstract_inverted_index":{"The":[0,45],"series":[1,9],"expansion":[2,10,53],"of":[3,11,14,31,54,57,66],"a":[4,15,38,58,63],"bivariate":[5,32],"distribution":[6],"and":[7,48],"the":[8,12,22,52,55],"output":[13,56],"nonlinearity":[16,59],"are":[17,34,60],"considered,":[18],"as":[19,21],"well":[20],"relationship":[23],"between":[24],"these":[25],"two":[26],"problems.":[27],"Three":[28],"distinct":[29],"expansions":[30],"distributions":[33],"presented":[35],"along":[36],"with":[37],"constructive":[39],"procedure":[40],"to":[41,62],"obtain":[42],"them":[43],"explicitly.":[44],"cross-covarianee":[46],"property":[47],"certain":[49],"results":[50],"on":[51],"extended":[61],"larger":[64],"class":[65],"random":[67],"processes.":[68]},"counts_by_year":[],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2025-10-10T00:00:00"}
