{"id":"https://openalex.org/W2012014667","doi":"https://doi.org/10.4236/ojs.2015.53021","title":"Trace of the Wishart Matrix and Applications","display_name":"Trace of the Wishart Matrix and Applications","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2012014667","doi":"https://doi.org/10.4236/ojs.2015.53021","mag":"2012014667"},"language":"en","primary_location":{"id":"doi:10.4236/ojs.2015.53021","doi":"https://doi.org/10.4236/ojs.2015.53021","is_oa":true,"landing_page_url":"https://doi.org/10.4236/ojs.2015.53021","pdf_url":"https://content.scirp.org/pdf/ojs_2015042716122565.pdf","source":{"id":"https://openalex.org/S2764794781","display_name":"Open Journal of Statistics","issn_l":"2161-718X","issn":["2161-718X","2161-7198"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Journal of Statistics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://content.scirp.org/pdf/ojs_2015042716122565.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089525862","display_name":"Thu Pham-Gia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154799132","display_name":"Universit\u00e9 de Moncton","ror":"https://ror.org/029tnqt29","country_code":"CA","type":"education","lineage":["https://openalex.org/I154799132"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"T. Pham-Gia","raw_affiliation_strings":["Universit\u00e9 de Moncton , Moncton , Canada","Universit\u00e9 de Moncton"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Moncton , Moncton , Canada","institution_ids":["https://openalex.org/I154799132"]},{"raw_affiliation_string":"Universit\u00e9 de Moncton","institution_ids":["https://openalex.org/I154799132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056518558","display_name":"Dinh Ngoc Thanh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I23582244","display_name":"Ho Chi Minh City University of Science","ror":"https://ror.org/05jfbgm49","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I23582244"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Dinh N. Thanh","raw_affiliation_strings":["University of Science , Hochiminh City , Vietnam","Ho Chi Minh City University of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science , Hochiminh City , Vietnam","institution_ids":["https://openalex.org/I23582244"]},{"raw_affiliation_string":"Ho Chi Minh City University of Science","institution_ids":["https://openalex.org/I23582244"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052697995","display_name":"Duong Thanh Phong","orcid":"https://orcid.org/0009-0006-4115-5510","observed_orcids":["https://orcid.org/0009-0006-4115-5510"]},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Duong T. Phong","raw_affiliation_strings":["Ton Duc Thang University , Hochiminh City , Vietnam","Ton  Duc Thang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ton Duc Thang University , Hochiminh City , Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Ton  Duc Thang University","institution_ids":["https://openalex.org/I141445968"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089525862"],"corresponding_institution_ids":["https://openalex.org/I154799132"],"apc_list":null,"apc_paid":null,"fwci":0.8921,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.80873604,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"05","issue":"03","first_page":"173","last_page":"190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9940999746322632,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9940999746322632,"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":0.001500000013038516,"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/T13141","display_name":"Statistical Methods and Applications","score":0.0010000000474974513,"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/wishart-distribution","display_name":"Wishart distribution","score":0.8519999980926514},{"id":"https://openalex.org/keywords/largest-eigenvalue","display_name":"largest eigenvalue","score":0.8050000071525574},{"id":"https://openalex.org/keywords/multivariate-analysis","display_name":"multivariate analysis","score":0.6159999966621399},{"id":"https://openalex.org/keywords/distributional-results","display_name":"distributional results","score":0.4970000088214874}],"concepts":[{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.9677278399467468},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.8097437620162964},{"id":"https://openalex.org/C58501165","wikidata":"https://www.wikidata.org/wiki/Q4820795","display_name":"Matrix normal distribution","level":4,"score":0.505835771560669},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4682658016681671},{"id":"https://openalex.org/C40851411","wikidata":"https://www.wikidata.org/wiki/Q3258368","display_name":"Inverse-Wishart distribution","level":4,"score":0.42366597056388855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4055657684803009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39089107513427734},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3478037714958191},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0878591239452362},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.05766966938972473},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4236/ojs.2015.53021","doi":"https://doi.org/10.4236/ojs.2015.53021","is_oa":true,"landing_page_url":"https://doi.org/10.4236/ojs.2015.53021","pdf_url":"https://content.scirp.org/pdf/ojs_2015042716122565.pdf","source":{"id":"https://openalex.org/S2764794781","display_name":"Open Journal of Statistics","issn_l":"2161-718X","issn":["2161-718X","2161-7198"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Journal of Statistics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.853.4859","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.853.4859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.scirp.org/journal/PaperDownload.aspx?paperID%3D55993","raw_type":"text"}],"best_oa_location":{"id":"doi:10.4236/ojs.2015.53021","doi":"https://doi.org/10.4236/ojs.2015.53021","is_oa":true,"landing_page_url":"https://doi.org/10.4236/ojs.2015.53021","pdf_url":"https://content.scirp.org/pdf/ojs_2015042716122565.pdf","source":{"id":"https://openalex.org/S2764794781","display_name":"Open Journal of Statistics","issn_l":"2161-718X","issn":["2161-718X","2161-7198"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Journal of Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2012014667.pdf","grobid_xml":"https://content.openalex.org/works/W2012014667.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W31208289","https://openalex.org/W1520752838","https://openalex.org/W1594931873","https://openalex.org/W1964125836","https://openalex.org/W1967215109","https://openalex.org/W1977176536","https://openalex.org/W1980455221","https://openalex.org/W1996103193","https://openalex.org/W1997651838","https://openalex.org/W2003953023","https://openalex.org/W2012324263","https://openalex.org/W2014269730","https://openalex.org/W2017862360","https://openalex.org/W2019837664","https://openalex.org/W2039227529","https://openalex.org/W2039491306","https://openalex.org/W2043206143","https://openalex.org/W2048642103","https://openalex.org/W2051218534","https://openalex.org/W2051964835","https://openalex.org/W2058614125","https://openalex.org/W2058898235","https://openalex.org/W2059648574","https://openalex.org/W2062241636","https://openalex.org/W2062529663","https://openalex.org/W2063698478","https://openalex.org/W2090092692","https://openalex.org/W2093973660","https://openalex.org/W2094255375","https://openalex.org/W2095198545","https://openalex.org/W2101756663","https://openalex.org/W2104416318","https://openalex.org/W2133806896","https://openalex.org/W2141020861","https://openalex.org/W2151286374","https://openalex.org/W2465516416","https://openalex.org/W2764959534","https://openalex.org/W3148198191"],"related_works":["https://openalex.org/W2053008018","https://openalex.org/W7100874079","https://openalex.org/W1967215109","https://openalex.org/W2043206143","https://openalex.org/W2058898235","https://openalex.org/W2058614125","https://openalex.org/W2962932180","https://openalex.org/W2981781402","https://openalex.org/W2941155329","https://openalex.org/W2003953023"],"abstract_inverted_index":{"The":[0],"trace":[1],"of":[2,22,43],"a":[3,35],"Wishart":[4],"matrix,":[5],"either":[6],"central":[7],"or":[8],"non-central,":[9],"has":[10],"important":[11],"roles":[12],"in":[13,26],"various":[14],"multi-variate":[15],"statistical":[16],"questions.":[17],"We":[18],"review":[19],"several":[20],"expressions":[21],"its":[23],"distribution":[24,42],"given":[25],"the":[27,41,44,46],"literature,":[28],"establish":[29],"some":[30],"new":[31],"results":[32],"and":[33],"provide":[34],"discussion":[36],"on":[37,40],"computing":[38],"methods":[39],"ratio:":[45],"largest":[47],"eigenvalue":[48],"to":[49],"trace.":[50]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-10-18T09:31:52.927876","created_date":"2016-06-24T00:00:00"}
