{"id":"https://openalex.org/W4307267201","doi":"https://doi.org/10.3390/axioms11110587","title":"Testing Multivariate Normality Based on t-Representative Points","display_name":"Testing Multivariate Normality Based on t-Representative Points","publication_year":2022,"publication_date":"2022-10-24","ids":{"openalex":"https://openalex.org/W4307267201","doi":"https://doi.org/10.3390/axioms11110587"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11110587","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110587","pdf_url":"https://www.mdpi.com/2075-1680/11/11/587/pdf?version=1669110153","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/11/587/pdf?version=1669110153","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110683819","display_name":"Jiajuan Liang","orcid":"https://orcid.org/0000-0003-2993-7692"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal University - Hong Kong Baptist University United International College","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiajuan Liang","raw_affiliation_strings":["Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China","Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China","institution_ids":["https://openalex.org/I12615008"]},{"raw_affiliation_string":"Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China","institution_ids":["https://openalex.org/I12615008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022294786","display_name":"Ping He","orcid":"https://orcid.org/0000-0002-1962-8071"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal University - Hong Kong Baptist University United International College","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping He","raw_affiliation_strings":["Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China","Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China","institution_ids":["https://openalex.org/I12615008"]},{"raw_affiliation_string":"Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China","institution_ids":["https://openalex.org/I12615008"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018109272","display_name":"Jun Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal University - Hong Kong Baptist University United International College","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Yang","raw_affiliation_strings":["Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, BNU-HKBU United International College, Zhuhai 519087, China","institution_ids":["https://openalex.org/I12615008"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110683819"],"corresponding_institution_ids":["https://openalex.org/I12615008"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.2092,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.88929001,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11","issue":"11","first_page":"587","last_page":"587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9987000226974487,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9987000226974487,"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/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.98089998960495,"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/normality","display_name":"Normality","score":0.8212600946426392},{"id":"https://openalex.org/keywords/normality-test","display_name":"Normality test","score":0.7546830177307129},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6622427105903625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.594508945941925},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5876228213310242},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.5762630105018616},{"id":"https://openalex.org/keywords/goodness-of-fit","display_name":"Goodness of fit","score":0.512911319732666},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.44988587498664856},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4338374137878418},{"id":"https://openalex.org/keywords/chi-square-test","display_name":"Chi-square test","score":0.4319302439689636}],"concepts":[{"id":"https://openalex.org/C2776157432","wikidata":"https://www.wikidata.org/wiki/Q1375683","display_name":"Normality","level":2,"score":0.8212600946426392},{"id":"https://openalex.org/C85031952","wikidata":"https://www.wikidata.org/wiki/Q3026029","display_name":"Normality test","level":3,"score":0.7546830177307129},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6622427105903625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.594508945941925},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5876228213310242},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.5762630105018616},{"id":"https://openalex.org/C132480984","wikidata":"https://www.wikidata.org/wiki/Q2034239","display_name":"Goodness of fit","level":2,"score":0.512911319732666},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.44988587498664856},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4338374137878418},{"id":"https://openalex.org/C32809988","wikidata":"https://www.wikidata.org/wiki/Q1071004","display_name":"Chi-square test","level":2,"score":0.4319302439689636},{"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/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11110587","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110587","pdf_url":"https://www.mdpi.com/2075-1680/11/11/587/pdf?version=1669110153","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b750c4e3005649d2bfdd99f3a2f406bf","is_oa":true,"landing_page_url":"https://doaj.org/article/b750c4e3005649d2bfdd99f3a2f406bf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 11, p 587 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/11/587/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110587","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 11; Pages: 587","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11110587","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110587","pdf_url":"https://www.mdpi.com/2075-1680/11/11/587/pdf?version=1669110153","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2268825060","display_name":null,"funder_award_id":"2022B1212010006","funder_id":"https://openalex.org/F4320320955","funder_display_name":"Hong Kong Baptist University"}],"funders":[{"id":"https://openalex.org/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4307267201.pdf","grobid_xml":"https://content.openalex.org/works/W4307267201.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W112198602","https://openalex.org/W278265956","https://openalex.org/W1518982701","https://openalex.org/W1576475658","https://openalex.org/W1606393937","https://openalex.org/W1972032974","https://openalex.org/W1974165523","https://openalex.org/W1979331196","https://openalex.org/W1990332275","https://openalex.org/W2000031724","https://openalex.org/W2019965196","https://openalex.org/W2020763192","https://openalex.org/W2030729276","https://openalex.org/W2031648200","https://openalex.org/W2033485191","https://openalex.org/W2040633213","https://openalex.org/W2040869849","https://openalex.org/W2040905109","https://openalex.org/W2044236880","https://openalex.org/W2045418783","https://openalex.org/W2060654009","https://openalex.org/W2071978833","https://openalex.org/W2089867491","https://openalex.org/W2090910286","https://openalex.org/W2151385137","https://openalex.org/W2156661350","https://openalex.org/W2169381307","https://openalex.org/W2181845779","https://openalex.org/W2745488303","https://openalex.org/W3110226374","https://openalex.org/W4213053668","https://openalex.org/W4238414465","https://openalex.org/W4285420823","https://openalex.org/W4300246981","https://openalex.org/W6643668116","https://openalex.org/W7052288925"],"related_works":["https://openalex.org/W3011049012","https://openalex.org/W1480720168","https://openalex.org/W2996853055","https://openalex.org/W1952448190","https://openalex.org/W2098576549","https://openalex.org/W2906455368","https://openalex.org/W40202125","https://openalex.org/W62326830","https://openalex.org/W2276542565","https://openalex.org/W2075879115"],"abstract_inverted_index":{"Testing":[0],"multivariate":[1,27,55],"normality":[2,56],"is":[3,31,75,120],"an":[4],"ever-lasting":[5],"interest":[6],"in":[7,21,69,137],"the":[8,12,18,22,34,42,59,63,86,93,109,114,124,128,138],"goodness-of-fit":[9],"area":[10],"since":[11],"classical":[13],"Pearson\u2019s":[14,95],"chi-squared":[15,96],"test.":[16,97],"Among":[17],"numerous":[19],"approaches":[20],"construction":[23],"of":[24,33,65,108,127],"tests":[25],"for":[26,54],"normality,":[28],"normal":[29,88],"characterization":[30,46,61,89],"one":[32,84],"common":[35],"approaches,":[36],"which":[37],"can":[38],"be":[39],"divided":[40],"into":[41,81],"necessary":[43,87],"and":[44,47,62,90],"sufficient":[45],"necessary-only":[48,60],"characterization.":[49],"We":[50],"construct":[51],"a":[52,78,82,104],"test":[53,112,130],"by":[57],"combining":[58],"idea":[64,74],"statistical":[66],"representative":[67],"points":[68],"this":[70],"paper.":[71],"The":[72],"main":[73],"to":[76,122],"transform":[77],"high-dimensional":[79],"sample":[80],"one-dimensional":[83],"through":[85],"then":[91],"employ":[92],"representative-point-based":[94,110],"A":[98],"limited":[99],"Monte":[100],"Carlo":[101],"study":[102],"shows":[103],"considerable":[105],"power":[106],"improvement":[107],"chi-square":[111],"over":[113],"traditional":[115],"one.":[116],"An":[117],"illustrative":[118],"example":[119],"given":[121],"show":[123],"supplemental":[125],"function":[126],"new":[129],"when":[131],"used":[132],"together":[133],"with":[134],"existing":[135],"ones":[136],"literature.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2022-10-31T00:00:00"}