{"id":"https://openalex.org/W4403638046","doi":"https://doi.org/10.3390/e26110889","title":"The Representative Points of Generalized Alpha Skew-t Distribution and Applications","display_name":"The Representative Points of Generalized Alpha Skew-t Distribution and Applications","publication_year":2024,"publication_date":"2024-10-22","ids":{"openalex":"https://openalex.org/W4403638046","doi":"https://doi.org/10.3390/e26110889","pmid":"https://pubmed.ncbi.nlm.nih.gov/39593834"},"language":"en","primary_location":{"id":"doi:10.3390/e26110889","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26110889","pdf_url":"https://www.mdpi.com/1099-4300/26/11/889/pdf?version=1729599039","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/11/889/pdf?version=1729599039","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058987912","display_name":"Yongfeng Zhou","orcid":"https://orcid.org/0000-0001-6282-5882"},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong-Feng Zhou","raw_affiliation_strings":["School of Mathematics, Renmin University of China, No. 59, Zhongguancun Street, Haidian District, Beijing 100872, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Renmin University of China, No. 59, Zhongguancun Street, Haidian District, Beijing 100872, China","institution_ids":["https://openalex.org/I78988378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044755810","display_name":"Yu-Xuan Lin","orcid":"https://orcid.org/0000-0002-1295-8094"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I4210123185","display_name":"Zhejiang Lab","ror":"https://ror.org/02m2h7991","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210123185"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Xuan Lin","raw_affiliation_strings":["Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai 519087, China","Research Center for Frontier Fundamental Studies, Zhejiang Lab, Kechuang Avenue, Zhongtai Sub-District, Yuhang District, Hangzhou 311121, China"],"raw_orcid":"https://orcid.org/0000-0002-1295-8094","affiliations":[{"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"]},{"raw_affiliation_string":"Research Center for Frontier Fundamental Studies, Zhejiang Lab, Kechuang Avenue, Zhongtai Sub-District, Yuhang District, Hangzhou 311121, China","institution_ids":["https://openalex.org/I4210123185"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110175938","display_name":"Kai\u2010Tai Fang","orcid":null},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai-Tai Fang","raw_affiliation_strings":["Department of Statistics and Data Science, Faculty of Science and Technology, BNU-HKBU United International College, 2000 Jintong Road, Tangjiawan, Zhuhai 519087, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, Faculty of Science and Technology, BNU-HKBU United International College, 2000 Jintong Road, Tangjiawan, Zhuhai 519087, China","institution_ids":["https://openalex.org/I12615008"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075151255","display_name":"Hong Yin","orcid":null},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hong Yin","raw_affiliation_strings":["School of Mathematics, Renmin University of China, No. 59, Zhongguancun Street, Haidian District, Beijing 100872, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Renmin University of China, No. 59, Zhongguancun Street, Haidian District, Beijing 100872, China","institution_ids":["https://openalex.org/I78988378"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5075151255"],"corresponding_institution_ids":["https://openalex.org/I78988378"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.543,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.70554027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"26","issue":"11","first_page":"889","last_page":"889"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9997000098228455,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9997000098228455,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9952999949455261,"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/skew","display_name":"Skew","score":0.7864742279052734},{"id":"https://openalex.org/keywords/alpha","display_name":"Alpha (finance)","score":0.6121233105659485},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5421354174613953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5087328553199768},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36052119731903076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33516639471054077},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.328019917011261},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.26556286215782166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22371196746826172},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21562480926513672}],"concepts":[{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.7864742279052734},{"id":"https://openalex.org/C64943373","wikidata":"https://www.wikidata.org/wiki/Q2651003","display_name":"Alpha (finance)","level":4,"score":0.6121233105659485},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5421354174613953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5087328553199768},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36052119731903076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33516639471054077},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.328019917011261},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26556286215782166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22371196746826172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21562480926513672},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C171606756","wikidata":"https://www.wikidata.org/wiki/Q506132","display_name":"Psychometrics","level":2,"score":0.0},{"id":"https://openalex.org/C49453240","wikidata":"https://www.wikidata.org/wiki/Q1592163","display_name":"Construct validity","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26110889","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26110889","pdf_url":"https://www.mdpi.com/1099-4300/26/11/889/pdf?version=1729599039","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:39593834","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39593834","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11592904","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11592904","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11592904/pdf/entropy-26-00889.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:1ebb7801a9b943ef8b94de9e5949d519","is_oa":true,"landing_page_url":"https://doaj.org/article/1ebb7801a9b943ef8b94de9e5949d519","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":"Entropy, Vol 26, Iss 11, p 889 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26110889","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26110889","pdf_url":"https://www.mdpi.com/1099-4300/26/11/889/pdf?version=1729599039","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G987722896","display_name":null,"funder_award_id":"2023TQ0326","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403638046.pdf","grobid_xml":"https://content.openalex.org/works/W4403638046.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W94194614","https://openalex.org/W1970375475","https://openalex.org/W1982914322","https://openalex.org/W1986021234","https://openalex.org/W2000359198","https://openalex.org/W2010004527","https://openalex.org/W2014268383","https://openalex.org/W2033076513","https://openalex.org/W2065902423","https://openalex.org/W2117897510","https://openalex.org/W2118020555","https://openalex.org/W2153193653","https://openalex.org/W2347499940","https://openalex.org/W2493411650","https://openalex.org/W2790585552","https://openalex.org/W3047856785","https://openalex.org/W4238414465","https://openalex.org/W4280503325","https://openalex.org/W4281398148","https://openalex.org/W4300580367","https://openalex.org/W4382786811","https://openalex.org/W4392735647","https://openalex.org/W6603863532","https://openalex.org/W6723461487","https://openalex.org/W6793047738"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4290802965","https://openalex.org/W97789383","https://openalex.org/W3087516072","https://openalex.org/W4289406402","https://openalex.org/W2727156679","https://openalex.org/W2067997904","https://openalex.org/W2364071303","https://openalex.org/W1483053255","https://openalex.org/W2896097814"],"abstract_inverted_index":{"Assuming":[0],"the":[1,15,22,34,40,43,50,58,70,74,77,80,83,88,105,126,155,182,195,218,225,232,250],"underlying":[2],"statistical":[3],"distribution":[4,52,134,184,234],"of":[5,19,24,42,69,76,85,107,115,128,131,154,172,181,212,258],"data":[6,28],"is":[7,136,215,229],"critical":[8],"in":[9,176,248],"information":[10],"theory,":[11],"as":[12,57],"it":[13],"impacts":[14],"accuracy":[16],"and":[17,21,79,87,110,164,179,187],"efficiency":[18],"communication":[20],"definition":[23],"entropy.":[25],"The":[26,112,169,190],"real-world":[27],"are":[29,101,174],"widely":[30],"assumed":[31],"to":[32,104,141,151,255],"follow":[33],"normal":[35,51],"distribution.":[36,63],"To":[37],"better":[38],"comprehend":[39],"skewness":[41],"data,":[44],"many":[45],"models":[46],"more":[47],"flexible":[48],"than":[49],"have":[53,120],"been":[54,121],"proposed,":[55],"such":[56],"generalized":[59],"alpha":[60],"skew-t":[61],"(GAST)":[62],"This":[64,242],"paper":[65,146,243],"studies":[66],"some":[67,92],"properties":[68],"GAST":[71,89,156,183,233,251],"distribution,":[72,157],"including":[73],"calculation":[75],"moments,":[78],"relationship":[81],"between":[82],"number":[84],"peaks":[86],"parameters":[90],"with":[91,185,217],"proofs.":[93],"For":[94,201],"complex":[95],"probability":[96,117],"distributions,":[97],"representative":[98,192],"points":[99,193],"(RPs)":[100],"useful":[102],"due":[103,140],"convenience":[106],"manipulation,":[108],"computation":[109],"analysis.":[111],"relative":[113],"entropy":[114],"two":[116,245],"distributions":[118],"could":[119],"a":[122,132,205,236],"good":[123],"criterion":[124],"for":[125,231],"purpose":[127],"generating":[129],"RPs":[130,153,173],"specific":[133],"but":[135],"not":[137],"popularly":[138],"used":[139],"computational":[142],"complexity.":[143],"Hence,":[144],"this":[145],"only":[147],"provides":[148],"three":[149,170],"ways":[150],"obtain":[152],"Monte":[158],"Carlo":[159,162],"(MC),":[160],"quasi-Monte":[161],"(QMC),":[163],"mean":[165],"square":[166],"error":[167],"(MSE).":[168],"types":[171,257],"utilized":[175],"estimating":[177],"moments":[178],"densities":[180],"known":[186],"unknown":[188,202],"parameters.":[189],"MSE":[191],"perform":[194],"best":[196],"among":[197],"all":[198],"case":[199],"studies.":[200],"parameter":[203,213],"cases,":[204],"revised":[206,226],"maximum":[207],"likelihood":[208],"estimation":[209,214],"(MLE)":[210],"method":[211,228],"compared":[216],"plain":[219],"MLE":[220,227],"method.":[221],"It":[222],"indicates":[223],"that":[224],"suitable":[230],"having":[235],"unimodal":[237],"or":[238],"unobvious":[239],"bimodal":[240],"pattern.":[241],"includes":[244],"real-data":[246],"applications":[247],"which":[249],"model":[252],"appears":[253],"adaptable":[254],"various":[256],"data.":[259]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}