{"id":"https://openalex.org/W4409999447","doi":"https://doi.org/10.3390/stats8020034","title":"Estimation of Weighted Extropy Under the \u03b1-Mixing Dependence Condition","display_name":"Estimation of Weighted Extropy Under the \u03b1-Mixing Dependence Condition","publication_year":2025,"publication_date":"2025-05-01","ids":{"openalex":"https://openalex.org/W4409999447","doi":"https://doi.org/10.3390/stats8020034"},"language":"en","primary_location":{"id":"doi:10.3390/stats8020034","doi":"https://doi.org/10.3390/stats8020034","is_oa":true,"landing_page_url":"https://doi.org/10.3390/stats8020034","pdf_url":"https://www.mdpi.com/2571-905X/8/2/34/pdf?version=1746091561","source":{"id":"https://openalex.org/S4210232718","display_name":"Stats","issn_l":"2571-905X","issn":["2571-905X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","jufo-1","norway-1","poland-20","russia-white-list-4","vabb-shw"],"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":"Stats","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2571-905X/8/2/34/pdf?version=1746091561","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112750332","display_name":"Radhakumari Maya","orcid":"https://orcid.org/0000-0003-1138-740X","observed_orcids":["https://orcid.org/0000-0003-1138-740X"]},"institutions":[{"id":"https://openalex.org/I20497027","display_name":"Cochin University of Science and Technology","ror":"https://ror.org/00a4kqq17","country_code":"IN","type":"education","lineage":["https://openalex.org/I20497027"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Radhakumari Maya","raw_affiliation_strings":["Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India"],"raw_orcid":"https://orcid.org/0000-0003-1138-740X","affiliations":[{"raw_affiliation_string":"Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India","institution_ids":["https://openalex.org/I20497027"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104156913","display_name":"Archana Krishnakumar","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20497027","display_name":"Cochin University of Science and Technology","ror":"https://ror.org/00a4kqq17","country_code":"IN","type":"education","lineage":["https://openalex.org/I20497027"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Archana Krishnakumar","raw_affiliation_strings":["Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India","institution_ids":["https://openalex.org/I20497027"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037817442","display_name":"M. R. Irshad","orcid":"https://orcid.org/0000-0002-5999-1588","observed_orcids":["https://orcid.org/0000-0002-5999-1588"]},"institutions":[{"id":"https://openalex.org/I20497027","display_name":"Cochin University of Science and Technology","ror":"https://ror.org/00a4kqq17","country_code":"IN","type":"education","lineage":["https://openalex.org/I20497027"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Muhammed Rasheed Irshad","raw_affiliation_strings":["Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India"],"raw_orcid":"https://orcid.org/0000-0002-5999-1588","affiliations":[{"raw_affiliation_string":"Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India","institution_ids":["https://openalex.org/I20497027"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083045521","display_name":"Christophe Chesneau","orcid":"https://orcid.org/0000-0002-1522-9292","observed_orcids":["https://orcid.org/0000-0002-1522-9292"]},"institutions":[{"id":"https://openalex.org/I4387155825","display_name":"Laboratoire de Math\u00e9matiques Nicolas Oresme","ror":"https://ror.org/03jm2hc44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210105918","https://openalex.org/I4387155825","https://openalex.org/I98702875"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Christophe Chesneau","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Nicolas Oresme (LMNO), Universit\u00e9 de Caen-Normandie, 14000 Caen, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Nicolas Oresme (LMNO), Universit\u00e9 de Caen-Normandie, 14000 Caen, France","institution_ids":["https://openalex.org/I4387155825","https://openalex.org/I98702875"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083045521"],"corresponding_institution_ids":["https://openalex.org/I4387155825","https://openalex.org/I98702875"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1930},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1930},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10001898,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"2","first_page":"34","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9253000020980835,"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/T13500","display_name":"Probability and Statistical Research","score":0.9253000020980835,"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":0.04899999871850014,"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/T10136","display_name":"Statistical Methods and Inference","score":0.01140000019222498,"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/extropy","display_name":"extropy","score":0.9369999766349792},{"id":"https://openalex.org/keywords/shannon-entropy","display_name":"Shannon entropy","score":0.8330000042915344},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.8159999847412109},{"id":"https://openalex.org/keywords/nonparametric-estimation","display_name":"nonparametric estimation","score":0.9300000071525574},{"id":"https://openalex.org/keywords/consistency","display_name":"consistency","score":0.843999981880188},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.9359999895095825},{"id":"https://openalex.org/keywords/time-series","display_name":"time series","score":0.6179999709129333},{"id":"https://openalex.org/keywords/dependent-observations","display_name":"dependent observations","score":0.5019999742507935},{"id":"https://openalex.org/keywords/scoring-rules","display_name":"scoring rules","score":0.5249999761581421},{"id":"https://openalex.org/keywords/reliability-theory","display_name":"reliability theory","score":0.5509999990463257}],"concepts":[{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6144272089004517},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.4993922710418701},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4946920573711395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49437952041625977},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.33943384885787964},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.21896135807037354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16380953788757324},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/stats8020034","doi":"https://doi.org/10.3390/stats8020034","is_oa":true,"landing_page_url":"https://doi.org/10.3390/stats8020034","pdf_url":"https://www.mdpi.com/2571-905X/8/2/34/pdf?version=1746091561","source":{"id":"https://openalex.org/S4210232718","display_name":"Stats","issn_l":"2571-905X","issn":["2571-905X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","jufo-1","norway-1","poland-20","russia-white-list-4","vabb-shw"],"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":"Stats","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jstats:v:8:y:2025:i:2:p:34-:d:1647919","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2571-905X/8/2/34/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:44668872f95f4ce1905621544e677bd5","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/44668872f95f4ce1905621544e677bd5","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,"listed_in":[],"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":"Stats, Vol 8, Iss 2, p 34 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/stats8020034","doi":"https://doi.org/10.3390/stats8020034","is_oa":true,"landing_page_url":"https://doi.org/10.3390/stats8020034","pdf_url":"https://www.mdpi.com/2571-905X/8/2/34/pdf?version=1746091561","source":{"id":"https://openalex.org/S4210232718","display_name":"Stats","issn_l":"2571-905X","issn":["2571-905X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","jufo-1","norway-1","poland-20","russia-white-list-4","vabb-shw"],"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":"Stats","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409999447.pdf","grobid_xml":"https://content.openalex.org/works/W4409999447.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1640831794","https://openalex.org/W1722646328","https://openalex.org/W1967211488","https://openalex.org/W1992387042","https://openalex.org/W1995875735","https://openalex.org/W1998047308","https://openalex.org/W2049197185","https://openalex.org/W2084345360","https://openalex.org/W2118020555","https://openalex.org/W2137295153","https://openalex.org/W2140120821","https://openalex.org/W2527257983","https://openalex.org/W2761017552","https://openalex.org/W2763636061","https://openalex.org/W2770078714","https://openalex.org/W2795168541","https://openalex.org/W2887167677","https://openalex.org/W3006618609","https://openalex.org/W3025136028","https://openalex.org/W3050798673","https://openalex.org/W3133287131","https://openalex.org/W3134108889","https://openalex.org/W3175059020","https://openalex.org/W4251288685","https://openalex.org/W4304185630","https://openalex.org/W4360847217","https://openalex.org/W4391748522","https://openalex.org/W6838025491"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Introduced":[0],"as":[1,21],"a":[2,60,84,98],"complementary":[3],"concept":[4],"to":[5],"Shannon":[6],"entropy,":[7],"extropy":[8,27,57,92],"provides":[9],"an":[10],"alternative":[11],"perspective":[12],"for":[13,90,111,121,182],"measuring":[14],"uncertainty.":[15],"While":[16],"useful":[17],"in":[18,28,41,101,167],"areas":[19],"such":[20],"reliability":[22],"theory":[23],"and":[24,74,104,137,148,158,171,185],"scoring":[25],"rules,":[26],"its":[29,39,133,160],"original":[30],"form":[31],"treats":[32],"all":[33],"outcomes":[34,46],"equally,":[35],"which":[36],"can":[37],"limit":[38],"applicability":[40],"real-world":[42],"settings":[43],"where":[44],"different":[45],"have":[47],"varying":[48],"degrees":[49],"of":[50,68,76,129,155,169,179],"importance.":[51],"To":[52],"address":[53],"this,":[54],"the":[55,65,72,130,152,156,163,177,180],"weighted":[56,91,186],"measure":[58],"incorporates":[59],"weight":[61],"function":[62],"that":[63],"reflects":[64],"relative":[66],"significance":[67],"outcomes,":[69],"thereby":[70],"increasing":[71],"flexibility":[73],"sensitivity":[75],"uncertainty":[77],"quantification.":[78],"In":[79],"this":[80],"paper,":[81],"we":[82],"propose":[83],"novel":[85],"recursive":[86,108,134],"non-parametric":[87],"kernel":[88,165],"estimator":[89,157,166],"based":[93],"on":[94],"\u03b1-mixing":[95],"dependent":[96],"observations,":[97],"common":[99],"setting":[100],"time":[102],"series":[103],"stochastic":[105],"processes.":[106],"The":[107,174],"formulation":[109],"allows":[110],"efficient":[112],"updating":[113],"with":[114],"sequential":[115],"data,":[116],"making":[117],"it":[118],"particularly":[119],"suitable":[120],"real-time":[122],"analysis.":[123],"We":[124],"establish":[125],"several":[126],"theoretical":[127],"properties":[128],"estimator,":[131],"including":[132],"structure,":[135],"consistency,":[136],"asymptotic":[138],"behavior":[139],"under":[140],"mild":[141],"regularity":[142],"conditions.":[143],"A":[144],"comprehensive":[145],"simulation":[146],"study":[147],"data":[149],"application":[150],"demonstrate":[151],"practical":[153],"performance":[154],"validate":[159],"superiority":[161],"over":[162],"non-recursive":[164],"terms":[168],"accuracy":[170],"computational":[172],"efficiency.":[173],"results":[175],"confirm":[176],"relevance":[178],"method":[181],"dynamic,":[183],"dependent,":[184],"systems.":[187]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-05-02T00:00:00"}
