{"id":"https://openalex.org/W4405080464","doi":"https://doi.org/10.3390/computation12120240","title":"Theil\u2019s Index of Inequality: Computation of Value-Validity Correction","display_name":"Theil\u2019s Index of Inequality: Computation of Value-Validity Correction","publication_year":2024,"publication_date":"2024-12-05","ids":{"openalex":"https://openalex.org/W4405080464","doi":"https://doi.org/10.3390/computation12120240"},"language":"en","primary_location":{"id":"doi:10.3390/computation12120240","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12120240","pdf_url":"https://www.mdpi.com/2079-3197/12/12/240/pdf?version=1733376918","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/12/12/240/pdf?version=1733376918","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033476947","display_name":"Tarald O. Kv\u00e5lseth","orcid":"https://orcid.org/0000-0002-6399-735X"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tarald O. Kv\u00e5lseth","raw_affiliation_strings":["Department of Industrial & Systems Engineering, University of Minnesota, Minneapolis, MN 55455, USA","Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial & Systems Engineering, University of Minnesota, Minneapolis, MN 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033476947"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.7255,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.95115057,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"12","issue":"12","first_page":"240","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10446","display_name":"Income, Poverty, and Inequality","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10446","display_name":"Income, Poverty, and Inequality","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9632999897003174,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/T12013","display_name":"Sustainable Development and Environmental Policy","score":0.9391999840736389,"subfield":{"id":"https://openalex.org/subfields/2308","display_name":"Management, Monitoring, Policy and Law"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/theil-index","display_name":"Theil index","score":0.8634922504425049},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.668903112411499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.629572868347168},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6163259744644165},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5866588354110718},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.5757830142974854},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5034677386283875},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.49952173233032227},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.48531001806259155},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.44259321689605713},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4317149817943573},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3489765524864197},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16920870542526245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13844791054725647}],"concepts":[{"id":"https://openalex.org/C154085013","wikidata":"https://www.wikidata.org/wiki/Q1655361","display_name":"Theil index","level":3,"score":0.8634922504425049},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.668903112411499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.629572868347168},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6163259744644165},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5866588354110718},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5757830142974854},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5034677386283875},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.49952173233032227},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.48531001806259155},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.44259321689605713},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4317149817943573},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3489765524864197},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16920870542526245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13844791054725647},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/computation12120240","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12120240","pdf_url":"https://www.mdpi.com/2079-3197/12/12/240/pdf?version=1733376918","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b0dccd67768b433aa8ebcabae814e4bc","is_oa":true,"landing_page_url":"https://doaj.org/article/b0dccd67768b433aa8ebcabae814e4bc","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 12, Iss 12, p 240 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation12120240","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12120240","pdf_url":"https://www.mdpi.com/2079-3197/12/12/240/pdf?version=1733376918","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","score":0.7599999904632568,"display_name":"No poverty"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405080464.pdf","grobid_xml":"https://content.openalex.org/works/W4405080464.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1993439287","https://openalex.org/W1995875735","https://openalex.org/W2293846112","https://openalex.org/W2515835243","https://openalex.org/W2841558445","https://openalex.org/W2883804316","https://openalex.org/W2964271360","https://openalex.org/W3119707283","https://openalex.org/W4210705228","https://openalex.org/W4211017761","https://openalex.org/W4230753018","https://openalex.org/W4285727085","https://openalex.org/W6726723774","https://openalex.org/W6766289239","https://openalex.org/W6774940269"],"related_works":["https://openalex.org/W2181432034","https://openalex.org/W3139259064","https://openalex.org/W2393199341","https://openalex.org/W2347682755","https://openalex.org/W2367161278","https://openalex.org/W2336508588","https://openalex.org/W2250648659","https://openalex.org/W3022280589","https://openalex.org/W2076067008","https://openalex.org/W3149282682"],"abstract_inverted_index":{"The":[0,139],"Theil":[1],"index":[2,63,85,112,141],"is":[3,17,32,53,144],"one":[4,13],"of":[5,10,28,35,45,56,83,94,110,121,135,149,162,168],"the":[6,57,81,95,101,133,136],"most":[7],"popular":[8],"indices":[9],"economic":[11,96,169],"inequality,":[12],"reason":[14],"for":[15,80],"which":[16,143],"no":[18],"doubt":[19],"due":[20],"to":[21,87,117,129,156],"its":[22,29,33,54],"convenient":[23],"additive":[24],"decomposition":[25],"property.":[26,59],"One":[27],"weaknesses,":[30],"however,":[31],"lack":[34,55],"any":[36],"intuitively":[37],"meaningful":[38],"interpretations.":[39],"Another,":[40],"and":[41,91,131,159,164],"more":[42],"serious,":[43],"limitation":[44],"Theil\u2019s":[46,111,150],"index,":[47,151],"as":[48],"argued":[49],"in":[50,78],"this":[51,62,104,115],"paper,":[52],"value-validity":[58,102],"That":[60],"is,":[61],"does":[64],"not":[65],"meet":[66],"a":[67,107,118,146],"particular":[68],"condition":[69,116],"based":[70],"on":[71],"metric":[72],"distances":[73],"between":[74],"income-share":[75,125],"distributions":[76,126],"required":[77],"order":[79],"range":[82],"potential":[84],"values":[86],"provide":[88],"true,":[89],"realistic,":[90],"valid":[92],"representations":[93,161],"inequality":[97],"characteristic.":[98],"After":[99],"outlining":[100],"condition,":[103],"paper":[105],"derives":[106],"simple":[108],"transformation":[109],"that":[113],"meets":[114],"high":[119],"degree":[120],"approximation.":[122],"Randomly":[123],"generated":[124],"are":[127],"used":[128,155],"demonstrate":[130],"verify":[132],"validity":[134],"corrected":[137],"index.":[138],"new":[140],"formulation,":[142],"simply":[145],"power":[147],"function":[148],"can":[152],"then":[153],"be":[154],"make":[157],"appropriate":[158],"reliable":[160],"absolute":[163],"relative":[165],"difference":[166],"comparisons":[167],"inequalities.":[170]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
