{"id":"https://openalex.org/W4407416675","doi":"https://doi.org/10.3390/e27020186","title":"A Novel Evaluation of Income Class Boundaries Using Inflection Points of Probability Density Functions: A Case Study of Brazil","display_name":"A Novel Evaluation of Income Class Boundaries Using Inflection Points of Probability Density Functions: A Case Study of Brazil","publication_year":2025,"publication_date":"2025-02-12","ids":{"openalex":"https://openalex.org/W4407416675","doi":"https://doi.org/10.3390/e27020186","pmid":"https://pubmed.ncbi.nlm.nih.gov/40003183"},"language":"en","primary_location":{"id":"doi:10.3390/e27020186","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020186","pdf_url":"https://www.mdpi.com/1099-4300/27/2/186/pdf?version=1739349441","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/1099-4300/27/2/186/pdf?version=1739349441","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051097308","display_name":"Rafael A. Bittencourt","orcid":"https://orcid.org/0000-0002-5399-1181"},"institutions":[{"id":"https://openalex.org/I1329807341","display_name":"Servi\u00e7o Nacional de Aprendizagem Industrial","ror":"https://ror.org/035c3nf67","country_code":"BR","type":"nonprofit","lineage":["https://openalex.org/I1329807341"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Rafael Bittencourt","raw_affiliation_strings":["Instituto Nacional de Ci\u00eancia e Tecnologia\u2014Geof\u00edsica do Petr\u00f3leo, Salvador 41650-010, Bahia, Brazil","Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-5399-1181","affiliations":[{"raw_affiliation_string":"Instituto Nacional de Ci\u00eancia e Tecnologia\u2014Geof\u00edsica do Petr\u00f3leo, Salvador 41650-010, Bahia, Brazil","institution_ids":[]},{"raw_affiliation_string":"Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil","institution_ids":["https://openalex.org/I1329807341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008083872","display_name":"Hernane Borges de Barros Pereira","orcid":"https://orcid.org/0000-0001-7476-9267"},"institutions":[{"id":"https://openalex.org/I1316675753","display_name":"Universidade do Estado da Bahia","ror":"https://ror.org/015n1m812","country_code":"BR","type":"education","lineage":["https://openalex.org/I1316675753"]},{"id":"https://openalex.org/I1329807341","display_name":"Servi\u00e7o Nacional de Aprendizagem Industrial","ror":"https://ror.org/035c3nf67","country_code":"BR","type":"nonprofit","lineage":["https://openalex.org/I1329807341"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Hernane Borges de Barros Pereira","raw_affiliation_strings":["Department of Education, Bahia State University, Salvador 41150-000, Bahia, Brazil","Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-7476-9267","affiliations":[{"raw_affiliation_string":"Department of Education, Bahia State University, Salvador 41150-000, Bahia, Brazil","institution_ids":["https://openalex.org/I1316675753"]},{"raw_affiliation_string":"Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil","institution_ids":["https://openalex.org/I1329807341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086861653","display_name":"Marcelo A. Moret","orcid":"https://orcid.org/0000-0003-0051-6309"},"institutions":[{"id":"https://openalex.org/I1316675753","display_name":"Universidade do Estado da Bahia","ror":"https://ror.org/015n1m812","country_code":"BR","type":"education","lineage":["https://openalex.org/I1316675753"]},{"id":"https://openalex.org/I1329807341","display_name":"Servi\u00e7o Nacional de Aprendizagem Industrial","ror":"https://ror.org/035c3nf67","country_code":"BR","type":"nonprofit","lineage":["https://openalex.org/I1329807341"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marcelo A. Moret","raw_affiliation_strings":["Department of Education, Bahia State University, Salvador 41150-000, Bahia, Brazil","Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-0051-6309","affiliations":[{"raw_affiliation_string":"Department of Education, Bahia State University, Salvador 41150-000, Bahia, Brazil","institution_ids":["https://openalex.org/I1316675753"]},{"raw_affiliation_string":"Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil","institution_ids":["https://openalex.org/I1329807341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075286554","display_name":"I. C. da Cunha Lima","orcid":"https://orcid.org/0000-0002-4525-2346"},"institutions":[{"id":"https://openalex.org/I1329807341","display_name":"Servi\u00e7o Nacional de Aprendizagem Industrial","ror":"https://ror.org/035c3nf67","country_code":"BR","type":"nonprofit","lineage":["https://openalex.org/I1329807341"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ivan C. Da Cunha Lima","raw_affiliation_strings":["Instituto Nacional de Ci\u00eancia e Tecnologia\u2014Geof\u00edsica do Petr\u00f3leo, Salvador 41650-010, Bahia, Brazil","Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-4525-2346","affiliations":[{"raw_affiliation_string":"Instituto Nacional de Ci\u00eancia e Tecnologia\u2014Geof\u00edsica do Petr\u00f3leo, Salvador 41650-010, Bahia, Brazil","institution_ids":[]},{"raw_affiliation_string":"Modelagem Computacional, Universidade SENAI CIMATEC, Salvador 41650-010, Bahia, Brazil","institution_ids":["https://openalex.org/I1329807341"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062833990","display_name":"Serge Galam","orcid":"https://orcid.org/0000-0002-9003-5420"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210116867","display_name":"Centre de Recherches Politiques de Sciences Po","ror":"https://ror.org/0266y7j75","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I205092303","https://openalex.org/I4210116867","https://openalex.org/I4210150854"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Serge Galam","raw_affiliation_strings":["CEVIPOF\u2014Centre for Political Research, Sciences Po and CNRS, 75007 Paris, France"],"raw_orcid":"https://orcid.org/0000-0002-9003-5420","affiliations":[{"raw_affiliation_string":"CEVIPOF\u2014Centre for Political Research, Sciences Po and CNRS, 75007 Paris, France","institution_ids":["https://openalex.org/I4210116867","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5062833990"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210116867"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":13.2196,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.98028786,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"27","issue":"2","first_page":"186","last_page":"186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10446","display_name":"Income, Poverty, and Inequality","score":0.9925000071525574,"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":0.9925000071525574,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9649999737739563,"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/T11742","display_name":"Economic Theory and Policy","score":0.9488000273704529,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and 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"}}],"keywords":[{"id":"https://openalex.org/keywords/income-distribution","display_name":"Income distribution","score":0.6978027820587158},{"id":"https://openalex.org/keywords/gini-coefficient","display_name":"Gini coefficient","score":0.6477011442184448},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5867058038711548},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.544161319732666},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5385926961898804},{"id":"https://openalex.org/keywords/inflection-point","display_name":"Inflection point","score":0.5346969962120056},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.49481719732284546},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.4737955927848816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47222092747688293},{"id":"https://openalex.org/keywords/lorenz-curve","display_name":"Lorenz curve","score":0.4647701382637024},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44934970140457153},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.38006776571273804},{"id":"https://openalex.org/keywords/economic-inequality","display_name":"Economic inequality","score":0.31014037132263184},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.23237699270248413},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2138921320438385},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.11229923367500305},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.09731730818748474},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09243506193161011},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07848057150840759}],"concepts":[{"id":"https://openalex.org/C519300510","wikidata":"https://www.wikidata.org/wiki/Q3915542","display_name":"Income distribution","level":3,"score":0.6978027820587158},{"id":"https://openalex.org/C2779206190","wikidata":"https://www.wikidata.org/wiki/Q162455","display_name":"Gini coefficient","level":4,"score":0.6477011442184448},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5867058038711548},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.544161319732666},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5385926961898804},{"id":"https://openalex.org/C74545648","wikidata":"https://www.wikidata.org/wiki/Q212794","display_name":"Inflection point","level":2,"score":0.5346969962120056},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.49481719732284546},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.4737955927848816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47222092747688293},{"id":"https://openalex.org/C99617461","wikidata":"https://www.wikidata.org/wiki/Q430378","display_name":"Lorenz curve","level":5,"score":0.4647701382637024},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44934970140457153},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.38006776571273804},{"id":"https://openalex.org/C513380476","wikidata":"https://www.wikidata.org/wiki/Q5055020","display_name":"Economic inequality","level":3,"score":0.31014037132263184},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.23237699270248413},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2138921320438385},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.11229923367500305},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.09731730818748474},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09243506193161011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07848057150840759},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27020186","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020186","pdf_url":"https://www.mdpi.com/1099-4300/27/2/186/pdf?version=1739349441","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:40003183","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40003183","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:11853787","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11853787","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11853787/pdf/entropy-27-00186.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:2ffcc8b558814b4a81438a11d66b5598","is_oa":false,"landing_page_url":"https://doaj.org/article/2ffcc8b558814b4a81438a11d66b5598","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 2, p 186 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e27020186","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020186","pdf_url":"https://www.mdpi.com/1099-4300/27/2/186/pdf?version=1739349441","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":[{"score":0.7400000095367432,"id":"https://metadata.un.org/sdg/1","display_name":"No poverty"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407416675.pdf","grobid_xml":"https://content.openalex.org/works/W4407416675.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W985360121","https://openalex.org/W1532007690","https://openalex.org/W1598619243","https://openalex.org/W1755524275","https://openalex.org/W1989536586","https://openalex.org/W2009388645","https://openalex.org/W2009768419","https://openalex.org/W2031849821","https://openalex.org/W2039033949","https://openalex.org/W2077738003","https://openalex.org/W2087804782","https://openalex.org/W2088197444","https://openalex.org/W2089282950","https://openalex.org/W2146376650","https://openalex.org/W2156405079","https://openalex.org/W2158056602","https://openalex.org/W2171903289","https://openalex.org/W2227075066","https://openalex.org/W2232848979","https://openalex.org/W2238367437","https://openalex.org/W2293223818","https://openalex.org/W2558582691","https://openalex.org/W2611332150","https://openalex.org/W2749385365","https://openalex.org/W2897554671","https://openalex.org/W3083742276","https://openalex.org/W3100752995","https://openalex.org/W3101924369","https://openalex.org/W3140662957","https://openalex.org/W3143425968","https://openalex.org/W3204386294","https://openalex.org/W3206138537","https://openalex.org/W3215143314","https://openalex.org/W4213186428","https://openalex.org/W4213427716","https://openalex.org/W4231194885","https://openalex.org/W4283704698","https://openalex.org/W4386255813","https://openalex.org/W6785637300"],"related_works":["https://openalex.org/W2184866710","https://openalex.org/W2792843647","https://openalex.org/W2355331590","https://openalex.org/W2898213959","https://openalex.org/W2381224631","https://openalex.org/W2385244442","https://openalex.org/W2972850664","https://openalex.org/W3102998086","https://openalex.org/W3158771754","https://openalex.org/W2351967401"],"abstract_inverted_index":{"Categorizing":[0],"a":[1,19,24,36,41,51,76,129],"population":[2,57,106],"into":[3,58],"different":[4],"income":[5,28,59,84,95,141,170,183],"classes":[6,60],"is":[7],"important":[8],"for":[9],"creating":[10],"effective":[11],"policies":[12],"and":[13,44,90,101,119],"analyzing":[14],"markets.":[15],"Our":[16],"study":[17],"develops":[18],"statistical":[20],"method":[21,82],"based":[22],"on":[23],"nationwide":[25],"survey":[26],"of":[27,66,104,134,143,182],"distribution.":[29],"We":[30,49,92],"use":[31],"these":[32],"data":[33,85],"to":[34,54,83,157],"create":[35],"cumulative":[37],"distribution":[38,43,103,184],"function":[39,70],"with":[40,97,128,172],"metalogistic":[42],"its":[45],"probability":[46,68],"density":[47,69],"function.":[48],"propose":[50],"new":[52],"way":[53],"divide":[55],"the":[56,63,67,72,102,105,116,151,164,179],"by":[61,150],"using":[62,139],"inflection":[64],"points":[65],"as":[71],"class":[73],"boundaries.":[74],"As":[75],"case":[77],"study,":[78],"we":[79,114,146,166],"apply":[80],"this":[81],"from":[86],"Brazil":[87],"between":[88],"2012":[89],"2022.":[91],"identify":[93,167],"five":[94,168],"classes,":[96,171],"both":[98],"their":[99,173],"boundaries":[100,174],"changing":[107,180],"over":[108],"time.":[109],"To":[110],"check":[111],"our":[112,122],"approach,":[113],"calculate":[115],"Gini":[117],"coefficient":[118],"find":[120],"that":[121,153],"results":[123],"closely":[124],"match":[125],"official":[126],"figures,":[127],"root":[130],"mean":[131],"square":[132],"deviation":[133],"less":[135],"than":[136,160],"1%.":[137],"By":[138],"individual":[140],"instead":[142],"family":[144],"income,":[145],"avoid":[147],"distortions":[148],"caused":[149],"fact":[152],"poorer":[154],"families":[155],"tend":[156],"be":[158],"larger":[159],"wealthier":[161],"ones.":[162],"In":[163],"end,":[165],"main":[169],"shifting":[175],"each":[176],"year,":[177],"reflecting":[178],"nature":[181],"in":[185],"society.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
