{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T22:55:39Z","timestamp":1772060139225,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,12,18]],"date-time":"2012-12-18T00:00:00Z","timestamp":1355788800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Soc Choice Welf"],"published-print":{"date-parts":[[2013,10]]},"DOI":"10.1007\/s00355-012-0715-x","type":"journal-article","created":{"date-parts":[[2012,12,17]],"date-time":"2012-12-17T19:19:05Z","timestamp":1355771945000},"page":"763-787","source":"Crossref","is-referenced-by-count":17,"title":["On the generalization and decomposition of the Bonferroni index"],"prefix":"10.1007","volume":"41","author":[{"given":"Elena","family":"B\u00e1rcena-Martin","sequence":"first","affiliation":[]},{"given":"Jacques","family":"Silber","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,12,18]]},"reference":[{"key":"715_CR1","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1007\/s003550000046","volume":"17","author":"R Aaberge","year":"2000","unstructured":"Aaberge R (2000) Characterizations of Lorenz curves and income distributions. Soc Choice Welf 17: 639\u2013653","journal-title":"Soc Choice Welf"},{"issue":"3","key":"715_CR2","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s10888-006-9050-8","volume":"5","author":"R Aaberge","year":"2007","unstructured":"Aaberge R (2007) Gini\u2019s nuclear family. J Econ Inequal 5(3):305\u2013322","journal-title":"J Econ Inequal"},{"issue":"3","key":"715_CR3","first-page":"493","volume":"63","author":"R Aaberge","year":"2005","unstructured":"Aaberge R, Bjerve S, Doksum K (2005) Decomposition of rank-dependent measures of inequality by subgroups. Metron Int J Stat 63(3):493\u2013503","journal-title":"Metron Int J Stat"},{"key":"715_CR4","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/0022-0531(70)90039-6","volume":"2","author":"AB Atkinson","year":"1970","unstructured":"Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2:244\u2013263","journal-title":"J Econ Theory"},{"key":"715_CR5","unstructured":"B\u00e1rcena-Martin E, Silber J (2012) On the generalization and decomposition of the Bonferroni index. Oxford poverty and human development initiative (OPHI) working paper 51"},{"key":"715_CR6","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S1049-2585(08)16011-2","volume":"16","author":"E B\u00e1rcena","year":"2008","unstructured":"B\u00e1rcena E, Imedio LJ (2008) The Bonferroni, Gini and de Vergottini indices. Inequality, welfare and deprivation in the European Union in 2000. Res Econ Inequal 16:231\u2013257","journal-title":"Res Econ Inequal"},{"issue":"1","key":"715_CR7","first-page":"421","volume":"44","author":"C Benedetti","year":"1986","unstructured":"Benedetti C (1986) Sulla interpretazione benesseriale di noti indici di concentrazione e di altri. Metron 44(1):421\u2013429","journal-title":"Metron"},{"key":"715_CR8","doi-asserted-by":"crossref","unstructured":"Berrebi ZM, Silber J (1985) Income inequality Indices and deprivation: a generalization. Q J Econ C: 807\u2013810","DOI":"10.2307\/1884380"},{"key":"715_CR9","volume-title":"Elementi di statistica generale","author":"CE Bonferroni","year":"1930","unstructured":"Bonferroni CE (1930) Elementi di statistica generale. Libreria seber, Firenze"},{"key":"715_CR10","volume-title":"Democracy, inequality and representation","author":"A Brandolini","year":"2008","unstructured":"Brandolini A, Smeeding TM (2008) Inequality patterns in western-type democracies: cross-country differences and time changes. In: Beramendi P, Anderson C (eds) Democracy, inequality and representation. Russell Sage Foundation, New York"},{"key":"715_CR11","unstructured":"Chakravarty SR (2005) The Bonferroni indices of inequality. In: International conference in memory of Gini C and Lorenz MO Universit\u2018a degli Studi di Siena, http:\/\/www.unisi.it\/event\/GiniLorenz05"},{"key":"715_CR12","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s10888-006-9054-4","volume":"5","author":"SR Chakravarty","year":"2007","unstructured":"Chakravarty SR (2007) A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality. J Econ Inequal 5:339\u2013351","journal-title":"J Econ Inequal"},{"issue":"414","key":"715_CR13","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.2307\/2234376","volume":"102","author":"FAE Coulter","year":"1992","unstructured":"Coulter FAE, Cowell F, Jenkins SP (1992) Equivalence scales relativities and the extent of inequality and poverty. Econ J 102(414):1067\u20131082","journal-title":"Econ J"},{"key":"715_CR14","first-page":"27","volume-title":"Encyclopedia of statistical sciences, vol 4","author":"C Dagum","year":"1983","unstructured":"Dagum C (1983) Income distribution models. In: Kotz S, Johnson NL, Read C (eds) Encyclopedia of statistical sciences, vol 4. Wiley, New York, pp 27\u201334"},{"key":"715_CR15","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0022-0531(80)90065-4","volume":"22","author":"D Donaldson","year":"1980","unstructured":"Donaldson D, Weymark JA (1980) A single-parameter generalization of the Gini indices of inequality. J Econ Theory 22:67\u201386","journal-title":"J Econ Theory"},{"key":"715_CR16","unstructured":"Giorgi GM (1998) Concentration index, Bonferroni. In: Kotz S, Read CB, Banks DL (eds) Encyclopedia of statistical sciences, vol 2. Wiley, New York, pp 141\u2013146"},{"issue":"1","key":"715_CR17","first-page":"1","volume":"49","author":"GM Giorgi","year":"2011","unstructured":"Giorgi GM (2011) Corrado Gini: the man and the scientist. Metron Int J Stat 49(1):1\u201328","journal-title":"Metron Int J Stat"},{"key":"715_CR18","first-page":"3","volume":"59","author":"GM Giorgi","year":"2001","unstructured":"Giorgi GM, Crescenzi M (2001) A proposal of poverty measures based on the Bonferroni inequality index. Metron Int J Stat 59:3\u201315","journal-title":"Metron Int J Stat"},{"issue":"1","key":"715_CR19","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1111\/j.1467-9779.2010.01494.x","volume":"13","author":"LJ Imedio Olmedo","year":"2011","unstructured":"Imedio Olmedo LJ, B\u00e1rcena Martin E, Parrado Gallardo EM (2011) A class of Bonferroni inequality indices. J Public Econ Theory 13(1):97\u2013124","journal-title":"J Public Econ Theory"},{"key":"715_CR20","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/0022-0531(76)90037-5","volume":"12","author":"SC Kolm","year":"1976","unstructured":"Kolm SC (1976) Unequal inequalities I. J Econ Theory 12:416\u2013442","journal-title":"J Econ Theory"},{"key":"715_CR21","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.2307\/2234247","volume":"103","author":"PJ Lambert","year":"1993","unstructured":"Lambert PJ, Aronson JR (1993) Inequality decomposition analysis and the Gini coefficient revisited. Econ J 103:1221\u20131227","journal-title":"Econ J"},{"issue":"4","key":"715_CR22","doi-asserted-by":"crossref","first-page":"805","DOI":"10.2307\/1913446","volume":"44","author":"F Mehran","year":"1976","unstructured":"Mehran F (1976) Linear measures of income inequality. Econometrica 44(4):805\u2013809","journal-title":"Econometrica"},{"key":"715_CR23","unstructured":"Piesch W (2005) Bonferroni-index und De Vergottini-index, vol 259. Diskussionspapiere aus dem Institut f\u00fcr Volkswirtschaftslehre der Universit\u00e4t Hohenheim, Germany"},{"key":"715_CR24","doi-asserted-by":"crossref","DOI":"10.1093\/0198281935.001.0001","volume-title":"On economic inequality","author":"A Sen","year":"1973","unstructured":"Sen A (1973) On economic inequality. Oxford University Press, Oxford"},{"key":"715_CR25","unstructured":"Sen A (1999) Foreword. In: Silber J (ed) Handbook on income inequality measurement. Kluwer, London"},{"key":"715_CR26","doi-asserted-by":"crossref","first-page":"485","DOI":"10.2307\/2297571","volume":"54","author":"AF Shorrocks","year":"1987","unstructured":"Shorrocks AF, Foster JE (1987) Transfer sensitive inequality measures. Rev Econ Stud 54:485\u2013497","journal-title":"Rev Econ Stud"},{"key":"715_CR27","doi-asserted-by":"crossref","unstructured":"Silber J (1989) Factors components, population subgroups and the computation of the Gini index of inequality. Rev Econ Stat LXXI:107\u2013115","DOI":"10.2307\/1928057"},{"key":"715_CR28","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/978-3-642-84250-4_15","volume-title":"Income and wealth distribution, inequality and poverty","author":"A Tarsitano","year":"1990","unstructured":"Tarsitano A (1990) The Bonferroni index of income inequality. In: Dagum C, Zenga M (eds) Income and wealth distribution, inequality and poverty. Springer, Berlin, pp 228\u2013242"},{"key":"715_CR29","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s003550050139","volume":"16","author":"C Zoli","year":"1999","unstructured":"Zoli C (1999) Intersecting generalized Lorenz curves and the Gini index. Soc Choice Welf 16:183\u2013196","journal-title":"Soc Choice Welf"}],"container-title":["Social Choice and Welfare"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-012-0715-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00355-012-0715-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-012-0715-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T14:26:58Z","timestamp":1559053618000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00355-012-0715-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,18]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["715"],"URL":"https:\/\/doi.org\/10.1007\/s00355-012-0715-x","relation":{},"ISSN":["0176-1714","1432-217X"],"issn-type":[{"value":"0176-1714","type":"print"},{"value":"1432-217X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,18]]}}}