{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T05:37:29Z","timestamp":1770701849467,"version":"3.49.0"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,1,31]],"date-time":"2021-01-31T00:00:00Z","timestamp":1612051200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,31]],"date-time":"2021-01-31T00:00:00Z","timestamp":1612051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s00180-021-01069-4","type":"journal-article","created":{"date-parts":[[2021,1,31]],"date-time":"2021-01-31T14:02:35Z","timestamp":1612101755000},"page":"2135-2159","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Decomposition of the Gini index by income source for aggregated data and its applications"],"prefix":"10.1007","volume":"36","author":[{"given":"Bin","family":"Shao","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,31]]},"reference":[{"key":"1069_CR1","volume-title":"Linear algebra with applications","author":"O Bretscher","year":"2013","unstructured":"Bretscher O (2013) Linear algebra with applications. Pearson, London"},{"key":"1069_CR2","unstructured":"EUR Data (2014) Income components of households (in EUR, based on the total household gross income). https:\/\/ec.europa.eu\/eurostat\/statistics-explained\/index"},{"key":"1069_CR3","doi-asserted-by":"publisher","first-page":"851","DOI":"10.4169\/000298910x523344","volume":"117","author":"A Farris Frank","year":"2010","unstructured":"Farris Frank A (2010) The Gini index and measures of inequality. Am Math Mon 117:851\u2013863","journal-title":"Am Math Mon"},{"key":"1069_CR4","doi-asserted-by":"crossref","unstructured":"Heshmati A (2004) A review of decomposition of income inequality. SSRN http:\/\/ssrn.com\/abstract=571703","DOI":"10.2139\/ssrn.571703"},{"key":"1069_CR5","unstructured":"IRS Data (2017) U.S. family income to \\$250,000 or more in. https:\/\/www.census.gov\/data\/tables"},{"key":"1069_CR6","first-page":"209","volume":"9","author":"MO Lorenz","year":"1905","unstructured":"Lorenz MO (1905) Methods of measuring the concentration of wealth. J Am Stat Assoc 9:209\u2013219","journal-title":"J Am Stat Assoc"},{"key":"1069_CR7","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s11205-007-9170-y","volume":"87","author":"S Lai","year":"2008","unstructured":"Lai S, Huang M, Jan M, Kapadia Asha S (2008) Statistical properties of generalized Gini coefficient with application to health inequality measurement. Soc Indic Res 87:249\u2013258","journal-title":"Soc Indic Res"},{"issue":"1","key":"1069_CR8","doi-asserted-by":"publisher","first-page":"151","DOI":"10.2307\/1928447","volume":"67","author":"I Lerman Robert","year":"1985","unstructured":"Lerman Robert I, Shlomo Y (1985) Income inequality affects by income source, a new approach and applications to United States. Rev Econ Stat 67(1):151\u2013156","journal-title":"Rev Econ Stat"},{"issue":"17","key":"1069_CR9","doi-asserted-by":"publisher","first-page":"2457","DOI":"10.1080\/00036846.2012.667553","volume":"45","author":"M Mauro","year":"2013","unstructured":"Mauro M (2013) A matrix approach to the Gini index decomposition by subgroup and by income source. Appl Econ 45(17):2457\u20132468","journal-title":"Appl Econ"},{"key":"1069_CR10","doi-asserted-by":"publisher","first-page":"451","DOI":"10.2307\/1885088","volume":"95","author":"AF Pyatt","year":"1980","unstructured":"Pyatt AF, Chen C, Fei J (1980) The distribution of income by factor components. Q J Econ 95:451\u2013473","journal-title":"Q J Econ"},{"key":"1069_CR11","unstructured":"Rudin W (1987) Real and complex analysis. McGraw-Hill, New York, pp 61, 71"},{"key":"1069_CR12","unstructured":"Shao B (2020) On the Gini index decomposition by subgroup for aggregated data, Preprint"},{"key":"1069_CR13","doi-asserted-by":"publisher","first-page":"107","DOI":"10.2307\/1928057","volume":"71","author":"J Sillber","year":"1989","unstructured":"Sillber J (1989) Factor components, population subgroups and the computation of the Gini index of inequality. Rev Econ Stat 71:107\u2013115","journal-title":"Rev Econ Stat"},{"key":"1069_CR14","unstructured":"Vernizzi A, Monti MG, Mussini M (2010) A Gini and concentration index decomposition with an application to the APK reranking measure. https:\/\/www.researchgate\/publication\/46466388"},{"key":"1069_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5797-2","volume-title":"Theory matrix","author":"F Zhang","year":"1999","unstructured":"Zhang F (1999) Theory matrix. Springer, New York"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-021-01069-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-021-01069-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-021-01069-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T06:19:43Z","timestamp":1744179583000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-021-01069-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,31]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["1069"],"URL":"https:\/\/doi.org\/10.1007\/s00180-021-01069-4","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,31]]},"assertion":[{"value":"7 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}