0642182 20260224164123.920251126235959.9 105004722433 001484483800001 10.1080/07350015.2025.2475964 13 s. P cav_un_epca*02511380735-0015434 (2025)1092-1104 Concentration indices Inequality measurement Middle class Optimal transport Measure transportation Multivariate quantiles cav_un_auth*0478146 Hallin Marc UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI BE Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0497844 Mordant G. DE https://library.utia.cas.cz/separaty/2025/SI/hallin-0642182.pdf https://www.tandfonline.com/doi/full/10.1080/07350015.2025.2475964 GA22-03636S GA ČR CZ cav_un_auth*0435411 Based on measure transportation ideas and the related concepts of quantile functions and regions, we propose multiple-output generalizations of the traditional univariate concepts of Lorenz and concentration functions, and the related Gini and Kakwani coefficients. These new concepts have a natural interpretation, either in terms of contributions of quantile regions to the expectation of some variable of interest, or in terms of the physical notions of work and energy, which sheds new light on the nature of economic and social inequalities. When based on center-outward quantile regions, the proposed concepts pave the way to a statistically sound definition, based on multiple attributes, of the notion, so far limited to bivariate characterizations, of middle-class—a notion of practical importance in various socio-economic and political contexts. WOS BB 10000 10100 10103 2026 RVO:67985556 https://hdl.handle.net/11104/0372933 S C SOCIALSCIENCES.MATHEMATICALMETHODS|ECONOMICS|STATISTICS&PROBABILITY 5.1 0.6 12.9 0.01694 4.227 9056 122 4.171 41.67 3.2 1207 Q1 2.400 84 Q1 79.6 0.76 Q1 87.9 2025 105004722433 SCOPUS PUBMED 001484483800001 WOS cav_un_epca*0251138 Journal of Business & Economic Statistics 43 4 2025 1092 1104 0735-0015 1537-2707