On the Decomposition by Subgroups of the Gini Index and Zenga's Uniformity and Inequality Indexes

By P. Radaelli. 2010

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$L$-functions, processes, and statistics in measuring economic inequality and actuarial risks (2009, methodology): “With the above notation, the uniformity index U can now be decomposed as the weighted average (see Radaelli [75] for details) U = ∑ i [W Ui Ai + BUi (1 − Ai)] ni· N (26) = W U A + BU (1 − A), where A = ∑ i Ai ni· N can be interpreted as the overall weight for the uniformity indices evaluated within ”
Approximation and decomposition of Gini, Pietra–Ricci and Theil inequality measures (2012, background): “…based on the ratios between lower and upper arithmetic means, and its group decomposition obtained by Radaelli, are worth mentioning (Zenga 2007; Radaelli 2008), amongst the most meaningful applications and discussions of group decomposition, at least the research by Quintano et al. (2009) on…”
WEALTH INEQUALITY: A SURVEY (2015, unknown): “We then have the following formula (Cowell 2013, Radaelli 2010) IGini (F ) = πPsPIGini (FP) + πRsRIGini (FR) + IGini (FBetw) , (17) which gives an exact formula for decomposing the Gini coefficient into the nonoverlapping subgroups P and R.”