A functional derivative useful for the linearization of inequality   indexes in the design-based framework
  Linearization methods are customarily adopted in sampling surveys to obtain approximated variance formulae for estimators of nonlinear functions of finite population totals - such as ratios, correlation coefficients or measures of income inequality - which can be usually rephrased in terms of statistical functionals. In the present paper, by considering the Deville (1991) approach stemming on the concept of design-based influence curve, we provide a general result for linearizing large families of inequality indexes. As an example, the achievement is applied to the Gini, the Amato, the Zenga and the Atkinson indexes, respectively. 
Lucio Barabesi, Giancarlo Diana, Pier Francesco Perri
stat.ME