Before revision:  We study different approaches to the estimation of the Gini index in presence of a heavy tailed data generating process, that is, one with Paretan tails and/or in the stable distribution class with finite mean but non-finite variance ( with tail index \alpha\in(1,2)).
After revision:  We study different approaches to the estimation of the Gini index in presence of a fat-tailed data generator process, i.e. one in the stable distribution class with finite mean but non-finite variance ( with tail index \alpha\in(1,2)).