For the decomposability property is a very practical one in Welfare analysis, most researchers and users favour decomposable indices such as the Foster-Greer-Thorbeck poverty index. This may lead to neglect the so important weighted indices like the Kakwani and Shorrocks ones which have interesting other properties in Welfare analysis. To face up to this problem, we give in this paper, statistical estimations of the gap of decomposability of a large class of such indices using the General Poverty Indices (GPI). The results are derived from a new asymptotic representation Theorem of L-statstics, in terms of functional empirical processes. The results then enable independent handling of targeted groups and next global reporting with significant confidence intervals. Data-driven examples are given with real data.

Keywords: Poverty measures; Empirical process; Multinomial law; Spatial statistical

Biography: Mr Haidara is a young statistician completing his Ph.D dissertation in Saint-Louis University (Senegal).