  For the decomposability property is very a practical one in Welfare analysis,
most researchers and users favor decomposable poverty 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 Indice (GPI) and of a new
asymptotic representation Theorem for it, in terms of functional empirical
processes theory. 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.
