Statistical estimation of gap of decomposability of the general poverty index

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.