  We set in this paper a coherent theory based on functional empirical
processes to consider both the poverty and the inequality indices in one
Gaussian field enabling to study the influence of the one on the other. We use
the General Poverty Index (\textit{GPI}), that is a class of poverty indices
covering the most common ones and a functional class of inequality measure
including the Entropy Measure, the Mean Logarithmic Deviation, the different
inequality measures of Atkinson, Champernowne, Kolm and Theil called Theil-like
Inequality Measures \textit{TLIM}. Our results are given in a unified approach
with respect to the two classes instead of their particular elements. We
provide the asymptotic laws of the variations of each class over two given
periods and the ratio of the variation and derive confidence intervals for
them. Although the variances may seem somehow complicated, we provide R codes
for their computations and apply the results for the pseudo-panel data for
Senegal with simple analysis.
