Poverty is usually defined as the extent to which individuals in a society or community fall below a minimal acceptable standard of living. An index of poverty is generally based on the proportion (α) of the poor people and their income distribution through the income gap ratio (β) (i.e., the average income gap of the poor people from the poverty line ω, taken as a ratio to ω itself) and other measures of income inequalities. In this context, the well-known Gini coefficient of income inequality plays a vital role. In view of the fact that the poverty indexes all relate to the income pattern of the poor, interpreted in some way or other, usually a censored (Gω) or truncated (Gα) version of the classical Gini coefficient (G) is incorporated in the formulation of such indexes. Among the various poverty indexes, πA= αβ, πτ = Gcω, and πs=α{β+(1-β)Gα} have been used more extensively than the others. Although each of πSand πTis justified on the grounds of certain plausible axioms, from a statistical point of view, generally, for smaller values of α and β, πτ is somewhat more conservative whereas πSis more anticonservative than they should have been ideally. This phenomenon is mainly due to the two forms of the Gini coefficientGcωandGα, which behave rather differently with the variation of α, β, and the income inequalities among the poor people. This calls for a more intensive study of the behavior of the Gini coefficient under various patterns of income inequality and its role in the formulation of poverty indexes. This examination leads to consideration of a more robust version of πS, namely, π*=αβ1-Gα. In this context, TTT transformations (usually arising in reliability theory and life testing problems) are incorporated to provide a new interpretation of the Gini coefficient; in light of this, the relationship betweenGαandGcωand suitable bounds for either of these indexes are studied in detail. These results, in turn, facilitate the study of the relative and absolute interpretations of these poverty indexes, in the light of which the weakness of the index πτ and the relative strengths of πSand π* have also been discussed.