Any empirical evidence for the income distribution version of the Kuznets's Curve?

The format should be following

-- Introduction: generally, introduce the ideas of income distribution and of inequality and welfare.

-- Main Content:

-- Definition and key characteristics of income inequality and poverty (with some specific examples)

-- Definition and key characteristics/measures of the ideas of welfare

-- Outline trends in inequality and its importance for development outcomes

-- Outline the concepts and tools used to assess income distribution (e.g. Lorenz Curve, Gini Coefficient and possibly others)

-- Explain the history and development of Kuznets' inverted U-shaped hypothesis and some evidences

(A good answer will comment on the methodological limitations of economic observations)

-- Conclusions