I am going to write about Lorenz curves and inference about them in a series of posts. This first post tries to explain why there are so much interests in Lorenz curves.

CDF and PDF are the first things come to mind when thinking of a distribution but there is another representation namely the Lorenz curve that is as widely used and estimated (if not more) in some contexts such as income distribution analyses. Here are the reasons that I can think for popularity of Lorenz curves:

1- Lorenz curve is more intuitive: it depicts the cumulative income percentage vs the cumulative population percentage which is easier to comprehend compared to say histogram.

2- Many concepts in poverty and inequality analysis (Gini coefficient, stochastic dominance, etc) can be more easily defined in terms of a Lorenz Curve.

3- A Lorenz curve completely characterizes a distribution.

4- Available data sets are often in the form of cumulative income percentages and cumulative population percentages.

5- Estimation and statistical inference for a Lorenz curve is easier (this one is debatable)

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