By using Chibisov–O’Reilly type theorems for uniform empirical and quantile processes based on stationary observations, we establish a weak approximation theory for empirical Lorenz curves and their inverses used in economics. In particular, we obtain weak approximations for empirical Lorenz curves and their inverses also under the assumptions of mixing dependence, often used structures of dependence for observations.

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Keywords Empirical concentration process, Empirical Lorenz process, Empirical process, Inverse Lorenz curve, Lorenz curve, Mixing, Quantile process, Stationarity, Weighted metric
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Journal Advances in Applied Probability
Csörgo, M, & Yu, H. (Hao). (1999). Weak approximations for empirical lorenz curves and their goldie inverses of stationary observations. Advances in Applied Probability, 31(3), 698–719. doi:10.1239/aap/1029955200