Distorted Lorenz curves: models and comparisons

The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve $$L$$ L by a function $$h$$ h , giving rise to a distorted Lorenz curve $${\widetilde{L}}=h\circ L$$ L ~ = h ∘ L . In this paper, we study, in a unified framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aaberge ( 2001 ) for orderings on the set of Lorenz curves. Then, we describe some particular models and investigate how changes in the parameters in the baseline Lorenz curve $$L$$ L affect the transformed curve $${\widetilde{L}}$$ L ~ . Our results are stated in terms of preservation of some stochastic orders between two Lorenz curves when both are distorted by a common function. Copyright Springer-Verlag Berlin Heidelberg 2014