Distorted Lorenz curves: models and comparisons

Miguel Sordo (), Jorge Navarro and José María Sarabia ()

Social Choice and Welfare, 2014, vol. 42, issue 4, 780 pages

Abstract: 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

Date: 2014
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DOI: 10.1007/s00355-013-0754-y

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