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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$L$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>L</mi> </math> </EquationSource> </InlineEquation> by a function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$h$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>h</mi> </math> </EquationSource> </InlineEquation>, giving rise to a distorted Lorenz curve <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${\widetilde{L}}=h\circ L$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mover accent="true"> <mi>L</mi> <mo stretchy="true">~</mo> </mover> <mo>=</mo> <mi>h</mi> <mo>∘</mo> <mi>L</mi> </mrow> </math> </EquationSource> </InlineEquation>. 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 (<CitationRef CitationID="CR2">2001</CitationRef>) 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$L$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>L</mi> </math> </EquationSource> </InlineEquation> affect the transformed curve <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$${\widetilde{L}}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mover accent="true"> <mi>L</mi> <mo stretchy="true">~</mo> </mover> </math> </EquationSource> </InlineEquation>. 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
