@article {Krause:2014:0034-6586:905,
title = "Parametric Lorenz Curves and the Modality of the Income Density Function",
journal = "The Review of Income and Wealth",
parent_itemid = "infobike://bpl/roiw",
publishercode ="bp",
year = "2014",
volume = "60",
number = "4",
publication date ="2014-12-01T00:00:00",
pages = "905-929",
itemtype = "ARTICLE",
issn = "0034-6586",
eissn = "1475-4991",
url = "https://www.ingentaconnect.com/content/bpl/roiw/2014/00000060/00000004/art00014",
doi = "doi:10.1111/roiw.12047",
keyword = "goodness of fit, C13, C16, D31, income distribution, inequality, modality, Lorenz curve",
author = "Krause, Melanie",
abstract = "Similar looking Lorenz curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz curve and the modality of its underlying income density: given a parametric Lorenz curve,
it is the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e., downwardsloping). The density modality of several important Lorenz curves such as the Pareto, Weibull, SinghMaddala parametrizations and hierarchical families of Lorenz
curves are discussed. A Lorenz curve performance comparison with Monte Carlo simulations and data from the UNUWIDER World Income Inequality Database underlines the relevance of the theoretical result: curvefitting based on criteria such as mean squared error or the Gini difference
might lead to a Lorenz curve implying an incorrectlyshaped density function. It is therefore important to take into account the modality when selecting a parametric Lorenz curve.",
}