The publication database is continuously updated. Documents from older years will also be added gradually.
Herlyn, E.; Radermacher, F. J.
A 1-1-1 relationship for World Bank Income Data and the Gini Journal Article
In: ECINEQ Working Paper 2018, vol. 473, 2018.
Abstract | Links | BibTeX | Tags: Approximation, English, income inequality, Lorenz curves, World Bank data
@article{Herlyn2018c,
title = {A 1-1-1 relationship for World Bank Income Data and the Gini},
author = {E. Herlyn and F. J. Radermacher},
url = {http://www.ecineq.org/milano/WP/ECINEQ2018-473.pdf},
year = {2018},
date = {2018-08-03},
journal = {ECINEQ Working Paper 2018},
volume = {473},
abstract = {The paper provides insights of significant practical relevance into the nature of empirical income distri-bution data, provided by World Bank (and by EU-SILC as well). The insight covers mature states and their economic and societal system. Proceeding from a Gini value .., as published by the World Bank, it is possible to derive, as close approximation, the actual income distribution, with standardised total income 1, and a mathematical representation. We call this the standard Lorenz curve LG. LG is of type LG = 0.6 ·P areto(ε) + 0.4 ·P olynomial(ε), where P areto(ε) and P olynomial(ε) are the Pareto and polynomial Lorenz curves for a parameter ε with ε = (1−G)/(1+G) and G = (1−ε)/(1+ε). If the total income level of the considered distribution is known, then the distribution of absolute income can also be derived. If, in addition, one knows the number of income earners, then one also knows the distribution of the absolute income within a population. All together our summarizing statement is: ”For mature economies, analysing World Bank and EU-SILC income data, there is essentially a cross-country and cross-year 1-1-1 correspondence between the GINI, the corresponding decile resp. quintile information and the respective standard Lorenz curve described above.” Some interesting mathematics is involved to reach the main result. The insights obtained will hopefully enable economists and social scientists to further develop their work in the field of income inequality and associated social phenomena.},
keywords = {Approximation, English, income inequality, Lorenz curves, World Bank data},
pubstate = {published},
tppubtype = {article}
}
Radermacher, F. J.
Lorenz Curves and Atkinson Theorem – Some Recent Insights Book Chapter
In: Ahn, H.; Clermont, M.; Souren, R. (Ed.): Nachhaltiges Entscheiden - Beiträge zum multiperspektivischen Performancemanagement von Wertschöpfungsprozessen, Chapter 4, pp. 49-72, Springer Gabler, Wiesbaden, 2016, ISBN: 978-3-658-12505-9.
Abstract | Links | BibTeX | Tags: English, Finite Sequence, Generalize Inverse, income distribution, Lorenz curves, Support Point
@inbook{Radermacher2016,
title = {Lorenz Curves and Atkinson Theorem – Some Recent Insights},
author = {F. J. Radermacher},
editor = {H. Ahn and M. Clermont and R. Souren},
url = {https://link.springer.com/chapter/10.1007/978-3-658-12506-6_4},
doi = {10.1007/978-3-658-12506-6_4},
isbn = {978-3-658-12505-9},
year = {2016},
date = {2016-01-20},
booktitle = {Nachhaltiges Entscheiden - Beiträge zum multiperspektivischen Performancemanagement von Wertschöpfungsprozessen},
pages = {49-72},
publisher = {Springer Gabler},
address = {Wiesbaden},
chapter = {4},
abstract = {This paper deals with Lorenz curves. They allow for the representation of ‘inequality’ or ‘variability’ independent from absolute magnitudes. The general case is concerned with individuals or objects with an associated non-negative value such as body mass, body height, wealth owned, economic value or return from a customer or product.},
keywords = {English, Finite Sequence, Generalize Inverse, income distribution, Lorenz curves, Support Point},
pubstate = {published},
tppubtype = {inbook}
}
Kämpke, T.
Proportionality-induced distribution laws Book Section
In: Income Modeling and Balancing, pp. 129–140, Springer, 2012.
Abstract | Links | BibTeX | Tags: convex stochastic order, English, Lorenz curve, Lorenz curves, Lorenz order
@incollection{kampke2015proportionality,
title = {Proportionality-induced distribution laws},
author = { T. Kämpke},
url = {https://link.springer.com/chapter/10.1007%2F978-3-319-13224-2_8
https://www.fawn-ulm.de/wp-content/uploads/2020/05/Proportionality_laws.pdf},
year = {2012},
date = {2012-04-14},
booktitle = {Income Modeling and Balancing},
pages = {129--140},
publisher = {Springer},
abstract = {Lorenz curves for income distributions are developed in a systematic way by relating individual incomes to averages of certain income groups. Each such distribution law yields an ordinary differential equation. Many of the differential equations allow explicit solutions leading to parametric kinds of Lorenz curves.},
keywords = {convex stochastic order, English, Lorenz curve, Lorenz curves, Lorenz order},
pubstate = {published},
tppubtype = {incollection}
}
Kämpke, T.; Radermacher, F. J.
Lorenz curves and partial orders Technical Report
2012.
Abstract | Links | BibTeX | Tags: Atkinson theorem, convex stochastic order, English, Lorenz curve, Lorenz curves, Lorenz order, majorization
@techreport{-,
title = {Lorenz curves and partial orders},
author = {T. Kämpke and F. J. Radermacher},
url = {https://www.fawn-ulm.de/wp-content/uploads/2014/06/Order_relations.pdf},
year = {2012},
date = {2012-04-05},
abstract = {We compile classical relations between the Lorenz order and majorization for finite discrete distributions and between the Lorenz order and the convex order for all other distributions. Simple transfers of the Pigou-Dalton type are extended as far as possible including approximations of continuous distributions.},
howpublished = {Diskussionspapier},
keywords = {Atkinson theorem, convex stochastic order, English, Lorenz curve, Lorenz curves, Lorenz order, majorization},
pubstate = {published},
tppubtype = {techreport}
}
Kämpke, T.; Radermacher, F. J.
Lorenz curves – history, state and some recent results Technical Report
2012.
Abstract | Links | BibTeX | Tags: convex stochastic order, English, Lorenz curve, Lorenz curves, Lorenz order
@techreport{-,
title = {Lorenz curves – history, state and some recent results},
author = {T. Kämpke and F. J. Radermacher},
url = {https://www.fawn-ulm.de/wp-content/uploads/2014/06/History.pdf},
year = {2012},
date = {2012-02-15},
abstract = {Lorenz curves are established under general conditions following an integral transform approachaging approximately 40 years. The derivation of this approach is given together with quite a few ex-planations, well known and widely-spread (yet well hidden?) facts from the literature, and some freshviews. The approach is based on relating the underlying distributions, typically income distributions,to probability distributions.The equity calculus, which is inspired by a notion of relative poverty, is shown to deliver a varietyof differential equations for Lorenz curves. Most admit one-parametric closed form solutions whilesolvability of others is still unsettled.},
howpublished = {Diskussionspapier},
keywords = {convex stochastic order, English, Lorenz curve, Lorenz curves, Lorenz order},
pubstate = {published},
tppubtype = {techreport}
}
Kämpke, T.; Radermacher, F. J.
Analytische Eigenschaften von Equity-Lorenzkurven Miscellaneous
Materialsammlung, 2011.
Abstract | Links | BibTeX | Tags: Lorenz curve, Lorenz curves, Lorenz order
@misc{-e,
title = {Analytische Eigenschaften von Equity-Lorenzkurven},
author = {T. Kämpke and F. J. Radermacher},
url = {https://www.fawn-ulm.de/wp-content/uploads/2014/06/Analytische_Eigenschaften.pdf},
year = {2011},
date = {2011-11-15},
abstract = {Das vorliegende Dokument entwickelt und beweist „Analytische Eigenschaften von Equity-Lorenzkurven“. Diese Resultate wurden von den Autoren überwiegend im Zusammenhang mit der Dissertation [1] an der RWTH Aachen erzielt. In der Dissertation steht die Präsentation der Theorie der Equity-Lorenzkurven und ökomische Ableitungen aus mathematischen Ergebnissen im Vordergrund. Die dazu korrespondierende mathematische Basis wurde am FAW/n entwickelt und befindet sich in Teilen in dieser Materialsammlung. Dies betrifft insbesondere Fragestellungen, die in [1] in Kapitel 8 behandelt werden. Sofern Aussagen in [1] genutzt werden, wird das hier als Fußnote festgehalten. Die hier formalisierten Aussagen sind teilweise allgemeiner als die Formulierungen in [1]. Es gibt ferner ergänzende Aussagen, die in [1] nicht vorkommen. Aus Vereinfachungsgründen bzw. systematischen Überlegungen wechseln manchmal auch die Bezeichnungen. },
howpublished = {Materialsammlung},
keywords = {Lorenz curve, Lorenz curves, Lorenz order},
pubstate = {published},
tppubtype = {misc}
}
Kämpke, T.
On duality transformations between Lorenz curves and distribution functions Miscellaneous
Diskussionspapier, 2011.
Abstract | Links | BibTeX | Tags: convex stochastic order, Lorenz curve, Lorenz curves, Lorenz order
@misc{-e,
title = {On duality transformations between Lorenz curves and distribution functions},
author = {T. Kämpke},
url = {https://www.fawn-ulm.de/wp-content/uploads/2014/06/Lorenz-duality.pdf},
year = {2011},
date = {2011-05-25},
abstract = {The relation between distribution functions and Lorenz curves is often denoted as their duality. Duality is established via transformations which can be understood as forward and backward transformations. It is often implicated that the interplay between distribution functions and Lorenz curves depends on the functions alone. It is the purpose of this short investigation to show that more than one transformation exists – at least in special cases.},
howpublished = {Diskussionspapier},
keywords = {convex stochastic order, Lorenz curve, Lorenz curves, Lorenz order},
pubstate = {published},
tppubtype = {misc}
}
Kämpke, T.
Selbstähnlichkeit von Lorenzkurven Miscellaneous
Diskussionspapier, 2011.
Abstract | Links | BibTeX | Tags: Lorenz curve, Lorenz curves, Lorenz order
@misc{-e,
title = {Selbstähnlichkeit von Lorenzkurven},
author = {T. Kämpke},
url = {https://www.fawn-ulm.de/wp-content/uploads/2014/06/Selbstaehnlichkeit-Lorenzkurven.pdf},
year = {2011},
date = {2011-01-12},
abstract = {Der Begriff der Selbstähnlichkeit wird auf Lorenzkurven angepasst. Hierzu werden Trankierungen von Lorenzkurven vorgenommen. Sofern eine Lorenzkurve mit allen ihren Trankierungen übereinstimmt oder eine Lorenzkuve nur den gleichen Ginikoeffizienten wie alle ihre Trankierungen hat, ist sie vom Paretotyp/Equitytyp.},
howpublished = {Diskussionspapier},
keywords = {Lorenz curve, Lorenz curves, Lorenz order},
pubstate = {published},
tppubtype = {misc}
}
Kämpke, T.
A straightforward and versatile calculus for income inequality Technical Report
2010.
Abstract | Links | BibTeX | Tags: Index numbers, Lorenz curve, Lorenz curves, welfare aggregation
@techreport{-e,
title = {A straightforward and versatile calculus for income inequality},
author = {T. Kämpke},
url = {https://www.fawn-ulm.de/wp-content/uploads/2014/06/Straightforward_calculus.pdf},
year = {2010},
date = {2010-01-01},
abstract = {A calculus based on one-parametric Lorenz curves is shown to enable versatile computations over income distributions. These computations focus on empirical as well as on conceptural issues. One empirical issue is the computation of the so-called equity parameter from support points of any Lorenz curve. One conceptual issue is a merger computation that allows for a novel separation of a population into a rich and a poor constituent. This separation allows that the two constituents mix rather than, conventionally, be divided by a given threshold value.},
keywords = {Index numbers, Lorenz curve, Lorenz curves, welfare aggregation},
pubstate = {published},
tppubtype = {techreport}
}
Kämpke, T.
The use of mean values vs. medians in inequality analysis Technical Report
2008.
Abstract | Links | BibTeX | Tags: income distribution, Lorenz curve, Lorenz curves, poverty line
@techreport{-f,
title = {The use of mean values vs. medians in inequality analysis},
author = {T. Kämpke},
url = {https://www.fawn-ulm.de/wp-content/uploads/2014/06/Median.pdf},
year = {2008},
date = {2008-10-10},
abstract = {Poverty lines that are proportional to either the mean value or the median of income distributions are compared by statistical properties and in the light of poverty axioms. Poverty lines are extended from all incomes such that any particular income is considered as smallest of all larger incomes. This induces classes of income distributions with the distributions for the median being much more unequal than for the mean value.},
keywords = {income distribution, Lorenz curve, Lorenz curves, poverty line},
pubstate = {published},
tppubtype = {techreport}
}