The publication database is continuously updated. Documents from older years will also be added gradually.
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}
}