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

## 2019 |

Herlyn, E; Radermacher, F J Income Distribution and Social Policy: Relevance for the Social Dimension of Sustainability Journal Article Cadmus, 4 (1), pp. 74-81, 2019. Abstract | Links | BibTeX | Tags: English, income distribution, social policy @article{Herlyn2019, title = {Income Distribution and Social Policy: Relevance for the Social Dimension of Sustainability}, author = {E. Herlyn and F. J. Radermacher}, url = {https://www.fawn-ulm.de/wp-content/uploads/2020/06/Income-Distribution-and-Social-Policy-EHerlyn-FJRadermacher-Cadmus-V4-I1-Reprint.pdf}, year = {2019}, date = {2019-10-12}, journal = {Cadmus}, volume = {4}, number = {1}, pages = {74-81}, abstract = {This publication provides clues to the phenomenon of increasing social division within rich societies. At the same time, it refers to more recent insights of a partly empirical, partly mathematical type, which make it possible to describe the income situation of mature states/market economies solely by means of the so-called Gini coefficient. The Gini coefficient is the most important parameter for describing inequalities. The fact that it can fully describe the situation in the case of income distribution is both surprising and practically helpful. The present paper also refers to some consequences of the analysis of income distributions for the interpretation of political processes. It also provides information on the so-called “efficient inequality range”. This describes the spectrum in which balance or inequality has a positive effect on societies. A variety of further details on the issues addressed can be found in the references given, in particular [4, 6, 9].}, keywords = {English, income distribution, social policy}, pubstate = {published}, tppubtype = {article} } This publication provides clues to the phenomenon of increasing social division within rich societies. At the same time, it refers to more recent insights of a partly empirical, partly mathematical type, which make it possible to describe the income situation of mature states/market economies solely by means of the so-called Gini coefficient. The Gini coefficient is the most important parameter for describing inequalities. The fact that it can fully describe the situation in the case of income distribution is both surprising and practically helpful. The present paper also refers to some consequences of the analysis of income distributions for the interpretation of political processes. It also provides information on the so-called “efficient inequality range”. This describes the spectrum in which balance or inequality has a positive effect on societies. A variety of further details on the issues addressed can be found in the references given, in particular [4, 6, 9]. |

## 2016 |

Radermacher, F J Lorenz Curves and Atkinson Theorem – Some Recent Insights Book Chapter 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} } 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. |

## 2015 |

Kämpke, T; Radermacher, F J Income Modeling and Balancing – A Rigorous Treatment of Distribution Patterns Book Springer International Publishing, 2015, ISBN: 978-3-319-13223-5. Abstract | Links | BibTeX | Tags: Balance, English, equity, income distribution, Weltfinanzsystem @book{Income_Modeling_Balancing_2015, title = {Income Modeling and Balancing – A Rigorous Treatment of Distribution Patterns}, author = {T. Kämpke and F. J. Radermacher}, url = {https://www.springer.com/gp/book/9783319132235}, doi = {10.1007/978-3-319-13224-2}, isbn = {978-3-319-13223-5}, year = {2015}, date = {2015-00-00}, publisher = {Springer International Publishing}, abstract = {This book presents a rigorous treatment of the mathematical instruments available for dealing with income distributions, in particular Lorenz curves and related methods. The methods examined allow us to analyze, compare and modify such distributions from an economic and social perspective. Though balanced income distributions are key to peaceful coexistence within and between nations, it is often difficult to identify the right kind of balance needed, because there is an interesting interaction with innovation and economic growth. The issue of justice, as discussed in Thomas Piketty’s bestseller “Capital in the Twenty-First Century” or in the important book “The Price of Inequality” by Nobel laureate Joseph Stiglitz, is also touched on. Further, there is a close connection to the issue of democracy in the context of globalization. One highlight of the book is its rigorous treatment of the so-called Atkinson theorem and some extensions, which help to explain under which type of societal utility functions nations tend to operate either in the direction of more balance or less balance. Finally, there are some completely new insights into changing the balance pattern of societies and the kind of coalitions between richer and poorer parts of society to organize political support in democracies in either case. }, keywords = {Balance, English, equity, income distribution, Weltfinanzsystem}, pubstate = {published}, tppubtype = {book} } This book presents a rigorous treatment of the mathematical instruments available for dealing with income distributions, in particular Lorenz curves and related methods. The methods examined allow us to analyze, compare and modify such distributions from an economic and social perspective. Though balanced income distributions are key to peaceful coexistence within and between nations, it is often difficult to identify the right kind of balance needed, because there is an interesting interaction with innovation and economic growth. The issue of justice, as discussed in Thomas Piketty’s bestseller “Capital in the Twenty-First Century” or in the important book “The Price of Inequality” by Nobel laureate Joseph Stiglitz, is also touched on. Further, there is a close connection to the issue of democracy in the context of globalization. One highlight of the book is its rigorous treatment of the so-called Atkinson theorem and some extensions, which help to explain under which type of societal utility functions nations tend to operate either in the direction of more balance or less balance. Finally, there are some completely new insights into changing the balance pattern of societies and the kind of coalitions between richer and poorer parts of society to organize political support in democracies in either case. |

## 2008 |

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} } 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. |

## 2001 |

Kämpke, T; Stark, M Equality functions Miscellaneous Diskussionspapier, 2001. Abstract | Links | BibTeX | Tags: differential equation, income distribution, Lorenz curve @misc{-g, title = {Equality functions }, author = {T. Kämpke and M. Stark}, url = {https://www.fawn-ulm.de/wp-content/uploads/2015/08/Equality_functions.pdf}, year = {2001}, date = {2001-07-01}, abstract = {The equality parameter as a highly aggregated index of an income distribution is complemented by the finer measure of an equality function. Lorenz curves with linear equality functions are developed and fitted to empirical data by squared error regression. The transition from equality parameters to equality functions significantly reduces regression errors. Relative poverty lines are subsequently introduced, computed approximately and their induced rankings of nations are investigated.}, howpublished = {Diskussionspapier}, keywords = {differential equation, income distribution, Lorenz curve}, pubstate = {published}, tppubtype = {misc} } The equality parameter as a highly aggregated index of an income distribution is complemented by the finer measure of an equality function. Lorenz curves with linear equality functions are developed and fitted to empirical data by squared error regression. The transition from equality parameters to equality functions significantly reduces regression errors. Relative poverty lines are subsequently introduced, computed approximately and their induced rankings of nations are investigated. |