Constructing indices of multivariate polarization ∗ by Chiara Gigliarano and Karl Mosler

Constructing indices of multivariate polarization ∗ by Chiara Gigliarano and Karl Mosler July 9 , 2007

Multivariate indices of polarization are constructed to measure effects of non-income attributes like wealth and education. Polarization is considered as the presence of groups which are internally homogeneous, externally heterogeneous, and of similar size. We propose a class of polarization indices which is built from measures of relative groups size and from decomposable indices of socio-econ...

An Inter-temporal Relative Deprivation Index

A general solution for robust linear programs with distortion risk constraints

Linear optimization problems are investigated that have random parameters in their m ≥ 1 constraints. In constructing a robust solution x ∈ R, we control the risk arising from violations of the constraints. This risk is measured by set-valued risk measures, which extend the usual univariate coherent distortion (= spectral) risk measures to the multivariate case. To obtain a robust solution in d...

Multivariate Lorenz dominance based on zonoids∗

The classical Lorenz curve visualizes and measures the disparity of items which are characterized by a single variable: The more the curve bends, the more scatter the data. Recently a general approach has been proposed and investigated that measures the disparity of multidimensioned items regardless of their dimension. This paper surveys various generalizations of Lorenz curve and Lorenz domina...

The declining middle class in one and many attributes ∗

A new multivariate approach is introduced to identify the middle class of a society and to measure its possible decline. The middle class is a properly defined central region in attribute space that contains a fixed portion of the population. The decline of the middle class is measured by comparing volumes of the middle class. The use of different notions of central regions is discussed in one ...