Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the violation of restrictions. Such a model turns out to be appropriate for many applications and, principally, for the mean-risk portfolio selection problem. Each...

The Gini index and the Gini mean difference of a univariate distribution are extended to measure the disparity of a general d-variate distribution. We propose and investigate two approaches, one based on the distance of the distribution from itself, the other on the volume of a convex set in (d...

Trimmed regions are a powerful tool of multivariate data analysis. They describe a probability distribution in Euclidean d-space regarding location, dispersion, and shape, and they order multivariate data with respect to their centrality. Dyckerhoff and Mosler (201x) have introduced the class of...

Compared with the broad supply of literature measuring socioeconomic gradients in the distribution of health, only little is know about the life course perspective regarding income related inequalities. This article combines the reowned concentration index approach with semiparametric estimation...

The paper presents an approach to the measurement of economic disparity in several commodities. We introduce a special view on the usual Lorenz curve and extend this view to the multivariate situation: Given a vector of shares of the total endowments in each commodity, the multivariate inverse...

We consider four orthant stochastic orderings between random vectors X and Y that have finitely discrete probability distributions in IRk. For each of the orderings conditions have been developed that are necessary and sufficient for dominance of Y over X. We present an algorithm that checks...