In this paper we investigate a new class of central regions for probability distributions on Rd, called weighted-mean regions. Their restrictions to an empirical distribution are the weighted-mean trimmed regions investigated by Dyckerhoff and Mosler (2011) for d-variate data. Furthermore a new...

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...

A new procedure, called DD-procedure, is developed to solve the problem of classifying d-dimensional objects into q Ï 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0, 1]q ....

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...

A new procedure, called D D α-procedure, is developed to solve the problem of classifying d-dimensional objects into q ≥ 2 classes. The procedure is nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0,1]<Superscript> q </Superscript>....</superscript>

ABSTRACTA Gini‐type concentration index is combined with semiparametric estimation techniques to derive a varying inequality index that works without a priori sample stratification. The new approach is used to investigate the question how income inequalities and income‐related gradients in...

The paper investigates Lorenz dominance and generalized Lorenz dominance to compare distributions of economic status in one and several attributes. Restrictions of these dominance relations are developed that focus on central parts of the distributions and facilitate their comparison. Copyright...