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A new grade measure of monontone multivariate separability. (English) Zbl 1135.62336
Cuadras, Carles M. (ed.) et al., Distributions with given marginals and statistical modelling. Papers presented at the meeting, Barcelona, Spain, July 17–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0914-3/hbk). 143-151 (2002).
Summary: It was shown by D.M. Cifarelli and E. Regazzini [Sankhyā 49, No. 3, 307–319 (1987; Zbl 0647.62023)] that maximal separation of two probability measures \(P\) and \(Q\) can be assessed by a maximal concentration curve of one of the probability measures with respect to the other. In case of two univariate distributions, one can measure their monotone separation by means of a monotone concentration curve and a related numerical index \(ar\). We extend this idea to a multivariate case. We discuss the properties of a proposed index of monotone separation of multivariate distributions, especially in relation to dependence and stochastic ordering, and show examples of how the index can be used in data analysis.
For the entire collection see [Zbl 1054.62002].
62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E15 Inequalities; stochastic orderings
Lorenz curve