Multivariate Majorization

Somesh Das Gupta and Subir Kumar Bhandari
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Somesh Das Gupta: Indian Statistical Institute
Subir Kumar Bhandari: Indian Statistical Institute

Chapter 3 in Contributions to Probability and Statistics, 1989, pp 63-74 from Springer

Abstract: Abstract The concept of univariate majorization plays a central role in the study of Lorenz dominance for income distribution comparisions in economics. The first part of this paper reviews different conditions which are equivalent to Lorenz dominance. The second part of the present paper poses the question whether such equivalences extend to the multivariate case. Some concepts of multivariate majorization are presented along with a few new results. For economic applications, the notion of a concave utility function on vector observations appears to play a crucial role in multivariate majorization. It is shown that such concavity follows from some easily understandable axioms.

Keywords: Concave Function; Pareto Distribution; Inequality Measure; Stochastic Matrix; Multivariate Case (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-3678-8_6

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DOI: 10.1007/978-1-4612-3678-8_6

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