Elementary multivariate rearrangements and stochastic dominance on a Fréchet class |
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Authors: | Koen Decancq |
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Institution: | 1. Center for Economic Studies, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000 Leuven, Belgium;2. CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium;3. Herman Deleeck Centre for Social Policy, University of Antwerp, B-2000 Antwerp, Belgium |
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Abstract: | A Fréchet class collects all multivariate joint distribution functions that have the same marginals. Members of a Fréchet class only differ with respect to the interdependence between their marginals. In this paper, I study orders of interdependence on a Fréchet class using two multivariate generalizations of the bivariate rearrangement proposed by Epstein and Tanny (1980) 4] and Tchen (1980) 16]. I show how these multivariate rearrangements are underlying multivariate first order stochastic dominance in terms of the joint distribution function and the survival function. A combination of both rearrangements is shown to be equivalent to the concordance order proposed by Joe (1990) 9]. |
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