Summary
Definitions of different strengths are given to the notion of ‘a stochastically larger component of a two-dimensional random vector.’ Some of them reduce to the known definitions of stochastic order relationship when the components are stochastically independent. The definitions and the approach are related to nonparametric problems.
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Yanagimoto, T., Sibuya, M. Stochastically larger component of a random vector. Ann Inst Stat Math 24, 259–269 (1972). https://doi.org/10.1007/BF02479756
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DOI: https://doi.org/10.1007/BF02479756