Summary
There are many possible candidates for measures of location of asymmetric probability distributions. This difficulty is compounded for multivariate distributions. It is the purpose of this paper to characterize the set of all possible measures of location for a given bivariate probability distribution. A closed, convex region in the plane will be constructed, any point of which is a reasonable measure of location. Reasonable here refers to the invariance of the region under certain transformations and order relations. The size of this region can be used to characterize the degree of asymmetry that a distribution possesses.
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References
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Blough, D.K. Measures of location in the plane. Ann Inst Stat Math 37, 545–555 (1985). https://doi.org/10.1007/BF02481124
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DOI: https://doi.org/10.1007/BF02481124