Abstract
§1. If a quantity α is to serve as a measure of the degree of relationship between two random variables X and Y, we will want to place three fundamental conditions on it, among others:
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I.
α should lie between two fixed finite bounds (say 0 and 1).
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II.
α should equal the lower bound if and only if X and Y are stochastically independent.
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III.
α should equal the upper bound if and only if X and Y are functionally dependent.
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Hoeffding, W. (1994). Stochastic Dependence and Functional Relationships. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_6
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