Association arrays in assessing forms of dependencies between bivariate random variables.
The bivariate distribution of pairs of random variables (X,Y) is said to be associated with respect to the classes of functions [unk] and [unk] if the product-moment correlation r[Phi(X),Psi(Y)] >/= 0 for all Phi euro [unk] and Psi euro [unk]. In the case in which both [unk] = [unk] = [unk](*) consist of all increasing functions, then the bivariate distribution of (X,Y) is said to be positive quadrant dependent. To apply the concept to data, I examine the correlations for classes of extremal functions that span by positive combinations the totality of functions Phi euro [unk] and Psi euro [unk] to investigate whether the pair of random variables (X,Y) are associated with respect to [unk] and [unk] and to assess the relative degree (or strength) of association when comparing two sets of random variables (X,Y) and (Z,W).
Karlin
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Department of Mathematics, Stanford University, Stanford, California 94305.