Abstract
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[Φ(X),Ψ(Y)] ≥ 0 for all Φ € [unk] and Ψ € [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 Φ € [unk] and Ψ € [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).
Keywords: bivariate strong association, positive quadrant dependence, representative association matrix, correlation versus association
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