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Consider a multivariate distribution of (X , Y) , where X is a vector of predictor variables and Y is a response variable. Results are obtained for comparing the conditional and marginal tail indices, ξ Y | X (x) and ξ Y , based on conditional distributions { F Y | X (⋅ | x) } and marginal distribution F Y , respectively. For a multivariate distribution based on a copula, the conditional tail index can be decomposed into a product of copula-based conditional tail indices and the marginal tail index. In some applications, one may want ξ Y | X (x) to be non-constant, and some new copula families are derived to facilitate this. [ABSTRACT FROM AUTHOR]