A bivariate family of copulas has been initiated by Cuadras-Aug´e (1981) and Marshall (1996). Recently Durante (2007) has considered this family as a general family of symmetric bivariate copulas indexed by a generator function and studied some of its dependence properties. In this paper, we obtain and describe further aspects of dependence for this family. For example, we have proved that the family has positive likelihood ratio dependence structure if and only if the family would reduce to some well-known copulas. We also derive several proper forms for the generator function of this family. On using a multivariate extension provided by Durante et al. (2007), some dependence properties are studied. Finally, some positive dependence stochastic orderings for two random vectors having a copula from the proposed families, are discussed.

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