Abstract Radial distribution (Pair correlation) functions are the primary linkage between macroscopic thermodynamics properties and intermolecular interactions of fluids and fluid mixtures. Numerous theories of mixtures exist based on the definition of the radial distribution functions. Utilization of such theories require the knowledge about mixture radial distribution functions and their relations. Generally the exact radial distribution functions of real fluid mixtures are not available. In this paper a number of approximations for the mixture radial distribution functions are presented. Application of these approximation can result in analytic mixture theories and mixing rules. A uniform statistical mechanical technique is presented through which one can derive equation of state mixing rules based on different RDF approximations. The relative merits of different sets of mixing rules derived by this technique and their applications for modeling of the behavior of mixtures are discussed.