In this work, a comprehensive mathematical model which rigorously describes the interaction between stimulated Raman scattering (SRS) and four-wave mixing (FWM) in distributed fiber Raman amplifiers (DFRAs) is presented. The parametric effects on DFRAs due to pump-pump FWM processes are completely characterized. Numerical simulations are contrasted with experimental measurements which were carried out with different configurations of DFRAs. The results validate the proposed mathematical model, which can be extended to include other non-linear effects. Finally, the pump-to-pump FWM effects on the spectral gain of a DFRA are analyzed.