Analytical expressions of equivalent noise figure and other noise characteristics of distributed fiber Raman amplifier (DFRA) are derived under complex conditions. These conditions include difference in polarization state and attenuation coefficients between pump and signal light as well as multiple wavelength pumping. Accordingly, their impact on DFRA performance and optical signal to noise ratio improvement (ΔOSNR) of concatenated DFRA+EDFA is investigated. With increasing DFRA on off gain, ΔOSNR increases first linearly and then logarithmically, resulting in saturation. Results of this work agree well with numerical simulation of existing work.