The higher bit rates, lower noise figure, decreasing the nonlinear penalty of fiber system, longer amplifier length, tight channel spacing and operating near the zero-dispersion wavelength are achieved by using Distributed Raman amplifiers (DRAs). In this paper, a new model of noise figure (NF) due to amplified spontaneous emission (ASE) is introduced for the DRA at different pump schemes: co-pumping, counter-pumping and bidirectional pumping.The variation of power conversion efficiency (PCE) with input pump power; input signal power and amplifier length for S-band is also investigated. It is found that, the NF increases exponentially with the fiber length and decreases exponentially with input signal power, power conversion efficiency (PCE) increases exponentially with the fiber length and input signal power and decreases exponentially with the input pump power. The obtained results show that, the noise figure (NF) reaches its minimum value of 8.6, 9.7 and 11 dB, while the PCE reaches its maximum value of 71%, 31% and 7% in counter-pumping, bidirectional pumping and co-pumping, respectively.