The gain and noise characteristics of distributed Raman amplification (DRA) based on random fiber laser (RFL) (including forward and backward random laser pumping) have been experimentally investigated through comparison with conventional bi-directional 1st-order and 2nd-order pumping. The results show that, the forward random laser pumping exhibits larger averaged gain and gain fluctuation while the backward random laser pumping has lower averaged gain and nonlinear impairment under the same signal input power and on-off gain. The effective noise figure (ENF) of the forward random laser pumping is lower than that of the bi-directional 1st-order pumping by ~2.3 dB, and lower than that of bi-directional 2nd-order pumping by ~1.3 dB at transparency transmission, respectively. The results also show that the spectra and power of RFL are uniquely insensitive to environmental temperature variation, unlike all the other lasers. Therefore, random-lasing-based distributed fiber-optic amplification could offer low-noise and stable DRA for long-distance transmission.