The properties of light wave propagation with stochastic scattering in a fiber are particularly attractive because of their influence in various applications.Unfortunately

no accurate theoretical model has been proposed to describe the randomness of the distributions and variations in scattering.In this paper

we propose a model to analyze the random variation in scattering with time and location.Then

we use the model to simulate stochastic scattering in distributed Fiber Raman Amplification（FRA）systems

including Rayleigh scattering and spontaneous Raman scattering

which are crucial limitations in the distributed FRA systems.The power density spectral errors between our simulations and the experimental measurements were within 5 dBc/Hz

rather than the conventional method with more than 10 dBc/Hz errors in high frequency region.It proves the accuracy of our model in describing the stochastic scattering spectra and distributions in FRAs.Our theory is a promising tool for optimizing the performance of distributed fiber systems

especially systems with distributed amplification such as fiber communication systems based on Raman amplifiers and random feedback fiber lasers.