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A model accurately describing amplified spontaneous emission noise in systems with distributed Raman gain is presented. Numerical simulations are corroborated with experimental results. Our model is used to study the interaction between signal and noise mediated by fiber nonlinearities for different propagation regimes. It is shown that for distances longer than 120 km and moderate signal powers, higher than 6 mW, the noise statistics deviates significatively from the Gaussian distribution.