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For compact modeling of the noise in devices, one of the following three methods is usually applied: 1) An equivalent circuit based approach, 2) the classical Langevin or Klaassen-Prins approach, or 3) the impedance field method. It is well known that for long-channel MOST (where mobility degradation due to a lateral field is absent), all three methods obtain the same result. But it is still not recognized how these methodologies need to be changed when the mobility starts to depend on the electric field. In this work we demonstrate how these methodologies can be adapted to incorporate mobility degradation and show that for any arbitrary mobility model μ(E) all the methods yield the same expressions for induced gate and drain noise current, which demonstrates the equivalence of the methods. We also present, for the first time, a general expression of induced gate noise which is valid for any mobility model (an expression of the drain current noise was already presented in our previous work) and some very general expressions of noise parameters that can be used for noise modeling with any kind of mobility model.