Under a Gaussian beam incidence, the fundamental statistical moments of Gaussian beam scattering fields from targets with arbitrary shapes are derived. Taking an ellipsoid-shaped target as an example, the correlation function, covariance, and incoherent component ratio of the scattering fields in three different materials are studied by the numerical method. The variation of the incoherent component ratio of the ellipsoidal target with the scattering angle is numerically obtained. The results show that the incoherent component takes only a small proportion of the total scattering components. The target pose, surface material and its roughness have influence on the incoherent component ratio. The smoother the rough surface is, the smaller the incoherent component ratio is. The incoherent component ratio of metal material is smaller than that of non-metallic painting material. The incoherent component ratio of the scattered field from the scaled target has a similar distribution with the above, except for some difference in value.