Reliable and computationally fast numerical models play a decisive role in the development of robust design and optimization tools for wave energy converter. This study presents an approach to consider model nonlinearities via statistical linearization method and its implementation in the probabilistic model of the WEC. The ISWEC (Inertial Sea Wave Energy Converter) is chosen as the case study and the analysis focuses on the main non-linearity of the system: the gyroscope dynamics. The probabilistic model, named Spectral Domain Model (SDM) is compared with its time domain and linear frequency domain counter parts in terms of probability distributions and power spectral densities of the device displacements, extracted power and computational costs. This work pursues to improve the computational effectiveness of the ISWECsimulation guaranteeing the fidelity of the expected numerical results.