The study of the statistical properties of the non-linear random wave had been earlier investigated. In this work we introduce a bi-parametric distribution of nonlinear stochastic processes, in studying the properties of second-order random processes with a narrow-band spectrum. This incidentally concerns the mechanics of the water waves. In particular, the expressions of the probability density function are further investigated, using this bi-parameter. This analysis will enable the designer to choose wave parameters, within a limit, that will yield an acceptable level of risk. Secondly,
such probabilistic based design criterion may result in substantial cost saving if uncertainties in the wave estimates are incorporated.