- The Rayleigh-Stokes model has been widely applied to represent the probability distribution function of crests and troughs of weakly nonlinear random processes. In this study, the parameter estimates for the three-parameter Rayleigh-Stokes probability distribution function are obtained from application of two moment-based empirical parameter estimation methods, i.e. conventional method of moments and method of linear moments. Monte-Carlo simulations are utilized to compare the performance of these parameter estimation approaches in estimating the parameters of the Rayleigh-Stokes distribution and also to evaluate the uncertainty of the extreme statistics. Additionally, the effect of sample size on the uncertainty of the model statistics is evaluated. Finally, the Rayleigh-Stokes model is utilized to estimate the probability distribution function of disturbed wave crests beneath a mini-TLP and the model performance is evaluated. Copyright 2011 by the International Society of Offshore and Polar Engineers (ISOPE).