Four-parameter Weibull probability distribution model for weakly non-linear random variables

The use of multi-parameter distribution functions that incorporate empirically derived parameters to more accurately capture the nature of data being studied is investigated. Improving the accuracy of these models is especially important for predicting the extreme values of the non-linear random variables. This study was motivated by problems commonly encountered in the design of offshore systems where the accurate modeling of the distribution tail is of significant importance. A four-parameter Weibull probability distribution model whose structural form is developed using a quadratic transformation of linear random variables is presented. The parameters of the distribution model are derived using the method of linear moments. For comparison, the model parameters are also derived using the more conventional method of moments. To illustrate the behavior of these models, laboratory data measuring the time series of wave run-up on a vertical column of a TLP structure and wave crests interacting in close proximity with an offshore platform are utilized. Comparisons of the extremal predictions using the four-parameter Weibull model and the three-parameter Rayleigh model verify the ability of the new formulation to better capture the tail of the sample distributions.

► A four-parameter Weibull distribution model is derived for peaks of weakly non-linear processes.
► The structural form is developed using a quadratic transformation of the linear random variable.
► The model parameters are estimated using both method of moments and the method of linear moments.
► The model performance is evaluated using measured wave run-up and wave crests from a TLP model test.
► The model is robust in capturing the sample distribution and estimating the extreme statistics.