This work investigates numerically two different methods of moments applied to Hermite derived probability distribution model and variations of Weibull distribution fitted to the short-term time series peaks sample of stochastic response parameters of a simplified jack-up platform model which represents a source of high non-Gaussian responses. The main focus of the work is to compare the results of short-term extreme response statistics obtained by the so-called linear method of moments (L-moments) and the conventional method of moments using either Hermite or Weibull models as the distribution model for the peaks. A simplified mass-spring system representing a three-legged jack-up platform is initially employed in order to observe directly impacts of the linear method of moments (L-moments) in extreme analysis results. Afterward, the stochastic response of the three-legged jack-up platform is analyzed by means of 3D finite element model. Bias and statistical uncertainty in the estimated extreme statistics parameters are computed considering as the “theoretical” estimates those evaluated by fitting a Gumbel to a sample of episodical extreme values obtained from distinct short-term realizations (or simulations). Results show that the variability of the extreme results, as a function of the simulation length, determined by the linear method of moments (L-moments) is smaller than their corresponding ones derived from the conventional method of moments and the biases are more or less the same.