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AbstractThe air gap response in harsh environments, a critical design issue for offshore platforms, is related to the wave run-ups due to wave-platform interactions and potentially results in serious wave impacts. Therefore, the reliable prediction of wave run-ups and air gap response in harsh environments is a challenging task and needs further study. In this study, probability analysis of the wave run-up data from an experimental study of a deepwater semi-submersible platform is conducted based on the three-parameter Weibull distribution model using the LH-moments method for parameter estimation.One of the highlights in the present study is that the explicit relationships between the first three LH-moments at arbitrary levels and the parameters of the Weibull distribution are established analytically. The accuracy of LH-kurtosis estimation is proposed to determine the appropriate level for probability analysis. The air gap response is more serious in quartering and beam seas than in head seas.In front of the columns along the wave incoming direction, especially the aft one, the wave run-ups show higher probability distributions leading to higher likeliness of suffering from negative air gap and wave impact accidents than the other platform areas. At the platform center, the wave run-up is significantly lower than the incident wave. The probability distributions based on LH-moments at the appropriate level can well represent large wave run-ups, except for that beyond the still-water air gap, where both measurement methods and probability analyses warrant further research.