A generalized probabilistic model of ice load peaks on ship hulls in broken-ice fields

On some occasions, especially when traveling in a broken ice field, the process of ice induced loads on ship hulls cannot be well modeled by traditional statistical models which are usually applied for this purpose. Examples of such are the one-parameter exponential and the Weibullʹs models. The fitting achieved by application of these models could generally result in underestimation of the predicted extreme values. Therefore a so-called generalized model, i.e. the three-parameter exponential model, is proposed in order to improve the process of fitting. The proposed model is actually a proportional combination of two one-parameter exponential models. It tends to give more conservative predicted extreme values as compared to the one-parameter exponential and the Weibullʹs models. Various approaches for estimation of the parameters are treated, i.e. the method of moments, the non-linear least square method, the non-linear least square method based on application of Kernel density estimation, and the maximum likelihood estimators. The fitting by means of the non-linear least square method was observed to give the best results. However, more stable predictions are provided by the maximum likelihood estimators.