This paper analyses peak ice loads on an inclined, rigid marine structure by using data from 2D combined finite-discrete element method simulations. The aim is look for answers to the questions: what type of distributions do peak ice loads follow, what type of data is needed for their analysis, and how should the data on peak ice loads be collected? In the simulations, an initially continuous ice sheet, modeled as a floating beam, breaks into smaller ice blocks as the sheet is pushed against the structure. Statistical tools were used to analyse the peak ice load distributions, error estimates, and peak ice load occurrences. Load distributions appeared to be right-skewed and thus non-normal. Gumbel distribution appeared to describe the data well. The results show that the large scatter in the ice load data is due to the ice-structure interaction process itself. Due to the scatter, a large number of observations are needed for studying peak ice load statistics: To reliably observe a 15% difference in peak loads due to a single parameter would require more than 80 observations in total. The results showed that high peak loads may occur even in the early stage of the ice-structure interaction process.