Investigating snow avalanches using a purely statistical approach raises several issues. First, even in the heavily populated areas of the Alps, there are few data on avalanche motion or extension. Second, most of the field data are related to the point of furthest reach in the avalanche path (run-out distance or altitude). As data of this kind are tightly dependent on the avalanche path profile, it is a priori not permissible to extrapolate the cumulative distribution function fitted to these data without severe restrictions or further assumptions. Using deterministic models is also problematic, as these are not really physically based models. For instance, they do not include all the phenomena occurring in the avalanche movement, and the rheological behaviour of the snow is not known. Consequently, it is not easy to predetermine extreme-event extensions. Here, in order to overcome this problem, we propose to use a conceptual approach. First, using an avalanche-dynamics numerical model, we fitted the model parameters (friction coefficients and the volume of snow involved in the avalanches) to the field data. Then, using these parameters as random variables, we adjusted appropriate statistical distributions. The last steps involved simulating a large number of (fictitious) avalanches using the Monte Carlo approach. Thus, the cumulative distribution function of the run-out distance can be computed over a much broader range than was initially possible with the historical data. In this paper, we develop the proposed method through a complete case study, comparing two different models.