Uncertainty and risk analysis is becoming an ever-increasing part of transport demand forecasting because it can significantly influence the feasibility of a transportation project. Probabilistic assessment using Monte Carlo simulation is one of the most common approaches to uncertainty evaluation. This method implies generating random draws from probability distributions for the input variables. Often the empirical data that allow fitting the distribution are not available or involve additional costs to be obtained. In this case, the modeler makes an assumption of the shape of the probability distribution and its parameters in a context of information shortage, and this assumption introduces additional error to the uncertainty analysis. The main goal of this study is to quantify the impact of the distribution choice on the estimates of the model uncertainty present in its attributes and, more specifically, of its shape, skewness, and correlations among variables by using the case study of a high-speed railway project in Portugal. The results suggest that the mode location of the distribution, its shape, and correlations significantly affect the outcome of the uncertainty analysis.