Requirements for a CAT-II/III capable service type of the Ground Based Augmentation System (GBAS) were derived from the definition of a safe landing of an aircraft within a pre-defined touchdown zone on the runway. The contributions to the total system error come from the navigation system on the one hand and the autopilot performance on the other hand. In order to quantitatively assess the touchdown performance of a given aircraft and its autopilot, Monte-Carlo simulations are performed and the results modelled. The touchdown performance is usually described by a fitted Gaussian distribution. This distribution is used for deriving the navigation system requirements. This paper argues that fitting the data to a Gaussian distribution is inappropriate and may lead to an underestimation of the residual risks of landing outside the touchdown box. It therefore describes two alternative methods to model the touchdown performance: a Gaussian overbound and a Johnson distribution. Both methods are described and the implications of modelling the performance in these ways are discussed.