The problem considered in this study is that of unrealistic ground motion estimates, which arise in the Cornell–McGuire method when the seismic hazard curve is calculated for extremely low annual probabilities of exceedance. This problem stems from using the normal distribution in the modelling of the variability of the logarithm of ground motion parameters. In this study, the database of the strong-motion seismograph networks of Japan was used to examine the distribution of the logarithm of peak ground acceleration (PGA). The normal distribution and the generalised extreme value distribution (GEVD) models were considered in the analysis, with the preferred model being selected based on statistical criteria. The results of the analysis demonstrated the superiority of the GEVD in the vast majority of considered examples. The estimates of the shape parameter of the GEVD were negative in every considered example, indicating the presence of a finite upper bound of PGA. Therefore, the GEVD provides a model that is more realistic for the scatter of the logarithm of PGA, and the application of this model leads to a bounded seismic hazard curve.