  In this paper, I introduce a novel approach to modelling the individual
random component (also called the intra-event uncertainty) of a ground-motion
relation (GMR), as well as a novel approach to estimating the corresponding
parameters. In essence, I contend that the individual random component is
reproduced adequately by a simple stochastic mechanism of random impulses
acting in the horizontal plane, with random directions. The random number of
impulses was Poisson distributed. The parameters of the model were estimated
according to a proposal by Raschke (2013a), with the sample of random
difference xi=ln(Y1)-ln(Y2), in which Y1 and Y2 are the horizontal components
of local ground-motion intensity. Any GMR element was eliminated by
subtraction, except the individual random components. In the estimation
procedure the distribution of difference xi was approximated by combining a
large Monte Carlo simulated sample and Kernel smoothing. The estimated model
satisfactorily fitted the difference xi of the sample of peak ground
accelerations, and the variance of the individual random components was
considerably smaller than that of conventional GMRs. In addition, the
dependence of variance on the epicentre distance was considered; however, a
dependence of variance on the magnitude was not detected. Finally, the
influence of the novel model and the corresponding approximations on PSHA was
researched. The applied approximations of distribution of the individual random
component were satisfactory for the researched example of PSHA.
