This paper investigates the impact of the different sources of excitation variability within the stochastic kriging framework recently developed by the authors for the estimation of the distribution of engineering demand parameters (EDPs) in applications that the seismic hazard is described through stochastic ground motion models. For a given seismic event, described by seismicity characteristics such as the moment magnitude and the distance to source, one can distinguish two type of uncertainties in the excitation description: (g.i) the stochastic sequence utilized within the excitation model; (g.ii) the predictive models relating the ground motion parameters, such as significant duration, arias intensity, or frequency properties of seismic waves, to the seismicity characteristics. The original formulation of the authors treats (g.i) as aleatoric uncertainty and (g.ii) as parametric uncertainty, including the latter in the model parameters for the risk characterization, representing the metamodel input. Implementation establishes the EDP distribution approximation by utilizing a database of EDP estimates for a set of different input parameters, considering replications of these estimates for different stochastic sequences for some small part of this database. The database with replications is first leveraged to approximate the heteroscedas-2466