The stochastic method of ground‐motion simulation specifies the amplitude spectrum as a function of magnitude (M) and distance (R). The manner in which the amplitude spectrum varies with M and R depends on physical‐based parameters that are often constrained by recorded motions for a particular region (e.g., stress parameter, geometrical spreading, quality factor, and crustal amplifications), which we refer to as the seismological model. The remaining ingredient for the stochastic method is the ground‐motion duration. Although the duration obviously affects the character of the ground motion in the time domain, it also significantly affects the response of a single‐degree‐of‐freedom oscillator. Recently published updates to the stochastic method include a new generalized double‐corner‐frequency source model, a new finite‐fault correction, a new parameterization of duration, and a new duration model for active crustal regions. In this article, we augment these updates with a new crustal amplification model and a new duration model for stable continental regions. Random‐vibration theory (RVT) provides a computationally efficient method to compute the peak oscillator response directly from the ground‐motion amplitude spectrum and duration. Because the correction factor used to account for the nonstationarity of the ground motion depends on the ground‐motion amplitude spectrum and duration, we also present new RVT correction factors for both active and stable regions.