The use of virtual safety assessment as the primary method for evaluating vehicle safety technologies has emphasized the importance of crash scenario generation. One of the most common crash types is the rear-end crash, which involves a lead vehicle and a following vehicle. Most studies have focused on the following vehicle, assuming that the lead vehicle maintains a constant acceleration/deceleration before the crash. However, there is no evidence for this premise in the literature. This study aims to address this knowledge gap by thoroughly analyzing and modeling the lead vehicle's behavior as a first step in generating rear-end crash scenarios. Accordingly, the study employed a piecewise linear model to parameterize the speed profiles of lead vehicles, utilizing two rear-end pre-crash/near-crash datasets. These datasets were merged and categorized into multiple sub-datasets; for each one, a multivariate distribution was constructed to represent the corresponding parameters. Subsequently, a synthetic dataset was generated using these distribution models and validated by comparison with the original combined dataset. The results highlight diverse lead-vehicle speed patterns, indicating that a more accurate model, such as the proposed piecewise linear model, is required instead of the conventional constant acceleration/deceleration model. Crashes generated with the proposed models accurately match crash data across the full severity range, surpassing existing lead-vehicle kinematics models in both severity range and accuracy. By providing more realistic speed profiles for the lead vehicle, the model developed in the study contributes to creating realistic rear-end crash scenarios and reconstructing real-life crashes.