Evaluation and testing are critical for the development of Automated Vehicles (AVs). Currently, companies test AVs on public roads, which is very time-consuming and inefficient. We proposed the Accelerated Evaluation concept which uses a modified statistics of the surrounding vehicles and the Importance Sampling theory to reduce the evaluation time by several orders of magnitude, while ensuring the final evaluation results are accurate. In this paper, we further extend this idea by using Piecewise Mixture Distribution models instead of Single Distribution models. We demonstrate this idea to evaluate vehicle safety in lane change scenarios. The behavior of the cut-in vehicles was modeled based on more than 400,000 naturalistic driving lane changes collected by the University of Michigan Safety Pilot Model Deployment Program. Simulation results confirm that the accuracy and efficiency of the Piecewise Mixture Distribution method are better than the single distribution.