Engine knock is one of the most limiting factors for modern SI engines to achieve higher efficiency targets. The stochastic nature of knock in Spark-Ignition (SI) engines hinders the predictive capability of RANS knock models which are based on ensemble averaged quantities. To this aim, a statistically grounded knock model was recently developed in the RANS formalism and improvements are introduced in this study. The model is able to infer a presumed log-normal distribution of knocking cycles from a single RANS simulations by transport equations for variances and turbulence-derived probability density functions (PDFs) for physical quantities. As a main advantage, the model is able to estimate the earliest knock severity experienced when moving the operating condition into the knocking regime. In this paper, the PDF-based knock model is applied to simulate the knock signature of a single-cylinder 400cm3 direct-injection SI unit with optical access operated at three spark timings, from knock-safe to heavy knocking conditions, respectively. The statistical prediction of knock resulting from the presented knock model is compared to the experimental evidence for all the investigated conditions. The agreement between the predicted and the measured knock distributions validates the presented knock model. Finally, the limitations and the unprecedented possibilities given by the proposed model are critically discussed, and special focus is given to the meaning of RANS knock prediction.